Physics secondary stage 2

™HÉ£e

Book Sector

2011 - 2012

Arab republic of egyptMinistry of Education

Book Sector

Foreword:Unit 1: Waves:

Chapter 1 : Wave Motion Chapter 2 : Sound Chapter 3 : Light

Unit 2: Fluid Mechanics: Chapter 4 : HydrostaticsChapter 5 : Hydrodynamics

Unit 3 : Heat:Chapter 6 : Gas LawsChapter 7 : Kinetic Theory of Gases Chapter 8 : Cryogenics (Low Temperature Physics)

Unit 4 : Dynamic Electricity and Electromagnetism:Chapter 9 : Electrical Current and Ohm's Law Chapter 10 : Magnetic Effects of Electric Current

and Measuring Instruments.Chapter 11 : Electromagnetic Induction.

Unit 5 : Introduction to Modern Physics:Chapter 12 : Wave Particle Duality Chapter 13 : Atomic Spectra Chapter 14 : Lasers Chapter 15 : Modern Electronics

General Revision : Appendixes :

Appendix 1 : Symbols and Units of Physical Quantities Appendix 2 : Fundamental Physical ConstantsAppendix 3 : Standard Prefixes Appendix 4 : Greek Alphabet Appendix 5 : Gallery of ScientistsAppendix 6 : Selected Physics Sites on the Internet

Table of Contents

1 : 7922347

81 : 13282117

134 : 182135159173

184 : 271185202

231273 : 382

274306324350

383 : 404407:418

406409411412413418

intensively. It is targeted to use genetics, atoms and lasers in the computer of the

future. It is a limitless world, enriched by imagination, where sky is the limit.

The scientific progress is a cumulative effort. This collective endeavor has led to

where we are today. A scholar of physics must be acquainted with such accumulated

knowledge in a short time, so that he could add to it within the limited span of his

life. In studying what others have found, we must skip details and trials, and extract

the end results and build on them.A global view is, therefore, more important at this

stage than being drowned in minute details that could be postponed to a later stage of

study.

This book is divided into 5 units. Unit 1 deals with waves, which are the basis of

communication in the universe. (Chapter 1) deals with wave motion, (chapter 2) with

sound, and (chapter 3) with light. Unit 2 deals with fluid mechanics, : hydrostatics

(chapter 4) and hydrodynamics (chapter 5). Unit 3 deals with heat, where (chapter 6)

deals with gas laws, (chapter 7) with the kinetic theory of gases and (chapter 8) deals

with low temperature physics. Unit 4 treats electricity, where (chapter 9) covers the

electric current and Ohm’s law, (chapter 10) covers the magnetic effects of electric

current and measuring instruments, while (chapter 11) covers electromagnetic

induction. Unit 5 gives an introduction to modern physics, where (Chapter 12) deals

Physics is the cornerstone of basic sciences. It deals with the understanding of

nature and what goes around us, big and small in this universe. It is the root of all

sciences. Interwined with it is chemistry which focuses on reactions between

materials, biology which deals with living creatures, geology which is involved with

the layers of the Earth, and astronomy which treats celestial objects. But in the end,

physics remains the mother of all sciences and the basis for the tremendous present

scientific and technological progress. Understanding physics means understanding

the laws governing this universe. Such understanding has led to the current industrial

development spearheaded by the West. The Arabs and Moslems were once the

pioneers of civilization in the world when they realized the importance of

understanding the laws of this universe. We owe them the discovery of most laws of

physics centuries before the West. The foundations of medicine, physics, chemistry,

astronomy, mathematics and music were all laid by Arab and Moslem scientists.

In fact, understanding physics and its applications converts a poor, and

underdeveloped society into an affluent and developed one. This has taken place in

Europe, US, Japan and South East Asia. Computers, satellites, cellular (mobile)

phones, and TV are all byproducts of physics. Genetics is currently being looked into

Foreword

with wave particle duality, (Chapter 13) deals with atomic spectra, and (chapter 14)

deals with lasers and their applications, while (chapter 15) covers modern electronics.

Suzanne Mubarak Science Exploration Center has carried out the preparation, and

the typing of manuscript as well as the design of the artwork.

In the end, we want the student to take liking to physics. For this is the way to the

future. We want the teacher to teach the subject of physics in an innovative way, to

arouse the interest of the students by constantly referring to the use and applications

of physics in the daily life. We hope that one day we will have great inventors and

industrialists among today's students.

Committee for the preparation of this new version

of the textbook.

Prof. Mustafa Kamal Mohammad Yussef,Ph.D.Prof. Mohammad Sameh Said ,Ph.D.Mustafa Mohammad El-Sayed ,Ph.D.Tarik Mohammed Tala'at Salama,Ph.D.Karima Abdel-Alim Sayed Ahmad

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electromagnetic waves spreading in space and the surrounding medium . When received bythe mobile antenna at the receiver, electromagnetic waves are transformed back intoelectrical signals and then to sound or even to an image.

We can see water waves but we cannot see the radio, TV or mobile waves. However,we can detect them. Water waves are mechanical waves, so are sound waves and waves invibrating strings. But radio, TV, and mobile waves are electromagnetic waves. Amongthese electromagnetic (em) waves, there are, for example, light waves and X-rays whichare used in radiology. Mechanical waves require a medium to propagate through, while(em) waves do not require a medium. They can propagate in space.

Mechanical Waves Mechanical waves require the following :-

1 ) a vibrating source.2 ) a disturbance transmitted from the source to the medium.3 ) a medium that carries a vibration.

There are many forms of vibrating sources :1 ) a simple vibrating pendulum (Fig 1 - 2).2 ) a tuning fork (Fig 1 - 3).3 ) a vibrating stretched wire (or string) (Fig 1- 4).4 ) a plumb (bob) attached to a vibrating spring (Yoyo) (Fig 1 - 5).

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Overview :

Many of us enjoy watching waves on the surface of water pushing a fishing float or aboat up and down, or even making waves by throwing a pebble in a pond or still water.Each pebble becomes a source of disturbance in the water, spreading waves as concentriccircles (Fig 1-1). Hence, waves are disturbances that spread and carry along energy.

Waves are not only water waves. There are, for example, radio waves. We often hear theannouncer say: "This is Radio Cairo on the medium wave 366.7 m". Also, TV stationstransmit both sound and image in the form of waves which are received by the aerial(antenna) . Such waves are transformed into electrical signals in the receiver, where theyare eventually converted back to sound (audio) and image (video). Also, the mobile phoneruns on waves. Sound signals are transformed into electrical signals then into

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Fig (1 -1)Waves spreading from a

point source

Chapter 1 Wave Motion

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Amplitude (A) (meter): is the maximum displacement of the vibrating object or the

distance between two points along the path of the object, where the velocity at one point is

maximum and zero at the other.

Complete Oscillation: is the motion of a vibrating body in the interval between theinstants of passing by one point along the path of its motion twice successively withmotion in the same direction and same displacement, i.e., at the same phase, relative to thestarting point of motion.

Frequency (ν) (Hertz or Hz): is the number of complete oscillations made by

a vibrating body in one second.

Periodic Time (T) (seconds): is the time taken by a vibrating body to make onecomplete oscillation, or the time taken by the vibrating body to pass by the same pointalong the path of motion twice successively with motion in the same direction and thesame displacement.

Simple Harmonic Motion: A vibrational motion in its simplest form is

called a simple harmonic motion, e.g., a

swing (Fig 1-6) or a simple pendulum (Fig

1-7). The vibration starts from point "a" then

increases to a positive maximum at "b" then

to zero at "a" then to negative maximum at

"c" then to zero at "a". and the cycle is

repeated continually (Fig 1-7 a ).

ν (1-1)1T=

Fig (1-6)A swing as an example ofa simple harmonic motion

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Fig (1 -5)

Yoyo

rest position

amplitude

4

To study vibrations, we need to define some relevant physical quantities such as:displacement, amplitude, complete oscillation, periodic time and frequency as follows:

Displacement (meter): is the distance of a vibrating body at any instant from its restposition or its equilibrium origin. It is a vector quantity.

Fig (1 -2)A pendulum

Fig (1 -3)A tuning fork

Fig (1 -4)A vibrating string

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Fig (1 -5)

Yoyo

rest position

amplitude

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Fig (1 -5)

Yoyo

rest position

amplitude

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Fig (1 -5)

Yoyo

rest position

amplitude

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Learn at Leisure

ResonanceAt a certain frequency, the amplitude of the

mechanical vibration may get out of hand, e.g., thecrushing of a glass cup due to nearby sound waves (Fig1-8), and the collapse of Tacoma bridge (USA) due tostrong winds in November 1940 (Fig 1-9). This conditionis called resonance. It is the cause of the collapse ofmany buildings. It occurs when a simple harmonicmotion is set at the natural (or resonant) frequency of thebuilding. Similar to mechanical resonance, there is alsoelectrical resonance which is the basis of tuning a radioor a TV receiver to a certain station, where one out ofmany electrical signals picked up by the aerial isamplified and made to coincide with the resonant frequency ofthe amplifier in the receiver when tuned to that particularstation.

Fig (1-9)Collapse of Tacoma bridge

(USA) due to the wind causingthe vibration of the bridge at thenatural (resonant) frequency of

the bridge

Fig (1-8)A glass cup crushed dueto nearby sound waves

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Fig (1-7 a)Displacement of a

pendulum bob as timegoes by

Fig (1-7 b)Displacement of a pendulum bob at different phases A, D are of the

same phase (same displacement and direction)B,C are not of the same phase (the same direction but not the

same displacement)

a bc

rest position

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Amplitude (A) (meter): is the maximum displacement of the vibrating object or the

distance between two points along the path of the object, where the velocity at one point is

maximum and zero at the other.

Complete Oscillation: is the motion of a vibrating body in the interval between theinstants of passing by one point along the path of its motion twice successively withmotion in the same direction and same displacement, i.e., at the same phase, relative to thestarting point of motion.

Frequency (ν) (Hertz or Hz): is the number of complete oscillations made by

a vibrating body in one second.

Periodic Time (T) (seconds): is the time taken by a vibrating body to make onecomplete oscillation, or the time taken by the vibrating body to pass by the same pointalong the path of motion twice successively with motion in the same direction and thesame displacement.

Simple Harmonic Motion: A vibrational motion in its simplest form is

called a simple harmonic motion, e.g., a

swing (Fig 1-6) or a simple pendulum (Fig

1-7). The vibration starts from point "a" then

increases to a positive maximum at "b" then

to zero at "a" then to negative maximum at

"c" then to zero at "a". and the cycle is

repeated continually (Fig 1-7 a ).

ν (1-1)1T=

Fig (1-6)A swing as an example ofa simple harmonic motion

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Longitudinal Waves:Imagine a mass “m” on a smooth horizontal surface attached to one end of a spring

whose other end is attached to a vertical wall. If we pull the mass in the direction of thespring and let it go, the mass moves around its rest position in an oscillatory motion towardthe spring and away (Fig 1-10). This is a simple harmonic motion. If we draw the curvethat the center of gravity of the mass makes with respect to its rest position, we will obtaina sine wave (Fig 1-11). This is what distinguishes a simple harmonic motion from anyother type of motion.

Fig (1-10)A vibrating spring

Fig (1-11)A sine wave resulting from a

simple harmonic motion

rest position

pulling the spring

releasing the spring

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Fig (1-13 b)Vertical displacement as a sine wave

Fig (1-14)A pulse resulting from part of a simple harmonic motion

spreading along a stretched rope

You can do this experiment yourself by using a long stretched rope. The far end isattached to a vertical wall while the near end is in your hand. When you move your hand upand down in the form of a pulse, you note that the wave spreads in a pulse form along therope. This is known as a traveling wave (Fig 1-14).

v

v

distance

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Fig (1-13 a)Vertical displacement in a simple harmonic motion

Thus, a vibrating source making a simple harmonic motion may generate a wavepropagating at velocity “v”. Each particle of the medium performs, in turn, a simpleharmonic motion about its equilibrium position. An example of this motion is thelongitudinal waves of sound in air.

Transverse Waves:

Imagine a mass “m” attached to a vertical spring. A long horizontal taut (stretched) rope

is also attached to this mass at the near end, while the other (far) end of the rope is attachedto a vertical wall.

When the mass “m” performs a simple harmonic motion in the vertical direction, thenthe near end of the rope performs the same motion. Consequently, the following parts ofthe rope do the same thing successively. Then the motion transfers horizontally along therope in the form of a wave at velocity “v”, while the other parts of the rope oscillatevertically in a simple harmonic motion about their rest positions. This wave is called atransverse wave (Fig 1-13 ).

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In conclusion, we may classify mechanical waves into two types:

1 ) Transverse waves

2 ) Longitudinal waves

In transverse waves, the particles of the medium oscillate about their equilibrium

positions in a direction perpendicular to the direction of the propagation of the wave.

In longitudinal waves, the particles of the medium oscillate about their equilibrium

positions along the direction of the propagation of the wave.

The work done by the oscillating source is converted to the particles of a string (or a

stretched rope) in the form of potential energy stored as tension in the string and kinetic

Fig (1-16)A vibrating spring forming a

longitudinal wave

Fig (1-17)A vibrating spring forming a

transverse wave

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A wave may also be continuous (called a traveling wave train) as long as the simple

harmonic motion of the source keeps on(Fig 1-15).

The stretched rope may be replaced by a spring in which a longitudinal wave (Fig 1-16)

or a transverse wave (Fig 1-17) may be generated . We conclude that as a source oscillates ,

the particles of the medium oscillate successively in the same way. The vibration transfers

first from the source to the particle of the medium next to it, then into the one connected to

it, then into the following ones and so on. Thus, the vibration or disturbance forms a wave,

since the wave is nothing but a disturbance (or energy) on the move along which energy is

carried through .

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Fig (1-15)A train wave spreading in a taut (stretched) rope due to a

continuous simple harmonic motion at the near end

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Fig (1-19)Wavelength in a transverse wave

wavelengthdirection of

propagationcrest

rest positionamplitude

direction ofvibration

Fig (1-20)Wavelength in a longitudinal wave

Thus, the wavelength is the distance between two successive points of the same phase

(Fig 1-21). Alternatively, it is the distance which the wave travels during one periodic

time (Fig 1-22).

The number of waves passing by a certain point along the wave path in one second is

called frequency.

disp

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energy manifested in the vibration of the particles of

the string.

Referring to (Fig 1-18), the points at maximum

upward displacement in the positive direction are

called crests, while the points of maximum downward

displacement are called troughs.

Observing any part of a vibrating string carrying a

transverse wave, we find that it has one crest and one

trough during one complete oscillation .

Frequency (ν) (Hertz) and wavelength (λ) (meter):

The distance between two successive crests or two

successive troughs in a transverse wave is called

wavelength (Fig 1-19). Similarly, the distance

between two successive contractions (compressions)

or two successive rarefactions in a longitudinal wave

is called wavelength (Fig 1-20).

Thus, we may represent the wavelength by either

of the two distances (AC) and (BD)(Fig 1-19 ). It is

to be noted that the two successive pairs of points (A,C) and (B, D) move in the same

way at the same time. We say they have the same phase, i.e.,the same displacement in

the same direction.

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Fig (1-18)A piece of foam floating on the top ofa wave (crest) or at bottom (trough)

direction of wave propagation

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The relation between frequency,wavelength and velocity of propagation:If a wave travels at velocity “v”, a distance equal to the wavelength “λ” , then the wave

takes time equal to the periodic time “T” to travel this distance.

This is a general relation for all types of waves.In all cases , within a periodic time “T” a wave travels a wavelength. Frequency is the number of oscillations in one second or the number of wavelengths

traveled by a wave propagating in a certain direction in one second.

v = T

T = 1

= 1T

ν

ν

Fig (1-22b)A train of waves at velocity “v” generated by a vibrator

v = λν

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Fig (1-22a)The distance which a wave moves

in a periodic time T is the wavelength

Fig (1-21)The distance after each one full vibration

completed in one period T is the wavelength

rest position

at the end of 1/4 period



at the end of one periodamplitude

at time t + T

at time t

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In a Nutshell.A wave is a disturbance which spreads and carries energy along. .Displacement is the distance of an object at any instant from its rest(equilibrium) position.. The amplitude of oscillation “A” is the maximum displacement of an oscillating objectfrom its rest position, or the distance between two points along the path of the oscillatingobject where the velocity at one point is maximum and at the other is nil. . A complete oscillation is the movement of a continuously vibrating body ( e.g. a simplependulum) is the interval between the instants of time as it passes by a certain pointalong its path twice successively with motion in the same direction.. Frequency “ν” is the number of complete oscillations produced by a vibrating object inone second and is equal to the inverse of the periodic time.

Frequency =

It is also the number of waves passing by a certain point along the path of a wave in onesecond.. Periodic time “T” is the time taken by a continuously vibrating body to perform one

complete oscillation, or the time taken by a continuously vibrating body ( e.g. a simplependulum ) to pass by a point along its path twice successively with motion in the samedirection.. Mechanical waves are either:1 ) transverse waves.2 ) longitudinal waves.. Transverse waves are waves in which the particles of a medium oscillate about theirequilibrium positions in a direction perpendicular to the direction of propagation of thewave.. Longitudinal waves are waves in which the particles of a medium oscillate about theirequilibrium positions along the same path of propagation of the wave.. Transverse waves comprise crests and troughs in succession.

1Periodic time

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Examples:-1) If the wavelength of a sound wave produced by a train is 0.6 m and the frequency is

550 Hz,what is the velocity of sound in air?

Solution:-

v = λ νv = 0.6 x 550 = 330 m/s

2) If the number of waves passing by a certain point in one second is 12 oscillations andthe wavelength is 0.1 m, calculate the speed of propagation.

Solution:-

v = λ νv = 12 X 0.1 = 1.2 m/s

3) Light waves propagate in space at speed 300 000km/s (3x108m/s), and the wavelengthof light is 5000 A˚ .What is the frequency of this light ?

1 Angstrom(A0 ) =10-10 m

Solution:-

c = v = 3 x 108 m/s

λ = 5 x 103 x 10-10 = 5 x10-7 m

c = λ ν

3 x 108 = 5 x 10-7 x ν

Hz = 3 x 108

5 x 10-7 = 6 x 1014ν

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Questions and DrillsI) Define

Wave - Transverse Wave - Longitudinal Wave - Wavelength

II) Complete:a) Displacement is ......b) Amplitude of oscillation is ......c) Complete oscillation is ......d) Periodic time is ......e) Frequency is ......

III) Essay question:Deduce the relation between frequency, wavelength and velocity of wave propagation.

IV) Put a tick sign (√) next to the right choice in the following :1) The relation between the velocity of propagation of the waves “v” in a medium , its

frequency and wavelength is :a) v = λν b) v = ν / λc) v = d) none (there is no correct answer)

2) Transverse waves are waves consisting of :a) Compressions and rarefactions b) Crests and troughsc) Crests and troughs, where the particles of the medium move short distances about

their equilibrium positions in a direction perpendicular to the direction of propagation.d) Compressions and rarefactions, where the particles of the medium move short

distances about their equilibrium positions along the direction of propagation of thewave .

3) If the wavelength of a sound wave produced by an audio ( sound producing) source is0 . 5 m , the frequency is 666 Hz ,then the velocity of propagation of sound in air is :a) 338 m / s b) 333 m / s c) 330 m / s d) 346 m / s

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λν

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. Longitudinal waves comprise compressions and rarefactions in succession .. Wavelength is the distance between two successive points along the direction ofpropagation of the wave, where the phase is the same (same displacement and samedirection).. The relation between frequency, wavelength and velocity of a wave is given by: v = λ ν

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4) If the velocity of sound in air is 340 m/s, for a sound of frequency (tone) 225 Hz , thewavelength(m) is :

a) 4/3 b) 3/4 c) 20 d) 3/2 5) Light of wavelength 6000 A˚(1A˚ = 10-10m ) propagates in space at velocity 300 x 103km/s,

its frequency is:(a) 4 x 1010 Hz (b) 4 x 1014 Hz

(c) 5 x 1014 Hz (d) 5 x 1012 Hz

6) Two waves whose frequencies are 256 Hz and 512 Hz propagate in a certain medium ,the ratio between their wavelengths isa) 2/1 b) 1/2 c) 3/1 d) 1/3

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Sound

Learn at Leisure

How does a bat see ?

A bat (Fig 2-1) does not see by its eyes. It transmits ultrasonic waves and detects thesurroundings by the echo. It works in this fashion as a radar or rather sonar (radar usingultrasonic waves).

Learn at Leisure

Imaging the embryoUltrasonic waves (not heard by human ear) are used to image an embryo. They are

considered the safest. Ultrasonic imaging depends on the reflections of sound (Fig 2-2 ).

Fig (2-2)Use of ultrasonic waves for imaging an embryo

Fig (2-1)A bat (ultrasonic radar)

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Overview :Sounds and tones are produced due to the vibration of objects. Such vibrations travel

through air or any other medium in all directions. When these vibrations reach the ear,they are transmitted through the auditory nerve, then the brain translates them to soundsand tones

Reflection and Refraction of Sound:Firstly: Reflection of Sound:

When a loud sound is produced at a suitable distance from a wall or a mountain, asound is heard back resembling the original one. It is generated due to the reflection fromthe wall or the mountain, appearing as if it were coming from behind the wall or themountain. This sound is called echo. Hence, echo is the repetiton of sound produced dueto reflection.

Sound waves propagate in air in the form of concentric spheres of successivecompressions and rarefactions, whose center is the source of the sound . If these waves areobstructed by a large obstacle, they are reflected back also in the form of concentricspheres of compressions and rarefactions,whose center appears as if it lay behind thereflecting surface and at a distance equal to the distance of the original source from thatsurface. According to the laws of reflection:

1) the angle of reflection is equal to the angle of incidence.2) the incident ray, the reflected ray and the normal to the surface at the point of

incidence all lie in one plane normal to the reflecting surface.Note that: the sound ray is a straight line indicating the direction of propagation of the

sound wave.

Chapter 2 Sound

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Sound

Fig (2-4)Sound travels easier at night

Learn at Leisure

Why does sound travel easier at night than during the day ? The velocity of sound in the air depends on the temperature of the air, since sound

waves propagate in hot air faster than in cold air. When sound travels between two layersof air of different temperatures, it undergoes refraction (Fig 2 - 4). The figure illustratesthe decrease of sound intensity as heard by an observer at a certain distance due to therefraction of sound upwards (leaking away), due to the increase of temperature on a hotday. At night, the sound is heard for longer distances due to the decrease of thetemperature of the air adjacent to the surface of the Earth compared to layers above.Therefore, sound at night is refracted more toward the surface of the Earth.

source observer

cold air

hot air

at daytime

hot air

cold air

ground

ground

at night

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Fig (2-3)Refraction of sound

v1

v2

Normal Normal

Hot air

Cold air

sinsin

vv

1

2

φΘ

=θ

Secondly: Refraction of soundWhen sound falls on a surface between two media, part of it is reflected back to the first

medium according to the laws of reflection, while the rest is transmitted to the secondmedium, deviating from its original path (Fig 2-3 ). Refraction of sound - upon transmittingfrom one medium to another - depends on the velocity of sound in these two media. Inother words :

This means that when the velocity of sound in the first medium v1 is greater than thevelocity of sound in the second medium v2, the sound refracts nearer to the normal, i.e., φ > θand vice versa. It is to be noted that the velocity of sound in gases decreases as their densityincreases, while in liquids and solids the velocity is affected by another factors,which ismore effective than denisty.

(2-1)

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Sound

Fig (2-7 b)Interference pattern

Fig (2-7 a)Interference fringesbetween two waves

Such sources may be obtained, for example, using two speakers for the same electricalsource (Fig 2-5). The connected arcs in the figure represent the positions of the maxima ofcompressions, while the dashed arcs represent the maxima of rarefactions. The distancebetween any two successive arcs or any two successive dashed arcs is the wavelength.

Due to the combination of two waves of equal frequency and amplitude (Fig 2-6), somepoints or regions exist where the compressions of the first source intersect thecompressions of the second source, and the rarefactions of the first source intersect therarefactions of the second source. In both cases, the path difference must equal m λ, wherem is an integer . Therefore, at such positions we have constructive interference, where theintensity of the wave increases (Fig 2-6 a). There are also points or regions where thecompressions of the first source intersect rarefactions of the second source or vice versa.Therefore, the path difference equals (m + ) λ , where m is an integer, then we havedestructive interference and the intensity of the wave diminishes to zero (Fig 2-6 b).

Learn at Leisure

Can we see the interference of sound waves ?The experiment of sound interference is similar to the ripple tank experiment, where

two sources vibrate and produce mechanical waves. These waves interfere producingregions of constructive interference and regions of destructive interference ( Fig 2-7).

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Fig (2-6 a)Constructive interference of the waves

resultant wave first wave

second wave of thesame phase

second wave at180˚ phase shift Fig (2-6 b)

Destructive interference of the waves

resultant wave first wave

Fig (2-5)Formation of constructive and destructive

fringes due to two sound sources

lines of constructive interference(maximum sound intensity)

lines of destructive interference (minimum sound intensity)

source 2source 1

Interference and diffraction of sound Firstly: Interference of sound

Interference is a combination of two waves or more of the same frequency, amplitude,and direction of propagation. Interference may be constructive (strengthing the intensity) ordestructive (weakening the intensity or eliminating it altogether). Fig(2-5) demonstrates theinterference of sound waves, which are longitudinal waves consisting of compressions andrarefactions. The two sources S1 and S2 emit waves of the same frequency and amplitude.

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3) It refracts upon traveling from one medium to another due to the difference in velocity(Fig 2 - 4) :

where φ is the angle of incidence and θ in the angle of refraction, v1 is velocity of soundin the first medium and v2 is the velocity of sound in the second medium.

4) Sound waves of equal frequency and amplitude interfere to produce regions ofconstructive interference (increase of intensity) and regions of destructive interference(decrease of intensity).

5) Sound diffracts when passing through a small aperture or a sharp edge, provided that thediscontinuity is comparable to the wavelength.

Superposition of waves Waves combine such that the resultant wave has intensity equal to the sum of intensities

of the individual waves (Fig 2-9 a). When the frequencies are slightly different while theamplitude is the same, this combination (superposition) leads to beats (Fig 2-9 b , c , d ).

If we move a tight wire or rope such that one pulse is generated (Fig 2-10 a ), then thispulse continues until it reaches the far end. If this end is attached to a sliding ring, then thereflected wave is positive ,i.e., in the same direction as the incident pulse. Whereas if thisend is fixed such that it cannot move, then the reflected wave is always reversed (Fig 2-10b). When the reflected wave meets the incident wave, constructive interference is producedin the first case (Fig 2-10 c ),and destructive interference is produced in the second case

(Fig 2-10 d).

Fig (2-9 a)The resultant wave is the sum of two waves

displacement

first wave

resultantwave

distance

sinsin

vv

1

2

φΘ

=θ

second wave

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Secondly: Sound Diffraction

What is meant by diffraction?Diffraction is a change (or bending) of the wave path when passing through a slit or an

aperture, small enough compared to the wavelength, or when passing by sharp edges in thesame medium.

We observe sound diffraction in our daily life. For example, if you speak in one roomand a window or a door is open, someone in the next room may overhear you , although heis not standing right next to the window or the door (Fig 2-8). The sound intensity in theneighboring room depends on the position of a listener in that room, being maximum ofcourse directly next to the opening. The spreading of sound in the neighboring room isattributed to diffraction .

Sound as a wave motionFrom above, we conclude that sound has wave properties :

1) It propagates in a medium in straight lines in all directions.2) It undergoes reflection when falling on a surface, and the angle of reflection equals the

angle of incidence.

Fig (2-8)Diffraction of sound through a door opening to a nearby room

spreading ofsound in the

form ofconcentric

spheres

door

room

audiosource

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thirdly

Fig (2-10b)Reflection of a pulse

incident pulse

far end free tomove (attached to a

sliding ring) far end fixed tothe wall

reflected pulsereflected pulse

firstly

fourthlysecondly

secondlyfirstly

fourthlythirdly

Fig (2-10c)Combination of two positive pulsespropagating in opposite directions

Fig (2-10d)Combination of two pulses one positive and the other

negative moving in opposite directions

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thirdly


incident pulse




firstly

fourthlysecondly

secondlyfirstly

fourthlythirdly




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destructiveinterference


Fig (2-9c)Formation of harmonic tones with time

Fig (2-9b)Formation of harmonic tones with distance

Fig (2-9d)Harmonic tones resemble two nearly equal interleaved combs

Fig (2-10a)Formation of an incident pulse

distancetime

string and hand at rest

hand moves up pulling thestring upwards

hand moves down

middle of the pulse

hand at rest

1

0

-1

1

-1

0

2

1

0

-1

-2

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distancetime



hand moves down

middle of the pulse

hand at rest

1

0

-1

1

-1

0

2

1

0

-1

-2

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distancetime



hand moves down

middle of the pulse

hand at rest

1

0

-1

1

-1

0

2

1

0

-1

-2

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distancetime



hand moves down

middle of the pulse

hand at rest

1

0

-1

1

-1

0

2

1

0

-1

-2

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distancetime



hand moves down

middle of the pulse

hand at rest

1

0

-1

1

-1

0

2

1

0

-1

-2

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Melde's Experiment Melde's experiment best illustrates standing waves on strings or wires. The apparatus is

shown (Fig 2-12). It consists of a vibrating source, connected to a soft string whose lengthranges from 2 to 3 meters. The other end of the string passes over a smooth pulley and isconnected at its free end to appropriate weights. When the source vibrates, a wave train isproduced in the string, which reflects upon reaching the pulley.The reflected and incidentwaves are combined (superposed or superimposed) to form standing waves. These standingwaves have nodes and antinodes (Fig 2-13), provided the source frequency has a certainvalue compared to the string (wire) length.

Fig (2-11c)A string fixed at both ends and

pulled in the middle

Fig (2-12)Melde's apparatus

waves generated at the middle andpropagating in both directions

waves reflected fromboth fixed ends tensiontension

vibratorpulley

weightsgenerator

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Standing ( Stationary ) Waves:Standing waves are formed when there is a continuous train of waves in a tight wire

( string, spiral spring, or rope) in one direction and a continuous train of waves reflected inthe opposite direction. These two wave trains interfere, giving a pattern of particles of themedium which appears localized, i.e., not moving to the right, or to the left but movingperpendicularly to the wire. This effect may be visualized by moving a spiral spring, (stringor rope) up and down in reciprocity from both ends (Fig 2-11 a), or fixing it from one endand moving the other end in a simple harmonic motion (Fig 2-11 b), or pulling a string -fixed from both ends - from the middle, such that waves are transmitted in both directionsand get reflected, and hence interfere (Fig 2-11 c).

Fig (2-11a)A spiral spring oscillating from both ends in reciprocity

two waves inopposite directions

node

antinode

antinode

node

node

antinodenode

Fig (2-11b)A spiral spring oscillating in a simple harmonic

motion at one end while fixed at the other

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node

antinode

antinode

node

node

antinodenode



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secondlyfirstly

fourthlythirdly



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Fig (2-14)Nodes and antinodes

Fig (2-15)The distance between twosuccessive nodes or two

successive antinodes is halfa wavelength 35

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The node is the position where the amplitude of the vibration is zero, while the antinodeis the position where the amplitude of the vibration is maximum. Nodes and antinodes arespaced at equal distances apart (Fig 2-14).

The wavelength of a standing wave is twice the distance between any two successiveantinodes or two successive nodes. As the weight in the experiment is increased, the tensionin the wire is increased, so is the velocity of propagation, and the frequency for the samewire length is also increased (Fig 2-15).

Fig (2-13a)A vibrating string showing a standing wave pattern

Fig (2-13b)Variation of standing wave patterns with the

ratio of the string length to the wavelength as time goes on

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node

antinode

antinode

node

node

antinodenode



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Since the arc is small

(2-2)

where m is the mass per unit lengh of the sting material.Vibration of strings:

If we have a tight string fixed on both ends and pulledfrom the middle then released to vibrate freely, we notethat the particles of the string vibrate perpendicularly toits length, i.e., perpendicularly to the direction ofpropagation of the wave. Such a vibration is transverse,i.e., transverse waves propagate on both halves of thestring in bolh directions until they reach the fixed ends,then they are reflected back in the opposite direction. Bymultiple reflections, the incident and reflected waves,interfere producing standing waves, where an antinode isformed at the middle, and a node is formed at each of thefixed ends.

A string vibrating in this way may produce different tones.The fundamental tone (the lowest frequency the string mayvibrate at on its own) will produce one antinode and twonodes (as above). The string may vibrate in many other ways.We may divide the wire into segments.

For example, we may have two segments (3 nodes and 2 antinodes), or 3 segments (4 nodes and3 antinodes) (Fig 2-17). When the string has one segment (λ = 2 ), it produces the fundamentalfrequency (first harmonic). When the string has two segments, it produces the first overtone

/ 2 Rθ =

FT / mv =

2FT / 2 RFc = =∴ Mv2

RFTR

v2 = = = FT / mFTM /

FT M

=

Fig (2-17)Formation of harmonics

fundamental tone(1st harmonic)

first overtone(2nd harmonic)

second overtone(3rd harmonic)

third overtone(4th harmonic)

l

l l

ll

l

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Since the arc is small

(2-2)

where m is the mass per unit lengh of the sting material.Vibration of strings:

If we have a tight string fixed on both ends and pulledfrom the middle then released to vibrate freely, we notethat the particles of the string vibrate perpendicularly toits length, i.e., perpendicularly to the direction ofpropagation of the wave. Such a vibration is transverse,i.e., transverse waves propagate on both halves of thestring in bolh directions until they reach the fixed ends,then they are reflected back in the opposite direction. Bymultiple reflections, the incident and reflected waves,interfere producing standing waves, where an antinode isformed at the middle, and a node is formed at each of thefixed ends.

A string vibrating in this way may produce different tones.The fundamental tone (the lowest frequency the string mayvibrate at on its own) will produce one antinode and twonodes (as above). The string may vibrate in many other ways.We may divide the wire into segments.

For example, we may have two segments (3 nodes and 2 antinodes), or 3 segments (4 nodes and3 antinodes) (Fig 2-17). When the string has one segment (λ = 2 ), it produces the fundamentalfrequency (first harmonic). When the string has two segments, it produces the first overtone

/ 2 Rθ =

FT / mv =

2FT / 2 RFc = =∴ Mv2

RFTR

v2 = = = FT / mFTM /

FT M

=

Fig (2-17)Formation of harmonics

fundamental tone(1st harmonic)

first overtone(2nd harmonic)

second overtone(3rd harmonic)

third overtone(4th harmonic)

l

l l

ll

l

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The node is the position where the amplitude of the vibration is zero, while the antinodeis the position where the amplitude of the vibration is maximum. Nodes and antinodes arespaced at equal distances apart (Fig 2-14).

The wavelength of a standing wave is twice the distance between any two successiveantinodes or two successive nodes. As the weight in the experiment is increased, the tensionin the wire is increased, so is the velocity of propagation, and the frequency for the samewire length is also increased (Fig 2-15).

Fig (2-13a)A vibrating string showing a standing wave pattern

Fig (2-13b)Variation of standing wave patterns with the

ratio of the string length to the wavelength as time goes on

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Questions and Drills

I) Essay questions 1) State the laws of reflection of sound.2) Show how to demonstrate the interference of sound.3) Explain : Sound is a wave motion.

II) Define:1) an antinode. 2) a node. 3) the wavelength of a standing wave.

III) Complete :1) The velocity of propagation of a transverse wave in a string is given by:v = ...................................... 2) The fundamental frequency produced in a string is given by:

ν = .....................................3) Keeping tension constant, the frequency of a string is.......................proportional to its length .4) Keeping the length of a string constant, the fundamental frequency is directly

proportional to .................................5) Keeping the length of the string and tension constant, the fundamental frequency is

inversely proportional to ................................

IV. Choose the right answer:1) Standing waves are formed by the combination of two waves propagating

a) in the same direction.b) in opposite directions provided they have equal frequency and intensity.c) in opposite directions without necessarily having equal frequency and intensity.d) in two perpendicular directions.

cyan magenta yellow black File: ch 3 fl ˙ Æ˝ ” 47

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Reflection and refraction of light Light propagates in straight lines in all directions, unless met by an obstructing medium.

If so, it undergoes reflection, refraction and partial absorption depending on the nature of

the medium. When a light ray falls on a surface separating two media - which are different

in optical density - then part of light is reflected and the rest is refracted, neglecting

absorption. We note from Fig (3-3) that each of the incident ray, reflected ray and refracted

ray as well as the normal to the surface at the point of

incidence all lie in one plane perpendicular to the separating

surface.

In the case of reflection : the angle of incidence is equal to

the angle of reflection

In the case of refraction : the ratio between the sine of the

angle of incidence in the first medium to the sine of the

angle of refraction in the second medium is equal to the ratio

φ

θ

Fig (3 – 2)

An electromagnetic wave consists of an electric fieldand a magnetic field perpendicular to each otherand to the direction of propagation of the wave

angle ofincidence reflected ray

incidentray

angle ofrefraction

second medium(glass)

first medium(air)

oscillating magnetic field

oscillating electric field

Fig (3 – 3)Reflection and refraction

of light

refracted ray


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Overview :Light is an indispensible form of energy. The Sun is the main natural source of energy to

us. The energy from the Sun is almost divided between heat and light. Thanks to the lightfrom the Sun, the plants perform photosynthesis, hence make their own food. Man dependson plants and animals, which in turn feed on plants.

We have seen before that sound has a wave nature. It propagates from a source causingmechanical waves in the medium. Light also has a wave nature. It is subject to the laws ofreflection, refraction, interference and diffraction. But light is different from sound in that itdoes not require a medium to propagate in. Light is part of an extensive range of wavescalled electromagnetic waves, which all travel at a constant speed in space equal to 3 x 108 m/s,while varying in frequency. This range of waves is called the electromagnetic spectrum (Fig 3-1). It includes, for example, radio waves, infrared, visible light, ultraviolet,

X- rays and Gamma rays. They all share common features. They are all transverseelectromagnetic waves, but of different frequencies (and wavelengths).

Electromagnetic waves consist of time varying electric and magnetic fields. Bothoscillate at equal frequency at the same phase, and are perpendicular to each other and tothe direction of propagation (Fig 3-2), hence called transverse waves.

Fig (3 – 1)

Electromagnetic spectrum

Chapter 3 Light


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nn

2

1= sin

sinφθ

n1 sin φ = n2 sin θ

2) The refraction of light is attributed to the difference in the speed of light, when light is

transmitted from one medium to another.

where v1 is the speed of light in the first medium, v2 is the speed of light in the secondmedium. Substituting equation (3-3) in (3-1), we have:

This is Snell’s law The absolute refractive index for the medium of incidence times the sine of the angle of

incidence is equal to the absolute refractive index of the medium of refraction times thesine of the angle of refraction.3) We can use refraction in analysing a bundle of light into its components of different

wavelengths, since the absolute refractive index varies with wavelength. Therefore, whitelight may be decomposed into its components. This can be seen, for example, in soap bubbles.

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Why refraction ?If light falls from a less dense medium onto a more dense medium ,the refracted ray

approaches the normal. This resembles a car in which one of its wheels goes through amuddy soil, while the other is free on the paved road. The wheel that goes into the mudbecomes slower. Therefore, the car changes direction (Fig 3-4). The opposite is also true, asin refraction from a more dense material to a less dense one. The refracted ray deviatesaway from the normal (Fig 3-5).

cnv =

n2n1

=v1v2 ( 3 - 3 )

( 3 - 4 )


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mediumrefractive index 1.002931.3330001.5010001.4610001.3610001.520001.660000

1.48500002.419000

AirWaterBenzineCarbon tetrachlorideEthyl alcoholCrown glassRock glass QuartzDiamond

of the speed of light in the first medium to the speed of light in the second medium. This

ratio is constant for these two media, and is called relative refractive index from the first

medium to the second medium, denoted by 1n2 :

Important facts

1) The speed of light in space ''c'' is one of the physical constants of the universe and is

equal to 3 x 108 m/s. It is larger than the speed of light in any medium ''v''. The ratio

= n is called the absolute refractive index for the medium and is always > 1.

The absolute refractive indices of some materials are listed below

SinSin

= v1

v2θsinsin = n

1 2

cvn = ( 3 - 2 )

( 3 - 1 )

cv


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Fig (3 – 5)Refraction from a more dense

medium to a less dense medium

Examples1) If a light ray falls on the surface of a glass slab whose refractive index is 1.5 at an angle

30˚, calculate the angle of refraction.

Solution

2) If the absolute refractive index of water is and glass , find

a) the relative refractive index from water to glass

b) the relative refractive index from glass to water.

Solutiona) The relative refractive index from water to glass

43

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1.5 = Sin 30Sinss

s∴ n = SinSin

sin = 0.51.5

sin

∴

∴

ss

= 0.333

θ

θ = 19˚ 28´

θ

θ

Fig (3 – 4)Refraction from a less dense

medium to a more dense medium

muddysoil

muddysoil

paved road reflectedray

incidentray

incidentray

reflectedray

glass

pavedroad

glass air


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∆Χ= λLd

∆ y ( 3 - 5 )

reaching the double slit have the same phase, hence, are coherent (having thesame frequency, amplitude and phase). Waves emanating from S1 and S2 arecylindrical and spread toward the observation screen C. On such a screen,waves coming from S1 and S2 combine and produce an interference pattern,appearing as a sequence of bright and dark straight parallel regions, which arethe interference fringes (Fig 3-7). The distance between two successive

fringes ∆y is given by:

where λ is the wavelength of the monochromatic source, R is the distancebetween the double slit and the observation screen and d is the distancebetween S1 and S2.

Therefore, this experiment may be used to determine the wavelength forany monochromatic light source.

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Interpretation of interference in Thomas Young’s experiment If light were not to manifest interference, we would

obtain fringes as in Fig (3-8a). We may interpret theformulas of constructive and destructive interferencepattern in Young’s experiment as follows. If thedistance of the screen from the double slit R is largerelative to the distance d between the two slits of thedouble slit, then we may consider the two rays r1, r2emanating from the double slit on their way to theobservation screen as nearly parallel. If θ is theinclination angle of the two rays, then the pathdifference between these two rays is ∆r (Fig 3-9). This

Fig (3 – 7)Interference

fringes

R

monochromaticlight soure

darkfringes

bright fringes

Secondslit

Firestslit ab

Fig (3 – 8) Fringes (a) resulting from

interference (b) if there were no interference


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Light DiffractionWhen a monochromatic light falls on a circular aperture in a screen, we expect that light

should form a circular bright spot on an observation screen, considering that lightpropagates in straight lines. But careful examination of the bright spot (called Airy’s disk),i.e., studying the light intensity, reveals the existence of bright and dark fringes (Fig 3-12).

Fig (3-13) demonstrates diffraction from a rectangular slit, while Fig (3-14) shows thediffraction pattern at a sharp edge of matter. In general, diffraction is evident when thewavelength of the wave is comparable to the dimensions of the aperture, and vice versa(Fig 3-15). In fact, there is no big difference between the mechanisms of interference anddiffraction. In both cases, combination (superposition) of waves is involved (Fig 3-16).

Fig (3 – 12)

Diffraction in a circular aperture

Airy’s disk

parallel rays

firstsecondary

bright spot

Fig (3 –13b) Distribution of light intensity on a screen with the

succession of fringes resulting from diffractionfrom a rectangular aperture

Fig (3 – 13a)Diffraction from a rectangular aperture

center of the central bright fringe

lightintensity

slit

light ray

central brightspot


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Learn at Leisure

Interpretation of diffractionFig (3-17) shows a plane wave advancing toward a screen in which there is a

rectangular slit. At an appropriate distance, there is a white parallel observation screen.According to the wave theory, points on the wave front at the slit may be considered assources of secondary wavelets. Light emanating from these secondary sources fall on theobservation screen at a point corresponding to the center of the slit as a lens collimates therays. In this case, wavelets have the same phase. Constructive interference results in abright fringe (Fig 3-17 a).

Fig (3 –17a)

Formation of the central bright fringe

Fig (3–17b)

Succession of the fringes


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circular aperture

plane edge

sphere Fig (3–14)Diffraction patterns from different obstacles

diffraction is moreevident from anarrow slit in

comparison with λ

the dimensions of theobstacle are large incomparison with λ

the dimensions of theobstacle are mediumin comparison with λ

the dimensions of theobstacle are small

incomparison with λFig (3 – 15)

Fig (3 – 16)

Diffraction is the interferenceof secondary wavelets fromdifferent points in the slit

razor edge

(b)

incidentwave

(a)

observationscreen

0.2d0.8d


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Resolving powerDiffraction places a limit on resolving details in an image. This limit is called the limit

of resolution. If we have two point sources, and light is emitted from each through acircular aperture, then each source forms separate fringes. When the distance between thetwo sources decreases, the fringes get closer, and it becomes difficult to identify one fromthe other. It is found that the angle between the centers of the two fringes under thiscondition is given by the approximate relation ∆θ = , where D is the aperture diameter.Thus, the ability to resolve two small objects is inversely proportional to the aperturediameter and directly to the wavelength (Fig 3-19). In the case of a microscope, the lenstakes the place of the aperture and the wavelength limits the ability of the microscope todistinguish between small objects. As λ decreases, we can discern details that were notseen before. This is the advantage of the electron microscope (Chapter 12).

Fig (3–19) Resolving power

a)as the two sources get closerto each other it becomesdifficult to separate them

visually because of diffraction

c) if the two sources aredrawing near to the

observer, then he canseparate them visually

d) bacteria appearing through an electron microscope and notappearing through an optical microscope

b) the resolution is nilas the objects get toosmall and too close

together.

λD

∆


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θθϕ

Light as a wave motionFrom above, we conclude that light 1) propagates in straight lines .2) reflects according to the laws of reflection .3) refracts according to the laws of refraction .4) light interferes, and as a result, light intensity increases in certain positions (bright

fringes)and diminishes to zero in other positions (dark fringes).5) light diffracts if obstructed by an obstacle .These are the same general properties of waves. Hence, light is a wave motion

Total reflection and the critical angle When a light ray travels from an optically dense medium (as water or glass) to a less

dense medium (as air), then the refracted ray deviates away from the normal (Fig 3-20). Asthe angle of incidence increases in the more dense medium (of high absolute refractiveindex), the refraction angle in the less dense medium (of low absolute refractive index)increases.

A point is reached when the angle of incidence in the more dense medium approachesa critical value φc when the angle of refraction in the less dense medium reaches itsmaximum, which is 90˚. Then,the refracted ray becomes tangent to the surface.

Fig (3–20) Incidence of light from a more optically dense medium to a less optically dense medium

(a) (b) (c) (d)


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= 1 x 1.331.6

= sin c 0.8313

Sin c = 1n1

= 11.33

= 0.7518sin

Fig (3–21) Optical fibers contain the

rays despite bending

Fig (3– 22) Optical fibers

Some Applications of Total Reflection I. Fiberoptics (Optical Fibers)

Fig (3-21) shows an optical fiber. It is athread-like tube of transparent material. When lightfalls at one end, while the angle of incidence isgreater than the critical angle, it undergoessuccessive multiple reflections until it emerges fromthe other end (Fig 3-22). Fig (3-23) shows a bundleof fibers which can be bent while containing lightso that light can be made to travel in non straightlines to parts hard to reach otherwise.

Fibers can be used to transmit light withoutmuch losses, and are widely used nowadays.

b) In the case of water

φc = 48˚ 45´

2)Using the information in the example above, find the critical angle for light fallingfrom glass onto water

SolutionUsing Snell’s law, n2 sin 90˚ = n1 sin φc

1.33 x 1 = 1.6 sin φc


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Learn at Leisure

The Bear’s fur The bear’s fur does not provide the bear with thermal

isolation only, but the fur hairs are massive optical fibers

which reflect ultraviolet rays. The fur appears white (Fig

3-26). because visible light reflects inside the hollow

transparent optical fibers, while the skin itself absorbs all

rays reaching it. Therefore, it is actually black.

Learn at Leisure

How an optical fiber worksIf we have a hollow tube and look through it to see a bright object on the other end, then

the object is easily seen. If the tube is bent, then the object cannot be seen. Yet, we may be

able to see it, if we use reflecting mirrors in the path of rays. Similarly, by using optical

fibers, while the ray is incident at an angle greater than the critical angle, then multiple

reflections take place, until the ray emerges from the other end, despite the bending of the

fibers.

II. The reflecting prism The critical angle between glass (refractive index 1.5) and air is 42˚. Therefore, a glass

prism whose angles are 90˚, 45˚, 45˚ is used to change the path of the rays by 90˚ or 180˚.

Such a prism may be used in optical instruments, as periscopes in submarines and

binoculars in the field (Fig 3-27).

Fig (3–26)

The bear’s fur


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Fig (3–24b)

Endoscopes

Fig (3–25) Optical fibers used to carry electrical signals

Fig (3–24c) Endoscope lens

Fig (3–24d) An image of esophogus

by optical fibers


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This can be explained as follows. On very hot days, the air layers adjacent to the surface

of the Earth are heated, their density decreases. Hence, their refractive index becomes

smaller than that of the upper layer. If we follow a light ray reflected off a palm tree, this

ray is traveling from an upper layer to one below. Therefore,if refracts away from the

normal, and keeps deviating taking a curved path. When its angle of incidence reaches

more than the critical angle, it undergoes total reflection and the curve goes up. To the eye

of the observer, the ray appears as if coming from under the surface of the Earth. The

observer thinks that there is a pond.

Deviation of light in a prism

When a light ray such as " a b " falls on the surface xy of a prism, it refracts in the prism

taking the path " bc ", until it falls on the surface xz and emerges in the direction "cd" (Fig

3-29). We notice from the figure that the light ray in the prism refracts twice. As a result,

the ray deviates from its original path by an angle of deviation α .

The angle of deviation α is the angle subtended by the directions of the extension of the

incident ray and the emerging ray. If the angle of incidence is φ1 , the angle of refraction

on the first surface is θ1 , the angle of incidence on the second surface is φ

2 , the angle of

emergence is θ2 and the apex angle of the prism is A, we note from the geometry (Fig

3-29).


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Fig (3–27) A reflecting prism

a) a reflecting prism changing thelight path by 90˚

b) a reflecting prism changingthe light path by 180˚

c) prisms in binoculars

Fig (3–28b) Reflection of the sky in the desert

gives the illusion of water

Prisms are better for this purpose than reflecting surfaces, first, because light totallyreflects from such a prism, while it is seldom to find a metallic reflecting surface whoseefficiency is 100%. Secondly, a metallic surface eventually loses its luster,and hence itsability to reflect decreases. This does not happen in a prism. The surface at which lightrays fall on a prism or the surface from which the rays emerge may be coated with non -reflective layer of material like cryolite (Aluminum fluoride and magnesium fluoride)whose refractive index is less than that of glass, to avoid any reflection losses on theprism, even little as they are.

III.MirageThis is a familiar phenomenon observable on hot days, as paved roads appear as if wet

(Fig 3-28 a). Also, an image of the sky is made on desert plains, where palm trees or hillsappear inverted giving the illusion of water (Fig 3-28 b).

Fig (3–28a)Paved roads appear as if wet


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But

Substituting for φ and θ we find that the refractive index can be determined from therelation

Experiment to determine the ray path through a glass prism and its refractive index:

Tools:An equilateral triangular prism (A = 60˚), pins, a protractor, a ruler.

Procedure:1) Place the glass prism on a sheet of drawing paper with its surface in a vertical position

and mark its position with a fine pencil line. Place two pins such that one of them (a) is very close to one side and the other (b) is about

10 cm from the first. The line joining them representsthe incident ray. Look at the other side of the prism tosee the image of the two pins, one behind the other.

Place two other pins c and d between the prism andthe eye such that they appear to be in line with thetwo pins a and b,i.e., the four pins appear to be in onestraight line.Locate the positions of the four pins.2) Remove the prism and the pins, join b and c to locate the

path of the ray (a b c d) from air to glass to air again.

n = SinSinsinsin

Fig (3– 31) Determination of light

ray path in a prism

0

0

(3 - 10)

emergingray

incidentray

n = Sin + A

2

Sin A2

αsin

sin

0


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Note also that the refractive index (n) depends on up the wavelength λ, then the

minimum angle of deviation depends also on the wavelength. Thus, if a beam of white light

falls on a prism set at the minimum angle of deviation, then the emerging light disperses

into spectral colors as illustrated in Fig(3-32). From this figure, it is concluded that the

violet ray has the largest deviation ( maximum refractive index). The visible spectral colors

into which the white light is dispresed are arranged by the order: red, orange, yellow,

green, blue, indigo and violet.

The thin prism:A thin prism is a triangular glass prism. Its apex angle is a few degrees and is in the

position of minimum deviation:

Since: and are small angles.

Thus,

(radians)

and (radians)

Substituting from (3-10), we find that the refractive index of the material of the thinprism is determined by

∝ = A (n - 1) (3 - 12)

Sin + A2

= + A2

Sin A2

= A2

sin ≅

≅sin

+ A2

A2

α

αα

0

0 0

n = Sin + A

2

Sin A2

sin

sin

α0

0

n = (3 - 11)α +AA0


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tn =

Sin + A2

Sin A2

s

s

α0

3) Extend dc to meet extended ab .The angle between them is the angle of deviation α.

4) Measure the angle of incidence φ1, the angle of refraction θ1, the inner incidence angle

φ2, the angle of emergence θ2 and the angle of deviation (α).5) Repeat the previous steps several times changing the angle of incidence and tabulate

the results.

Find the minimum angle of deviation and the corresponding angles φ˚ and θ˚ .- Then obtain the refractive index from equation (3-10).

The dispersion of light by a triangular prism:It has been proven previously that in the case of

minimum deviation, the refractive index may bedetermined from the relation:

where (n) is the refractive index,αo is minimum angle ofdeviation, and (A) is the angle of the prism.

Since the angle of the prism is constant for a certain prism,so the minimum angle of deviation changes by changing therefractive index. As the refractive index increases, theminimum angle of deviation increases and vice versa.

Angle of theprism A

angle ofincidence φ1

Angle of innerincidence φ2

angle of refraction θ1

angle ofemergence θ2

Angle ofdeviationα

Fig (3–32) A prism disperses the

spectrum


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In a Nutshell

.Laws of reflection of light :1) Angle of incidence = Angle of reflection2) The incident ray, the reflected ray, and the normal to the reflecting surface at the

point of incidence, all lie in one plane perpendicular to the reflecting surface.

.Light refracts between two media because of the different velocities of light in the twomedia v1 & v2

.Laws of refraction of light :1) The ratio between the sine of the angle of incidence in the first medium, to the sine

of the angle of refraction in the second medium is constant, and is known as therefractive index 1n2

where φ is the angle of incidence in the first medium, and θ is the angle of refractionin the second medium

2) The incident ray, the refracted ray, and the normal to the surface of separation at thepoint of incidence, all lie in one plane normal to the surface of separation.

• The relative refractive index between two media is the ratio between the velocity of lightin the first medium v1 and the velocity of light in the second medium v2

• The absolute refractive index for a medium is given by :

where c is the velocity of light in free space and v is the velocity of light in the medium.• Snell s law :

n1sinφ = n2 sinθ

sin φsin θ1n2 =

n = CVcv

1 n2 = V1

V2

v

v

,


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Dispersive Power When white light falls on a prism, the light disperses into its spectrum due to the

variation of the refractive index with wavelength.(α

0)r = A (nr - 1)

(α0)b = A (nb - 1)

where nr is the refractive index for red and nb for blue. Subtracting,

(α0)b - (α0)r = A (nb - nr) ( 3 - 13)

The LHS represents the angular dispersion between blue and red. For yellow (middlebetween blue and red), the angle is :

(α0)y = A (ny - 1) (3 - 14)

where ny is the refractive index for yellow. If (α0)y is the average of (α0)r and (α

0)b, then

nyis the average of nr and nb. We define as :

where is the dispersive power, and is independent of the apex angle.

= nb - nr

ny - 1 −

( 3 - 14)( α0)b

(α0)y

( α0)rωα=

ωα

ωα


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n = Sin + A

2

Sin A2

s

s

• Refractive index of the prism material is given by:

where n is the refractive index, α˚ is the minimum angle of deviation. • The minimum angle of deviation in a thin prism is :

α˚ = Α (n - 1)

• The angular dispersion for a thin prism is :

(α0)b - (α

0)r= Α (nb -nr)

• where (α0)b is the minimum deviation angle of the blue ray, and (α

0)r is the minimum

deviation angle of the red ray. • The dispersive power :

where (α0)y is the minimum angle of deviation of the yellow light, and ny is the refractive

index for the yellow light.

α0

= b r

y

= n b - n r

n y - 1

ωα(α )b0 (α )r0

(α )y0

ωα


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• The distance between two successive similar fringes (either bright or dark) is :

where λ is the wavelength of light employed, R is the distance between the double slitand the screen, and d is the distance between the two slits. • Light is a wave motion. • The critical angle is the angle of incidence in the more dense medium, corresponding to

an angle of refraction in the less dense medium equal to 90˚.• The absolute refractive index is equal to the reciprocal of the sine of the critical angle

when light travels from this medium into air or vacuum.

• Total internal reflection takes place when the angle of incidence in the more densemedium is greater than the critical angle.

• The mirage is a phenomenon that can be explained by total internal reflection. • The angle of the apex of the prism is given by:

A = θ1 + φ2

• The angle of deviation is given by:

α = (φ1 + θ2) - A

where φ1 is the angle of incidence θ2 is the angle of emergence • In the case of minimum deviation :

φ1 = θ2 = φ0

θ1 = φ2 = θ 0

∆y = λRd

n = 1Sin cs


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I) Essay questions1) Explain why light is considered to be a wave motion .2) Describe an experiment to demonstrate the interference of light. 3) Explain how mirage is formed.

II) Define : a) the relative refractive index between two media. b) the absolute refractive index for a medium. c) the critical angle.d) the angle of deviation.

III) Complete : a) The distance between two successive bright fringes is given by ....................................b) Snell’s law states that : ......................................................c) The angle of deviation in a thin prism is given from relation :.....................d) The dispersive power is: ......................................................

IV) Choose the right answer :1) When light reflects :

a) the angle of incidence is less than the angle of reflection.b) the angle of incidence is greater than the angle of reflection.c) the angle of incidence is equal to the angle of reflection.d) there is no right answer above .

2) When light refracts, the ratio ,where φ is the angle of incidence and θ is the angleof refraction is: a) constant for the two media.b) variable for the two media.

sin φsin θ


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7) The angle of incidence in a medium is 60˚ and the angle of refraction in the secondmedium is 30˚. Then the relative refractive index from the first to the second medium is :a) 3 b) c) d) 2

8) An incident ray at an angle 48.5˚ on one of the faces of a glass rectangular block (n =1.5), the angle of refraction is :

a)20˚ b)30˚ c) 35˚ d) 40˚

9) In an experiment it was found that the minimum angle of deviation is 48.2˚ Given thatthe angle of the prism is 58.8˚, the refractive index of the material of the prism is : a) 1.5 b) 1.63 c) 1.85 d) 1/1.85

10) If the critical angle for a medium to air is 45˚, then the absolute refractive index is : a) 1.64 b)2 c)1.7 d) 2

11) A thin prism has an angle of 5˚. Its refractive index is 1.6. It produces a minimum angleof deviation equal to :

a) 5˚ b) 6˚ c) 8˚ d) 3˚

12) A ray of light falls on a thin prism at an angle of deviation 4˚ and its apex angle 8˚.Itsrefractive index is :

a) 1.5 b)1.4 c) 1.33 d) 1.6

122


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Chapter 4 Hydrostatics

= mv

ρVol

Overview

Fluids are materials which can flow. They are liquids and gases. Gases differ fromliquids in compressibility. Gases are compressible, while liquids are incompressible. Thus,liquids occupy a certain volume, while gases can fill any volume they occupy, i.e., thevolume of the container.

Density

Density is a basic property of matter. It is the mass per unit volume (kg / m3)

where Vol is the volume

Density varies from one element to another due to:1) difference in atomic weights2) difference in interatomic or intermolecular distances or molecular spacings.We know that bodies of less density float over more dense liquids. The following tableshows density for different material.

(4 -1)

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2) Measuring density is used in clinical medicine, such as measuring blood and urinedensities. Normal blood density is 1040 kg / m3 – 1060 kg / m3. High density indicateshigher concentrations of blood cells and lower concentrations indicate anemia. The normal urine density is 1020 kg / m3. In some diseases, salts increase and cause theurine density to increase.

Pressure

Pressure at a point is the average force which acts normal to unit area at that point. Ifforce F is normal to a surface of an area A, then the affected pressure P on the surface isdetermined by the following relation:

Learn at Leisure

Elephant’s foot vs human foot Because the pressure is the force per unit area, the

pressure due to a pointed high heel is greater than thepressure due to an elephant’s foot, since the area of thepointed heel is very small (Fig 4 – 1).

(4 - 3) P = FA

Meaning of pressureFig (4–1)

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The ratio of density of any material to that of water at the same temperature is called therelative density of the material (no units). The relative density of a material, is equal to :

=

=

Applications to density1)Measuring density is of great importance in analysis, such as measuring the density of the

electrolyte in a car battery. When the battery is discharged, the density of the electrolyte (dilutesulfuric acid) is low due to chemical reaction with the lead plates and the formation of leadsulfate. When the battery is recharged, the sulfate is loosened from the lead plates and go backto the electrolyte, and the density increases once more. Thus, measuring the density indicateshow well the battery is charged.

Material

Solids:Aluminum†

Brass CoperGlassGoldIceIronLead

PlatinumSteelSugerWax

Liquids:Ethyl Alchol

BenzeneBlood

Gasoline

2700860088902600

19300910

79001140021400

783016001800

790900

1040690

KeroseneMercuryGlycerin

Water

Gases:Air

AmmoniaCarbon dioxide

Carbon mono oxideHelium

HydrogenNitrogenOxygen

82013600

12601000

1.290.761.961.250.18

0.0901.251.43

the mass of a certain volume of matter at a certain temperaturethe mass of the same volume of water at the same temperature

(4 - 2) the density of the material at a certain temperaturethe density of water at the same temperature

Densitykg/m3Material Density

kg/m3

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acted upon by two forces: its weight downwards and the force due to the pressure of theliquid around it. As the depth of the liquid increases, the pressure increases (Fig 4 – 3).

To calculate the pressure (P), we imagine a horizontal plate x ofarea A at depth h inside a liquid of density ρ (Fig 4 – 4). This plateacts as the base of a column of the liquid. The force acting on the platex is the weight of the column of the liquid whose height is h andwhose cross section is A.

Because the liquid is incompressible, the force resulting from theliquid pressure must balance with the weight of the column(of theliquid. The volume of this column is Ah and its mass Ahρ, hence itsweight Fg is given by :

Fg = Ahρgwhere g the acceleration due to gravity. The pressure due to the

liquid from under the plate x (acting upwards) must be :

Pressure increases with liquid depth

pressure Po

pressure P

Fig (4 – 3)

P = =FA

AhρgA

(4 − 4)... P = hρg

Fig (4 – 4)Calculation of the pressure

of a column of liquid

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c) pressure on the surface of an object is equalto the pressure on the surface of a similar sizeof the liquid of the same volume and shape

Fig (4 – 2)

a) pressure inside a liquid is perpendicularto any surface inside the liquid

b) pressure is perpendicular to the surface of animmersed body at every point

Pressure at a point inside a liquid and its measurement.

If you push a piece of foam under water and let it go, it will rise and float. This indicatesthat water pushes the immersed foam by an upward force. This force is due to the pressuredifference across this piece of foam.

At any point inside a liquid, the pressure acts in any direction. The direction of the forceon any surface is normal to that surface. The pressure on a body is the same as the pressureon a volume of the liquid that has the same shape of the body in case this body wereremoved. In other words, the liquid occupying the same size which a body would occupy is

d) in a certain size of a liquid there is equilibriumbetween two forces: the weight of the liquid andthe pressure due to the remainder of the liquid.

Pressure in a liquid

PdA

PdA

PdA

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Balance of liquids in a U - shaped tubeLet us take a U - shaped tube filled with an appropriate amount of water. Let us add a

quantity of oil in the left branch of the tube, until the level of oil reaches level C at a height

ho over the separating surface AD between water and oil, noting that both liquids do not

mix. Let the height of the water in the right branch be hw above level AD (Fig 4 – 7).

Because the pressure at A = pressure at D

... Pa + ρogho = Pa + ρwghw

where Pa is the atmospheric pressure, ρo the density of oil, ρw

the density of water. Thus, ho ρo = hwρw or

Measuring ho and hw, we may determine practically the

density of oil, knowing the density of water.

Atmospheric Pressure

Torcelli invented the mercury barometer to measure the atmospheric pressure. He took a

1 m long glass tube and filled it completely with mercury and turned it upside down in a

tank of mercury. He noticed that the level of mercury went down to a certain level that

measured 0.76 m from the surface of mercury in the tank. The void above the column of

mercury in the tube is vacuum (neglecting mercury vapor) is called Torcelli vacuum.

(4 -6)

Balance of liquidsin a U - shaped tube

Fig(4 – 7)

ρoρw

hwho

=

oilwater

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tics Taking into consideration the fact that the free surface of the liquid is subject to

atmospheric pressure Pa ,then the total pressure at a point inside a liquid it depth d is given

by:

P =Pa + h ρ g

Practical observations show indeed that the liquid pressure at

a point inside it increases with increasing depth and with

increasing density at the same depth.

Thus, we conclude :

1) All points that lie on a horizontal plane inside a liquid has the

same pressure.

2) The liquid that fills connecting vessels rise in these vessels to

the same height, regardless of the geometrical shape of these

vessels provided that the base is in a horizontal plane

(Fig 4 – 5).

Therefore, the average sea level is constant

for all connected seas and oceans.

3) The base of a dam must be thicker than that

the top to withstand the increasing pressure

at increasing depths (Fig 4 – 6).

(4 − 5)

Fig (4 – 6)Dams must be thicker at the base to

withstand the pressure at increasing depths

Fig (4 – 5)Water rises to the same

level in connecting vessels

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tics From Fig (4 – 8), the height h of the mercury column in the tube is constant, wether the

tube is upright or inclined. Taking two points A, B in one horizontal plane (Fig 4 – 9),

such that A is outside the tube at the surface of mercury in the tank, while B is inside the

tube. The pressure at B = the pressure at A. Thus:

Pa = ρgh

This means that the atmospheric pressure is equivalent to the

weight of a column of mercury whose height is 0.76 m and cross

sectional area 1m2 at OC° at sea level. This is known as S.T.P.

(standard temperature and pressure). Since the density of mercury

at O C° is 13595 kg/m3 and g = 9.8 m/s2

Pa = 1 Atm = 0.76 x 13595 x 9.81

= 1.013 x 105 N/m2

Mercury height in a barometer is not affected by the tilting of the manometer

Fig (4 – 8)

vacuum

mercury

atmospheric pressure

Fig (4 – 9)A simple barometer

(4 - 7)

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Applications to Pressure

1) Blood is a viscous liquid pumped through a complicated network of arteries and veins

by the muscular effect of the heart. This is called steady flow (chapter 5). In the case ofturbulent flow (chapter 5), there is noise which can be detected by a stethoscope. Thereare two values for blood pressure: the systolic pressure, as blood pressure is maximum(normally 120 Torr). This occurs when the cardiac muscle contracts and blood ispushed from the left ventricle to the aorta onto the arteries. The diastolic pressure is theminimum blood pressure (normally 80 Torr) when the cardiac muscle relaxes.

2) When a tire is well inflated (under high pressure) the area of contact with the road is assmall as possible, while an underinflated (low pressure) tire has large contact area. Asthe area of contact with the road increases, friction increases and consequently, the tireis heated. Air pressure in a tire can be measured by a pressure gauge (Fig 4 – 12).

Fig (4-12)Measuring tire pressure with a pressure gauge

graduated scale

intake from the tire

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tics Manometer

The manometer is a U - shaped tube containing a proper amount of liquid of a knowndensity. One end is connected to a gas reservoir. The level of the liquid in the manometermay rise in one branch and go down in the other. Taking two points A,B in one horizontalplane in the same liquid (Fig 4 – 11 a), we have the pressure at B = the pressure A

When P- the pressure of the gas enclosed in the reservoir - is greater than Pa, ρgh is theweight of a column the liquid in the free end of the manometer above point B and is thedifference between P and Pa (Fig 4 -11a),

P = Pa + ρghIn the case P < Pa (Fig 4 – 11 b),

P = Pa - ρghi.e., the level of the liquid in the free end branch is lower than the level of the liquid in

the end connected to the gas reservoir by a height h. In many cases, it suffices to measurethe pressure difference,

∆ P = P - Pa = ρgh (4 - 8)Knowing the liquid density ρ in the manometer and the height difference h between the

liquid levels in the two branches and the acceleration due to gravity g,we can calculate ∆P.Knowing Pa ,we may determine P of the gas enclosed in the reservoir.

a) when gas pressure > atmospheric pressure

b)when gas pressure < atmosphericpressure

Fig (4-11)Manometer

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1) A solid parallelepiped (5cm x 10cmx 20cm) has density 5000kg /m3 is placed on a

horizontal plane. Calculate the highest and lowest pressure. (g = 10 m/s2)

Solution

For the highest pressure it is placed on the side with the least area (5 cm x 10 cm), where

the force is the weight.

For the lowest pressure, it is placed on the side of the greatest area (10 cm x 20cm)

2) Find the total pressure and the total force acting on the base of a tank filled with salty

water of density 1030 kg/m3. If the cross-section of the base is 1000 cm2 , the height of

the water is 1cm and the surface of the water is exposed to air. Take g = 10 m/s2 and the

atmospheric pressure = 1 Atm = 1.013 x 105N/m2

Solution

Total pressure

P = Pa + ρg h

= 1.013 x 105 + 1030 x 10 x 1

= (1.013 + 0.103) x 105 = 1.116 x 105 N/m2

Total force F = P x A = 1.116 x 105 x 1000 x 10-4

= 1.116 x 104 N

P = FA

= 5 x 10 x 20 x 10-6 x 5000 x 1010 x 20 x 10-4

= 2500 N/m2

P = FA

= 5 x 10 x 20 x 10-6 x 5000 x 105 x 10 x 10-4

= 10 4Fg

Fg

N/ m 2)

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If pressure P is exerted to the small piston, this pressure is transmitted to the liquid and,subsequently, to the surface of the large piston. If the force applied to the small piston is fand the force affecting the large piston is F, and because the pressure on both pistons mustbe the same at equilibrium at the same horizontal plane, then :

(4 - 9)From this relation, it is clear that if force f affects a small piston, a large force F is

generated on the large piston. The mechanical advantage of the hydraulic press η is givenby:

(4 - 10)

Thus, the mechanical advantage of a hydraulic press is determined by the ratio of thelarge piston to the small piston. Referring to Fig (4 – 15), it is clear that if the small pistonmoves down a distance y

1 under the influence of f, then the large piston moves up a

distance y2 under the effect of F. According to the law of conservation of energy, the work

done in both cases must be the same (for 100% piston efficiency),

This shows that the mechanical advantage of thepiston may alternatively be expressed as the ratio y

1/y

2

P = fa

= FA

F = Aa

f

η

(Fig 4-15)Mechanical advantage

cylinder

liquid

(4 - 11)y1

y2

F = f

f y1

= F y2

y2

y1

fF =

f

f

f

y1

y2

= =Ff

Aa

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Fig (4-14)Hydraulic Press

b) a weight of 1 kg to the left generates aforce equivalent to 100 kg to the right if the

ratio of the two cross sectional areas is 1:100

Pascal’s principle

Consider a glass container (Fig 4 – 13) partially filled withliquid and equipped with a piston at the top. The pressure at apoint A inside the liquid at depth h is P =P1 + hρg where P1 isthe pressure immediately underneath the piston, which resultsfrom the atmospheric pressure, as well as the weight of the pistonand the force applied on the piston. If we increase the pressure onthe piston by an amount ∆P, by placing an additional weight onthe piston. We note that the piston does not move inside becausethe liquid is incompressible. But the pressure underneath thepiston must increase in turn by ∆P. This raises the pressure atpoint A by ∆P. This make the pressure P =P1 + ρgh + ∆ P .

Pascal formulated this result as follows :When pressure is applied on a liquid enclosed in a container, the pressure is

transmitted in full to all parts of the liquid as well as to the walls of the container. This isknown as Pascal’s principle or Pascal’s rule.

Application to Pascal’s rule : hydraulic Press

The hydraulic press (Fig 4 – 14) consists of a small piston whose cross sectional area is“a” and a large piston whose cross sectional area is “A”. The space between the twopistons is filled with an appropriate liquid.

a) force to the left is transmitted tothe right

cross sectional area A

cross sectional area a

Fig (4-13)Increase of weight on the

piston increases thepressure in the liquid

1kg100kg

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3) The caterpillar also uses Pascal’s rule (Fig 4 – 19).4) A diver wears a diving suit and a helmet to protect him

from pressures at large depths. At low (shallow)depths, the diver - without the helmet - blows air in hissinuses to balance the external pressure (Fig 4 – 20). Atlarge depths, the diving suit is appropriately inflatedwith air, and the helmet protects the diver’s head fromcrushing pressures (Fig 4 – 21).

ExamplesA hydraulic press has cross sectional area 10cm2 which is acted on by a force of 100N.

The large cross sectional area is 800 cm2. Taking g = 10m/s2 ,calculate :a) the largest mass that can be lifted by the press b) the mechanical advantage of the press c) the distance traveled by the small piston so that the large piston moves a distance of 1cm

SolutionThe force acting on the large piston :

Fig (4-19) A hydraulic caterpillar

Fig (4-21) Diving at large depths (500 m)

Fig (4-20)Diving at low depths

NF = 100 x 800 = 8 x 1010

3

Fa

FA=

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hydraulic liquid

Learn at Leisure

Applications to Pascal’s rule

1) The hydraulic brake in a car uses Pascal’s rule as the brakingsystem uses a brake fluid. Upon pushing on the brake pedal witha small force and a relativeley long stroke (distance), thepressure is transmitted in the master brake cylinder, hence, ontothe liquid and the whole hydraulic line, then to the piston of thewheel cylinder outwardly, and finally to the brake shoes and thebrake drum. A force of friction results, which eventually stopsthe car. This type of brakes is called drum brake (rear brake) (Fig4 – 16). In the case of the front (disk) brake (Fig 4 – 17), the forcesresulting from the braking action press on the brake pads whichproduce friction enough to stop the wheel. It should be noted thatthe distance traveled by the brake shoes in both cases is small becausethe force is large.

2) In another application to Pascal’s rule, a hydraulic lift uses a liquidto lift up cars in gas stations (Fig 4 – 18). Fig (4-17)

Front brakes

Fig (4-16)Rear brakes

Fig (4-18) A hydraulic lift

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1) Horizontal forces cancel each other out , because each two opposite forces are equal inmagnitude and opposite in direction.

2) As to forces in the vertical direction, we find that the weight of the liquid enclosed in volumeVol in which (Fg)

L = Vol

ρg acts downwards. Since this liquid is static, the liquid must exerton the enclosed liquid an equal force Fb upwards , which is equal to the weight of theenclosed liquid. This force results from the difference of the pressure on the upper and lowersurfaces of the parallepiped which is ∆P x A

Substituting, noting that Ah is the volume:

where (Fg)l is the weight of the displaced liquid.

We see that Fb is equal to the weight of the parallepiped of theenclosed liquid. Equilibrium requires that the force Fb worksupwards, and it is named buoyancy (buoyant force-upthrust).

The relation between the weight of a body in airand the weight when immersed in a liquid

If we substitute the virtual parallepiped by a solid parallepiped of thesame shape and volume and of density ρs (Fig 4 – 22 b), the buoyancy(upthrust or buoyant force) which the liquid exerts on the solidparallepiped remains the same Fb acting upwards. The liquid isdisplaced a distance ∆h. The weight of the parallepiped representingthe immersed body (Fg)s acts downwards. The resultant force on

Fb = Volρg = (Fg)l (4 - 12)

Fig (4-22b)Archimedes’ rule using a real parallepiped

instead of a virtual parallepiped

Fb = ∆P X A∆P = P1 - P2 = h1ρg - h2ρg = (h1 - h2) ρg∆P = hρgFb = Ahρg

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= 8000 x 1100

= 80 Cmy1 cm

a)To calculate the largest mass that can be lifted by the large piston,

b)To calculate the mechanical advantage,

c)To calculate the distance traveled by the small piston,

Buoyancy and Archimedes’ Principle We are familiar with the following observations:

1)An object can be easily lifted if immersed under water level, whereas it might be difficultto lift at in air.

2) A piece of foam floats when immersed in water. 3) An iron nail sinks in water while a large steel ship floats. 4) Balloons filled with helium rise up.

We can interpret the above observations as follows :When an object is immersed under the liquid surfacethen the object exerts a force on the liquid.Consequently, the fluid (liquid or gas) pushes backby an equal and opposite force (Newton’s third law). Thisforce is called buoyancy. It acts in all directions,but thenet effect is upwards. The buoyancy is given by the weightof the liquid displaced by the immersed body. To showthis, let us imagine the existence of a volume Vol of theliquid as a virtual parallepiped whose cross sectional area isA and height h.This parallepiped is acted upon by forces in alldirections (Fig 4 – 22 A). This part of the liquid (like any otherpart of stable liquid) does not move, so it is in equilibrium:

m = Fg

= 8 x 103

10 = 800 Kgkg

= Ff

= Aa

= 80010

= 80

Fig (4-22a)Archimedes’ rule considering

a virtual parallepiped

η

fy F y1 2=

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difference between the body’s weight in air and the buoyancy of the liquid (Fg)s = (Fg)s - Fbwhere (Fg)s is the weight of the body while totally immersed in the liquid, (Fg)s is its

weight in air and Fb is the buoyancy (Fig 4 – 24). Concluding from above, we may formulate Archimedes’ principle as follows: A body

partially or fully immersed in a fluid (liquid or gas) is pushed upwards by a forceequal to the weight of the volume of the fluid displaced partially or fully by the body.

Learn at Leisure

Archimedes’ rule and Newton’s law

The immersed body replaces an equal size of the liquid. Because liquids areincompressible, such a body displaces a volume of the liquid equal to the volume of theimmersed body (or part of it that is immersed). This displaced liquid acts as a mass placedon the surface of the liquid. Its weight presses on the surface of the liquid. Thus, thepressure on each point of the liquid increases by this amount. Because we calculate thebuoyancy on the body as the difference between two forces acting on the surface of theimmersed body, then this difference stays the same. Hence, buoyancy on the immersedbody is unchanged by the displacement. It is equal to the weight of the displaced liquid(Fig 4 – 12). We can understand what happens as that the weight of the immersed body actson the liquid as a whole, then the liquid acts back with buoyancy as a reaction equal inmagnitude and opposite in direction (Newton’s third law). In the case when the weightbalances out with buoyancy, we have equilibrium, and the body remains suspended in theliquid. If the weight of the body exceeds buoyancy, the body sinks to the bottom where itsettles there. If the weight of the body is less than buoyancy, the body floats on top of thesurface where it settles afloat, while the weight of the displaced liquid whose volume isequal to the volume of the immersed part of the body, which is then equal to the weight ofthe floating body.

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(displacement of the liquid). In the case of gases, there is buoyancy force as well, and it actsupwards. But it is not mandatory that the volume of the displaced gas is equal to the volumeof the immersed body, since gases are compressible. But buoyancy must be equal to theweight of the displaced gas. This is why balloons filled with helium rise up (Fig 4 – 27).

Learn at Leisure

The story of Archimedes and the crown Archimedes was one of the most celebrated scientists of Ancient Greece. There is an

interesting story of Archimedes’ discovery of his rule. When Heron-king of Syracuse (oneof ancient Greek cities)- doubted that his new crown might not have been made of puregold, he summoned Archimedes to seek his counsel as to whether or not the crown wasrigged, without destroying the crown of course. Archimedes was first at a loss. But one day,he was bathing in a tub. He noticed that as he dipped himself in the tub the water level rose.Archimedes brought the crown and submerged it in a water filled tub and measured thedisplaced (overflown) water. He then calculated the density of the material of the crown.He then repeated the experiment on a similar block of pure gold of the same mass, andmeasured the volume of the displaced water. He found that this volume was different. Heconcluded that the maker cheated and used less dense and hence cheaper materials. It isoften told that Archimedes was euphoric with joy as he got this idea. He came out from thetub, and ran out naked shouting: “Eureka Eureka (I found it – I found it)". This expressionhas been ever since coined as a mottofor scientific discovery. Question:was the displaced water for therigged crown more or less than thatfor equal mass of pure gold? (Fig4-28).

Fig (4-28)The crown’s story

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1) Hydrotherapy technique is prescribed to patientswho are unable to lift limbs because of disease orinjury in the associated muscles or joints. When abody is immersed in water it becomes, in effect,nearly weightless. As a result, the force requiredto move the limb is greatly reduced, and thetherapeutic exercise becomes possible.

2) Weightlessness experiments may involveimmersion in containers filled with a liquid whoseconcentration is adjusted so that buoyancy cancelsout the weight.

3) A submarine floats when its tanks are filled with air,and submerges when those tanks are filled with water.Fish and Wales also fill air sacs with air to enablethem to float, and empty them from air when they gounder.

4) A diver breathes air under compression when divingto shallow depths, to equate the pressure. At largerdepths, the diver adjusts the pressure in the divingsuit to control the buoyancy force (Fig 4 – 26).

Learn at Leisure

Is there buoyancy for gases ?In the case of liquids, the volume of the displaced

liquid equals the volume of the immersed body,because liquids are incompressible. Then, the forceacting on the body upwards is equal to the weight ofthe displaced liquid as a reaction to the immersion

Fig (4-25)A submarine floats and sinks by

emptying or filling water tanks

Fig (4-26)A diver floats or dives depending onthe varying density of the diving suit

Fig (4-27)A balloon filled with helium

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Why does a ship float while an iron nail sinks ?It is noted that a ship is of large mass but contains large voids and spaces, which cause it

to displace plenty of water, hence large buoyancy pushes the ship upwards. Part of the ship(hull) remains submerged in water for the ship to be afloat. This submerged part is whatcauses the displacement of water of an equal volume causing buoyancy to balance out withthe weight of the ship (4 – 29). As the cargo on the ship increases, the submerged partincreases to build up more buoyancy enough to keep the ship afloat (Fig 4 – 30a). The ironnail sinks because the buoyancy force on it is small due to its small volume (Fig 4 – 30 b).

Learn at Leisure

The Dead Sea Have you noticed the difference between swimming in the sea, the Nile, and swimming

pools? The Dead Sea in Jordan is enclosed. It is not connected to any sea or ocean. The saltconcentration is very high. No one drowns in the dead sea (why ?)

Fig (4-29)A ship floats despite its massive weight

Fig (4-30b)A ship floats despite its massive weight

while a nail sinks

Fig (4-30a)The part of the boat that is submerged

depends on the weight

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In a Nutshell

I.Definitions and Basic Concepts • The density (ρ) is the mass per unit volume (kg/m3)• The pressure P at a point is the normal force acting on a unit surface area (N/m2).• All points lying in the same plane have the same pressure. • The atmospheric pressure is equivalent to the pressure produced by the weight of a

mercury column of height about 0.76 m and base area 1m2 at 0°C• The units of atmospheric pressure are :

a) Pascal (1 N / m 2).b) Bar (10 5 N / m 2).c)cm Hg.d) Torr (mm. Hg).

• The manometer is an instrument for measuring the difference in the pressure of a gasinside a container and the outer atmospheric pressure. • Pascal’s principle : The pressure applied on an enclosed liquid is transmitted undiminished to every

portion of the liquid and to the walls of the container. • Archimedes’ principle :

A body immersed wholly or partially in a fluid experiences an upthrust force(buoyant force) in the vertical direction equal to the weight of the liquid displaced bythe body.• The weight of the volume displaced = volume of the immersed body x density of the

liquid x the acceleration due to gravity. • The immersed body in the liquid is acted upon by two forces, the upthrust force Fb and

the weight of the body (Fg)s.

If (Fg)s = Fb the body will be suspended in the liquid.

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5) If the ratio between large and small piston diameters is 9:2. The ratio between the twoforces on the two pistons are :a) 9:2 b) 2: 9 c) 4:18d) 81 : 4 e) 4:81

6) A body has mass 5 kg in air, its weight when immersed in liquid becomes 40 N. If theacceleration due to gravity is 10 m / s2, then the upthrust force on the body is : a) 10 kg b) 10 N c) 35 kgd) 35 N e) 90 N

7) A piece of wood floats on water such that 1/4 its volume appears over the water surface.If the water density is 1000 kg / m3 , the wood density is then : a) 1333 kg / m3 b) 250 kg / m3 c) 750 kg/m3

d) 1000 kg / m3 e) 500 kg / m3

8) The lead density is greater than the copper density, the copper density is greater than thatof aluminum. If we immerse a number of cubes with equal volumes of these metals inwater and weigh them then, compared to their weights in air: a) the decrease of weight of the lead cube is greater than the decrease of weight of the

copper cube. b) the decrease of weight of the aluminum cube is greater than the decrease of weight of

the copper cube. c) the decrease of weight of the aluminum cube is equal to the decrease of weight of the

lead cube. d) the decrease of weight of the aluminum cube is less than the decrease of weight of the

lead cube. e) the decrease of weight of the lead cube is less than the decrease of weight of the

copper cube.

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I) Put mark ( ) to the correct statement:1) The following factors affect the pressure at the bottom of a vessel except one, tick it:

a) the liquid depth in the vessel. b) the density of the liquid c) the acceleration due to gravity. d) the atmospheric pressure. e) the area of the vessel base.

2) Which of the following factors have no effect on the height of mercury column in abarometer?a) the density of mercury b) the cross sectional area of the tube. c) atmospheric pressure. d) the acceleration due to gravity. e) the temperature of mercury.

3) When a ship moves from river water to sea water,which of the following statements is right ? a) the water density increases and the ship sinks slightly. b) the water density increases and the ship floats upwards slightly c) the water density decreases and the ship sinks slightly.d) the water density decreases and the ship floats slightly. e) the water density does not change and nothing happens.

4) The water pressure at the bottom of the High Dam lake on the dam body depends on :a) the area of the water surface.b) the length of the dam. c) the depth of the water. d) the thickness of dam wall.e) the density of wall substance.

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5) A vessel on a table contains two liquids: oil and water. A wooden cube is placed on the

top surface of the upper liquid. Describe what happens to the two liquids, the wooden

cube, the bottom of the vessel and the table.

IV) Drills :

1) The pressure on the base of a cylinder containing oil with diameter 8 m is 1.5 x 103

N/m2. Find the total force on the base.

(7.54 x 104 N)

2) A difference in pressure of 3.039 x 105 N/m2 is recommended for air in a car tire. If the

atmospheric pressure is 1.013 x 105 N/m2 ,calculate the absolute pressure of air in the

tire in atmospheric units.

(4 Atm)

3) A fish tank of cross-sectional area 1000 cm2 contains water of weight 4000N. Find the

pressure on its base.

(0.4 x 104 N/m2)

4) The large and small piston diameters of a hydraulic press are 24cm and 2cm

respectively. Calculate the force that must be applied to the small piston to obtain a force

of 2000 N on the large piston. Then calculate the mechanical advantage.

(13.9 N, 144)

5) A piece of aluminum has a mass of 250 gram in air. When immersed in water it has an

an apparent mass of 160 gram and it has 180 gram in alcohol. Calculate the densities of

aluminum and alcohol if the density of water is 1000 kg /m3 and g = 9.8 m / s 2

(2777.8 kg / m3, 777.8 kg/m3)

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the floating part of an ice cube is :a) 90 % b) 10 % c) 100 %d) 80 % e) 20 %

10) A body is immersed wholly in a liquid. If the body density is greater than the liquiddensity,then the upthrust force exerted by the liquid on the body will be :a) equal to the mass of liquid displaced by the body. b) equal to the mass of the immersed body.c) equal to the volume of the liquid displaced by the body.d) equal to the weight of the liquid displaced by the body.e) greater than the body weight.

II) Define each of the following :1. Density 2. Pressure at a point3. Pascal’s principle 4. Archimedes’ principle

III) Essay questions :1) Prove that the pressure (P) at depth (h) in a liquid is determined from the relation.

P = Pa + ρgh

where Pa is the atmospheric pressure, ρ the liquid density and g is the acceleration due togravity.2) Describe the manometer and show how it can be used for measuring a gas pressure

inside a container. 3) What is meant by Pascal’s principle ? Describe one of its applications.4) Show that the resultant forces on an immersed body is given by :F = (ρl – ρs) g Vol ,

where ρl and ρs are the densities of the liquid and the body respectively,g is theacceleration due to gravity and Vol is the volume of the body. Explain the consequences ofthis relation.

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3 Atm. Calculate the depth of the lake (density of water 1000 kg/m3, 1 Atm =

1.013x105 N/m2, g = 9.8 m/s2 ).

(20.673 m)

7) A man carries a mercury barometer with readings 76 cm Hg and 74.15 cm Hg at the

lower and upper floors, respectively. Calculate the average density of air between the

two floors if mercury density is 13600 kg / m3, the building height is 200m and g =

9.8m/s2.

(1.258 kg/m3)

8) A manometer containing mercury is attached to gas enclosed in a container. If the

difference height in the manometer is 25 cm.

Calculate the pressure difference and the absolute pressure of the enclosed air in units of

N/m2 (1Atm = 1.013 x 105 N/m2, mercury density = 13600 kg/m3 and g=9.8 ms2)

(0.3332x105 N/m2, 1.3462x105 N/m2).

9) The volume of a huge balloon filled with hydrogen is 14x104m3. Find the maximum

lifting force acting on it, if the hydrogen density is 0.092 kg/m3, air density is1.29

kg/m3 and the mass of the balloon with its accessories is 8x104 kg. (g = 10m/s 2).

(87.72x104 N)

Unit 2 : F

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2) In steady flow, the velocity of the liquid at each point is independent of time.

3) The flow is irrotational, i.e., there is no vortex motion.4)If no forces of friction exist between the layers of the liquid the flow is nonviscous .If

there is friction it is viscous.

Turbulent flow

If the velocity of flow of a liquid exceeds a certain limit, steadyflow changes to turbulent flow, which is characterized by theexistence of vortices (Fig 5–2). The same thing happens to gasesas a result of diffusion from a small space to a large space or fromhigh pressure to low pressure (Fig 5 – 3).

Rate of flow and the continuity equation We shall focus on steady flow. Consider a flow tube such that:1) the liquid fills the tube completely.2) the quantity of the liquid entering the tube at one end equals

the quantity of the liquid emerging out from the other endwithin the same time.

3) the velocity of the liquid flow at any point in the tube doesnot change with time. There is a relation that ties the rate offlow of the liquid with its velocity and cross sectional area.This relation is called the continuity equation. Tounderstand what the continuity equation entails, we choose

two perpendicular planes normal to the streamlines at the twosections (Fig 5 - 4). The cross sectional area at the first plane isA1 and the cross sectional area at the second plane is A2. The volume rate of flow is thevolume of the liquid flowing through area A1 in unit time.We have Qv = A1v1, where v1 isthe velocity of the liquid at section A1. The mass of the liquid (of density ρ) flowing in unittime is called the mass rate of flow Qm ,which is given by:

Fig (5-3)Smoke changes from steady

to turbulent flow

Fig (5-2)Vortices due to turbulent

flow or a violent motion of abody through a liquid


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Fig (5-1)Streamlines

Overview

Hydrodynamics (Fluid dynamics) deals, with fluids in motion. We must distinguish

between two types of fluid motion, steady flow and turbulent flow.

Steady flowIf a liquid moves such that its adjacent layers slide with respect to each other smoothly,

we describe the motion as a laminar flow or a streamline (steady) flow. In this type offlow, particles of the liquid follow continuous paths called streamlines.Thus, we mayvisualize the liquid as if it is in a real or virtual tube containing a flux of streamlinesrepresenting the paths of the different particles of the liquid (Fig 5 – 1). These streamlinesdo not intersect, and the tangent at any point along the streamline determines the directionof the instantaneous velocity of each particle of the liquid at that point. The number ofstreamlines crossing perpendicularly a unit area at a point (density of streamlines)expresses the velocity of flow of the liquid at that point. Therefore, streamlines cram up atpoints of high velocity and keep apart at points of low velocity. Conditions of Steady Flow 1)The rate of flow of the liquid is constant along its path, since the liquid is incompressible

and the density of the liquid is independent of distance or time.


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Fig( 5-5)Basis for the continuity equation

(5-1)

V1

V2

= A2

A1

v1

v2 (5-2)

Qm=ρQv=ρ A1 v1

Similarly, the mass rate of flow through

area A2 is ρQv = ρA2v2. Since the mass rate

of flow is constant in steady flow

ρ A1 v1 = ρ A2 v2

A1 v1= A2 v2

This is the continuity equation leading to

From this relation, we see that the velocity of the liquid at any point in the tube isinversely proportional to the cross sectional area of the tube at that point. The liquid flowsslowly where the cross sectional area A1 is large and flows rapidly, when the cross sectionalarea A2 is small (Fig 5 – 5). To understand the continuity equation better, we consider a smallamount of liquid ∆m = ρ∆Vol, where ∆Vol = A1 ∆x1 ,where ∆x1 is the distance traveled by theliquid in time ∆t . Thus, ∆x1 = v1 ∆t. Then ∆Vol = A1v1 ∆t. This same value must emerge fromthe other side of the tube, since the liquid is incompressible ,i.e, ∆Vol = A2v2 ∆t . Thus, wemust emphasize that the rate of flow of the liquid is a volume rate Qv (m3/s), or a mass rate offlow (kg/s). Both of these rates are constant for any cross section. This is called theconservation of mass, which leads to the continuity equation.

Fig (5-4)Model for deducing the continuity equation

A1

A2


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Learn at Leisure

Hardening of the arteries The body controls the blood flow in the arteries by muscles surrounding these arteries.

When these arteries contract, the radius of the artery decreases. From the continuityequation (5 – 1), the blood velocity must hence increase. When they relax, the bloodvelocity decreases. With age, these muscles lose that elasticity, and this is called hardeningof the arteries, and hence these muscles lose the ability to control the blood flow. Ascholestrol(fats) precipitates on the inner walls of these blood vessels, the radius decreasesfurther which increases the possibility of coagulation (formation of a clot) which blocks theblood stream, leading to angina pectoris. The patient takes medication to ensure theliquidity of the blood to prevent the coagulation. However, if the dose is excessive, hemight end up with hemorrhage or (internal bleeding). It is known that one of theconstituents of blood is platelettes, which are responsible for normal coagulation to stopbleeding. Thus, viscosity of the blood and its composition play a vital role is man’s life.

Learn at Leisure

Measuring blood pressureMeasuring blood pressure is one of the ways to check on the performance of the heart.

The sphygmomanometer is a type of manometer (Fig 5 – 9). It consists of a cuff in the

form of an air bag wrapped around the patient’s arm. A hand pump is used to inflate thebag and a mercury manometer is used to measure the pressure in the bag. The pressure is

increased in the air bag, until the blood flow ceases momentarily in the brachial artery. A

stethoscope is used to indicate the soundness of the artery’s muscle in pushing the blood.


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Blood circulation in human bodyThe circulatory system consists of a huge network of blood vessels including arteries,

veins, down to capillaries (Fig 5– 8) .The heart pumps blood through this network at a rateof 5 liters per minute (or 8.33x10-5 m3/s) with a normal pulse rate of 70 pulse per minute.The pumping rate may reach 25 liters per minute or 180 pulse per minute with excessiveactivity .Calculating the velocity of flow in the aorta (2 cm diameter),we find that the bloodvelocity is 26.5 cm/s (check the calculation). If we add up all the capillaries, we find thatthe collective cross section is 0.25m2 (what is the velocity?).

brain

arms andshoulders

lungs

heart

trunkand

organs

legs

arteries

aortaartery

pulmonaryartery

veins

veins

veins

veins

Fig (8-5)A simplified diagram for blood circulation


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tics The pressure in the air bag is decreased gradually, until

the pressure exerted by the heart is sufficient to push

the blood through, and open up the brachial artery.

The sudden flow of the blood in the nearly closed

artery causes a turbulent flow which produces a hiss,

which the doctor can hear with the stethoscope, while

the doctor monitors the reading on the manometer in

mm Hg. This reading is the systolic pressure (normally

120 mm Hg). As the pressure in the air bag decreases,

the hiss remains audible in the stethoscope, until the

pressure in the air bag is equal to the lowest pressure

exerted by the heart when the brachial artery is fully

open (diastolic pressure). Then,blood flows steadily and

the hiss disappears. The reading on the manometer in this case (when the heart is in rest or

relaxation) is normally 80 mm Hg. If the systolic pressure exceeds 150 mm Hg, the patient

has hypertension which might cause brain hemorrhage, and hence stroke. If the diastolic

pressure exceeds 90 mm Hg, the heart-which is supposedly then at rest -has extra pressure,

causing fatigue and eventually fibrosis in the heart muscle, leading to heart failure or

cardiac arrest.

Fig (5 - 9)Sphygmomanometer


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Solution

The aorta cross section is given by

The collective cross section for 30 main arteries is given by

Thus, the velocity of the blood in the main arteries is 0.044 m/s. Consequently, the

blood velocity in capillaries is much smaller, which gives time for the tissues to exchange

oxygen and carbon dioxide as well as nutrients and excretion products. Divine wonder is

countless.

Viscosity

We observe viscosity as follows :

1) We hang two funnels each on a stand and put a beaker under each. We pour alcohol inone funnel and a similar volume of glycerine in the other, and observe the velocity offlow of each. We notice that the flow velocity of alcohol is higher than that of

glycerine.

2) Take two similar beakers, one containing a certain volume of water and the other anequal volume of honey .Stir the liquid in both beakers with a glass rod .Which of the two

liquids is easier to stir ? Then, we remove the rod .We notice that :

(0.007) 2

v 0.3330

0.44m/s2 =×

=4

(0.33) = (0.0035) 2 (30) v22

A1 = r 21 = (0.007) 2 m2

A2 = r 22 x 30

= (0.0035) 2 x 30 m22

A1 v1 = A2 v2

0.044 m/s


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1) A water pipe 2 cm diameter is at the entrance of an apartment building. The velocity ofthe water in it is 0.1m/s. Then, the pipe tapers to 1cm diameter. Calculate

a) the velocity of the water in the narrow pipe.

b) quantity of the water (volume and mass) flowing every minute across any section ofthe pipe (density of water = 1000 kg/m3) .

Solution

a) A1 v1= A2 v2

π (0.01m)2 (0.1 m/s) = π (0.005m)2 v2

b)The volume rate of flow (m3/s) is given by the relation

Thevolume rate of flow (m3/min) is given by

The mass flowing per minute

The mass rate of flow (kg/min) is given by

2) The average velocity of blood in aorta ( radius 0.7 am ) for an adult is 0.33 m/s From theaorta, blood is distributed to main arteries (each radius 0.35cm). If we have 30 main arteries,calculate the velocity of blood in each.

Q x 60 = 3.14 x 10-5 x 60 = 188.4 x 10-5 m3 /min

= 3.14 x 10-5 x 103 = 3.14 x 10-2

= 3.14 x 10-5 x 103 x 60 = 1.884 K

v 10 10

0.4m/s2

-4

-5= π × ×π × ×

=0 12 5

..

= x 10-4 x 0.1 x 2.5 x 10-5 x 0.4

= 3.14 10 m /s -5 3×

or

Qm

Qm


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a) Friction forces exist between the lower plate and the liquid layer in contact with it. Thisforce is due to the adhesive forces between the molecules of the solid surface and thecontacting liquid molecules. This leads to zero velocity of the layer in contact with thestationary plate. Similarly, the upper layer moves at the same velocity of the upper plate.

b) The existence of another friction (shear) force between each liquid layer and the adjacentone, which resists the sliding of the liquid layers with respect to each other. Thisproduces a relative change in velocity between any two adjacent layers. Thus, viscosityis the property responsible for resisting the relative motion of liquid layers .This type offlow is called nonturblent viscous laminar flow (or viscous steady flow), since no

vortices occur.

Coefficient of Viscosity

Referring to Fig (5 – 6), we find that for the moving plate to maintains its constant

velocity, a force F must exist. This force is directly proportional to both velocity and area

of the moving plate A, and inversely proportional to the distance between the plates d.

where (Eta) is a constant of proportionality called viscosity coefficient, given by

The coefficient of viscosity ( Ns/m2 or kg/m s ) may be defined as :

the tangential force acting on unit area, resulting in unit velocity difference between

two layers, separated by unit distance apart .

F AVsv

d

(5 - 3)

(5 - 4)

F Avdvs

=

vsFdAv

FAv/d

=

vs


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Force acting on the upper layer of a liquid

liquid

Layers of a liquid slide with respect to each other

Fig (6-5)Friction between layers of a liquid

a) Water is easier to stir, which means that water resistance to the glass rod is less thanthe resistance of honey.

b) The motion in honey stops almost immediately after we remove the rod, while itcontinues for a little while longer in water .

3) We take two long similar measuring cylinders and fill them to the end, one with water andthe other with glycerine. Then , take two similar steal balls and drop one in each liquid, andrecord the time each ball takes in each liquid to hit the bottom. We observe that the time inwater is less. Thus, the glycerine resistance to the ball motion is greater .

We, thus, conclude :-

1) Some liquids such as water and alcohol offer little resistance to the motion of a body inthem, and are easy to flow. We say they have low viscosity

2) Other liquids such as honey and glycerine are not as easy to move through ,i.e.,theyoffer high resistance to body motion, and are said to have high viscosity.To interpret viscosity, imagine layers of liquid trapped between two parallel plates, one

stationary and the other moving with velocity v (Fig 5 –6). The liquid layer next to thestationary plate is stationary, while the layer next to the moving plate is moving at v. The layersin between move at velocities varying from o to v. The reason for this is as follow :

d


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Syphon:can a liquid go up ?

Suction of air from one end of a hose while the other

end is submerged in a liquid causes the liquid to rise up

to a certain head (vertical distance), then to flow

downwards (Fig 5 – 13). People often use this technique

to draw gasoline from a car tank. This seems contrary to

gravity. This phenomenon is called syphon. It can be

explained as follows. The liquid molecules attract each

other as beads in a chain (Fig 5 –14). The molecules may

go up to a certain distance overcoming gravity, then

come back down and flow from the free end of the hose.

Liquids have another property, called surface tension,

when the molecules of the liquid at the surface attract

each other as a membrane. This is the same theory of the

formation of air bubbles, in which the internal pressure

balances out with the external pressure and the surface

tension, so they do not blow up, unless this balance is

disturbed. Another property is capillarity, where

molecules of the container pull the molecules of the liquid by forces of adhesion. The

surface of the liquid is curved due to the surface tension in the capillary. This property is

responsible for drawing water in the stem of plants through the capillaries, so that the plant

can obtain its water and nutrients from the soil and even out to the foliage.

Fig (5-13)Syphon

Fig (5-13)Beads of liquid pulling each other


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tics Applications of Viscosity

1-Lubrication :Metallic parts in machines have to be lubricated from time to time. This process leads to:

a) reduction of heat generated by friction. b) protecting machine parts from corrosion (wear).

Lubrication is carried out using highly viscous liquids. If we use water (low viscosity),it will soon seep away or sputter from the machine parts due its low adhesive forces.Therefore, we must use liquids with high adhesive (high viscosity), so they remain incontact with the moving machine parts.

2-Moving vehicles When a car attains its maximum speed, the total work done by the machine which is

supplied by the burnt fuel, acts most of the time against air resistance and the forces offriction between the tires and the road. At relatively low and medium velocities, airresistance to moving bodies resulting from air viscosity is directly proportional to thevelocity of the moving body. When the velocity exceeds a certain limit, then the airresistance is proportional to the square velocity rather than the velocity,leading to anoticeable increase in fuel consumption. Therefore, it is advisable not to exceed such alimit ( 80 – 90 km/h )

3-In medicine :Blood precipitation rate : when a ball undergoes a free fall in a liquid, it is under three

forces : its weight, buoyancy of the liquid and friction between the ball and the liquid due to

viscosity. It is found that such a ball attains a final velocity which increase with its radius. This is applied in medicine by taking a blood sample and measuring its precipitation rate. The

doctor may then decide if the size of red blood cells is normal or not. In the case of rheumaticfever and gout, red blood cells adhere together, and therefore, their volume and radius increaseand the sedimentation ( precipitation ) rate increases. In the case of anemia, the precipitation rateis below normal, since the red cells break up. Hence, their volume and radius decrease .


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I) Define

1) fluid 2) viscosity 3) coefficient of viscosity

II) Essay questions

1) Prove that the velocity of a liquid at any point in a tube is inversely proportional to thecross sectional area of the tube at that point.

2) Explain the property of viscosity.

3) Illustrate some applications of viscosity.

III) Drills

1- Water flows in a horizontal hose at a rate of 0.002 m3/s, calculate the velocity of the

water in a pipe of cross sectional area 1cm2 . (20 m/s)

2- Water flows in a rubber hose of diameter 1.2 cm with velocity 3 m/s. Calculate the

diameter of the hose if the velocity of the emerging water is 27 m/s . (0.4cm)

3- A main artery of radius 0.035 cm branches out to 80 capillaries of radius 0.1 mm. If the

velocity of blood through the artery is 0.044 m/s ,what is the velocity of blood in each

of the capillaries? (0.0067 m/s)

4- The cross sectional area of a tube at point A is 10 cm2 and at point B is 2cm2. If the

velocity of water at A is 12 m/s, what is the velocity at B ? (60 m/s)

5- The cross sectional area of a water pipe at the ground floor is 4x 10-4m2. The

velocity of the water is 2 m/s. When the pipe tapers to a cross sectional area of 2 x

10-4m2 at the end, calculate the velocity of the flow of water at the upper floor.

(4m/s)


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cyan magenta yellow black File: Ch 6 fl ˙ Æ˝ ” 135cyan magenta yellow black File: Ch 6 fl ˙ Æ˝ ” 134

cyan magenta yellow black File: Ch 6 fl ˙ Æ˝ ” 134

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It can be concluded that :- Gas molecules are in a state of continuous random motion.- In their motion, they collide with each other and collide with the walls of the container- The distance between the molecules is called intermolecular distance (more or less

constant for different gases at the same conditions).

The evidence of the existence of intermolecular distances can be shown as follows:

When a graduated cylinder filled with ammonia gas is placed upside down on another

cylinder filled with hydrogen chloride gas (Fig 6-2), a white cloud of ammonium chloride is

formed, then it grows and diffuses until it occupies all the space within the two cylinders.

This can be explained as follows. Hydrogen chloride gas molecules - in spite of their

higher density - diffuse upwards, through spaces separating ammonia gas molecules, where

they combine together forming ammonium chloride molecules, which diffuse to fill the

Fig (6 – 2)Presence of gas intermoleculor distances

diffusion of awhite cloud of

ammoniumchloride

remove thepaper

a b c

ammonia gas

paper

Hydrogenchloride gas

(NH3)

(HCl)

A cloud ofAmmonium

chloridediffuses to fill

the twocylinders(NH4Cl)


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Chapter (6) The Gas Laws

Overview It can be shown that gas molecules are in continuous random motion called Brownian

motion as follows:If we examine candle smoke through the microscope,we notice that the smoke

particles move randomly. The motion of the carbon particles is caIled Brownian motion,after Brown, an English botanist who discovered for the first time in 1827 that tiny pollengrains suspended in water moved randomly.

Interpretation of Brownian motionAir (gas) molecules move in a haphazard (random) motion in all directions with

different velocities. During their motion, they collide with each other and collide withsmoke particles. Due to the resultant force on a smoke particle, it will move in a certaindirection through a short distance and so on, always moving, colliding, and changingdirection. The reason for this is that the gas molecules are in a free motion (due to heat)and in constant collision, so they change their direction randomly (Fig 6-1).

Fig (6 – 1)Motion of molecules materials

c. solid molecules undergo avibrational motion

b. liquid molecules undergo atranslational and vibrational

motion

a. gas molecules undergo arandom translational motion


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Firstly: the relation between the volume and pressure of a gas atconstant temperature (Boyle’s law) :

To study the relation between the volume of a fixed mass of gas and its pressure at

constant temperature, the apparatus shown in Fig (6- 3) is used. It consists of a burette (A)

connected by a length of rubber tube to a glass reservoir (B) containing a suitable amount

of mercury. (A) and (B) are mounted side by side onto a vertical stand attached to a base

provided by three screws with which the stand is adjusted vertically. The reservoir (B) is

movable along the stand either upwards or downwards and can be fixed at any desired

position.Procedure:1- The tap (A) is opened and the reservoir (B) is

raised until the mercury level in burette A is

about half full, taking into account that the

mercury levels are the same in both sides.

(Fig 6-3a) .

2- The tap (A) is then closed. The volume of the

enclosed air is measured, let it be (Vol)1. Its

pressure is also measured, let it be P1, which

equals the atmospheric pressure Pa (cmHg)

which may be determined using a

barometer.

3- The reservoir (B) is then raised a few

centimetres and the volume of the enclosed

air is measured (Vol)2. The difference

Fig (6 – 3)Boyle’s apparatus

(a)

(b)

(c)


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upper cylinder. Also, ammonia gas molecules - in spite of their lower density - diffuse

downwards through spaces separating hydrogen chloride gas molecules, where they

combine forming ammonium chloride molecules, which diffuse to fill the lower cylinder.

Accordingly, we can conclude that there are large spacings separating the gas molecules,

known as intermolecular spacings. This is to be tied to the compressibility of gases. These

large intermolecular spacings allow gas molecules to get packed together when pressed.

Thus, a volume occupied by a gas decreases with increased pressure.

Gas Laws

Experiments performed to evaluate the thermal expansion of a gas are complicated. The

volume of a gas is affected by changes in pressure as well as by temperature. This

difficulty does not arise in the case of solids or liquids, as these are very much less

compressible.

In order to make a full study of the behavior of a gas, as regards volume, temperature and

pressure, three separate experiments have to be carried out to investigate the effect of each

pair, respectively, i.e., we study the relation between two variables only, keeping the third

constant.These experiments are

1- The relation between the volume and pressure at constant temperature (Boyle’s law).

2- The relation between the volume and temperature at constant pressure (Charle’s law).

3- The relation between the pressure and temperature at constant volume (Pessure law or

Jolly’s law).

We are going to study each of these three relations.


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The effect of temperature on the volume of a gas at constant pressure:

We have already known that gases contract by cooling and expand by heating. But, doesthe same volume of different gases at constant pressure expand by the same amount?

To show this, let us do the following experiment:1- Take two flasks of exactly equal volume, each fitted with a cork through which a tube

bent 90˚ is inserted. In each tube, there is athread of mercury of length 2 or 3 cm. Fill one ofthe flasks with oxygen and the other with carbondioxide or air. Submerge the two flasks in avessel filled with water as shown in Fig (6 - 5).

2- Pour hot water into the vessel and notice thedistance moved by the mercury thread in bothtubes. You will find that these distances areequal. This indicates that equal volumes ofdifferent gases expand equally when heated through the same temperature rise . Inother words, they have the same volume expansion coefficient.

Volume expansion coefficient of a gas at constant pressure αv is defined as :"It is the increase in volume at constant pressure per unit volume at 0˚C for 1˚Crise in temperature ".

O2CO2

Fig (6 – 5)Effect of temperature on the volume

of a gas at constant pressure


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between the two levels of mercury in both sides (h) is determined . In this case, thepressure of the enclosed air (cmHg) is P2 = Pa + h (Fig 6 - 3 b).

4- Repeat the previous step by raising the reservoir (B) another suitable distance andmeasure (Vol)3 and P

3 in the same manner.

5- The reservoir (B) is then lowered until the mercury level in (B) becomes lower than itslevel in (A) by a few centimeters. Then, the volume of the enclosed air is measured(Vol)4 and its pressure (P4) is determined P

4 = Pa - h, where h is the difference between

the two levels of mercury in both sides (Fig 6-3c).6- The previous step is repeated once more by lowering (B) another suitable distance. Then

(Vol)5 and P5 are measured in the same manner.

7- Plot the volume of the enclosed air (Vol) and the reciprocal pressure ( ).We obtaina straight line (Fig 6 - 4) Thus, we can conclude that:

,i.e.,the volume of a fixed mass of gas is inverselyproportional to the pressure, provided that thetemperature remains constant. This is "Boyle’s law". Boyle’s law can be written in another form, as:

PVol = Const. i.e., is : at a constant temperature, the productPVol of any given mass of a gas is constant.

1P

Fig (6 – 4)Relation between volume and

reciprocal pressure of gas

Vol1P

V = constP

constVol

(6 - 1)


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Secondly: the relation between the gas volume and its temperature atconstant pressure (Charle’s law) :

To investigate the relation between the gas

volume and its temperature at constant pressure,

the apparatus shown in Fig(6 - 6a) is used. It

consists of a capillary glass tube 30 cm long and

about 1 mm diameter with one end closed. The

tube contains a short pellet of mercury enclosing

an amount of air inside it whose length is

measured by a ruler stand. The apparatus is

equipped with a thermometer inside a glass

envelope. We follow the folowing procedure:

1- The glass envelope is packed with crushed ice

and water. It is then left until the air inside the

glass tube has fully acquired the temperature of melting ice(0˚C).

2- The length of the enclosed air is then measured, and since the tube has a uniform

cross-section, the length of the encloscd air is taken as being proportional to its volume

(Vol )o˚c3- The ice and water are removed from the envelope and steam is passed through the top

and out at the bottom for several minutes to be sure that the temperature of air becomes

100˚C . Then, the length of the enclosed air is measured. It is taken as a measure of its

volume (Vol )100˚C.

4- A relation between Vol and t˚C is plotted (Fig 6-6b). We see that such a relation is astraight line,which if extended will intersect the abscissa at -273˚C .

Charle’s apparatus Fig (6 – 6a)

Corksteam outlet

pellet ofmercury

steam inlet

glassenvelope

capillarytube


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5- Repeating this experiment several times for different gases and measuring the amount ofincrease of gas pressure at constant volume for the same rise in temperature, we find:

a- At constant volume, the pressure of a given mass of gas increases by increasingtemperature.

b- At constant volume, equal pressures of gases increase equally, when heated throughthe same range of temperatures.We define the pressure expansion coefficient of a gasat constant volume (βp) as :

“lt is the increase in gas pressure at constant volume per unit pressure at 0˚C forcm degree rise in temperature”. It is found to be the same for all gases.

Thirdly: the relation between the pressure and temperature of a gas atconstant volume (pressure law or Jolly’s law):

It was found experimentally that the increase

in gas pressure is directly proportional to the

initial pressure at 0˚C (P0˚C) as well as to the

rise in its temperature, (∆t˚C). This is expressed

as follows:

∆P P0˚C ∆ (t˚C)

∆P = βP P0˚C ∆ (t˚C)

where βp is a constant value. It is the pressure Fig (6 – 8)

thermometer

mercury

Jolly’s apparatus

∝

(6-3)β = ∆∆P

P tO

βP (t˚C)∆P

0˚C∆O


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The effect of temperature on the pressure of a gas at constant volume:1- To investigate how the pressure of a gas depends on temperature, the apparatus shown

(Fig 6-7a) may be used. The gas under test is confined in a flask by mercury in a Utube. The flask is fitted with a cork. The surfaces of mercury in the two branches (A)and (B) have the same level at x,y. Thus, the pressure of the enclosed air isatmospheric. We then determine the temperature of air. Let it be t1˚C.

2- Submerge the flask in a vessel containing lukewarm water at t2˚C. You will notice thatthe level of mercury decreases in branch A, while it rises in branch B (Fig 6-7b).

3- We pour mercury in the funnel C, until the level of mercury in branch A returns to themark x then the volume of the enclosed air in the flask at t2˚C is equal to the volumeat t1˚C (Fig 6-7c).

4- We notice that the surface of mercury in branch B exceeds that in branch A by anamount” h” (cm). This means that the pressure of the enclosed air has increased as a resultof the temperature rise from t1˚C to t2˚C by an amount equal h (cmHg)( Fig 6-7c).

Fig (6 – 7)Effect of the temperature on the

pressure of a gas at constant volume

C

(c)(b)(a)


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expansion cofficient of a gas with temperature, at constant volume.It is the same for all

gases.

To measure βp of a gas at constant volume, Jolly’s apparatus shown in Fig (6-8) is used.

It consists of a glass bulb (A). The bulb is joined to a capillary tube (B) bent in the form of

two right angles. The bulb and the tube are mounted on a vertical ruler attached to a board

which is fixed on a horizontal base provided with 3 leveling screws.

The capillary tube (B) is connected to a mercury reservoir (C) by means of a rubber

tube.

We follow the following procedures:

1- Determine the atmospheric pressure (Pa) using a barometer.

2- Pour mercury in (A) to 1/7 of its volume to compensate for the increase in its volume

when heated, so that the volume of the remaining part is still constant, (the volume

expansion coefficient of mercury is seven times the volume expansion coefficient of

glass).

3- Submerge reservoir (A) in a beaker filled with water and pour mercury in the free end

(C), until it rises in the other branch to mark (X).

4- Heat water in the vessel to the boiling point and wait until the temperature settles, and

the mercury level in the branch connected to the reservoir stops decreasing.

5- Move the free end (C) upwards until the the mercury level in the other branch rises to

the same mark X. Then, measure the difference in height between the mercury levels in

the two branches (h). From this, determine the pressure of the enclosed air P, which is

equal to the atmospheric pressure (cm Hg) plus h, i.e., P=Pa+h6- Move the branch (C) downwards and stop heating. Then let the reservoir cool down to

nearly 90˚C. Then move the branch (C) upwards until the mercury level in the branchconnected to the reservoir rises to mark X.


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Other Forms of Charle’s and Jolly’s (pressure) laws :1- Refering to (Fig 6-9),

we note that the triangles ABC and ADE are similar. Therefore: BC = (Vol)1DE = (Vol)2AC = T1AE = T2Vol ∝ T

= const.

Thus, at constant pressure, the volume of a fixed mass of gas is directly proportional to

its temperature on the Kelvin scale. This is another formulation of Charle’s law.

2- Using Fig.(6-10), the following relation can be obtained in a similar way:

That is

or P ∝ TThus, at constant volume, the pressure of a fixed mass of gas is directly proportional to

its temperature on the Kelvin scale. This is another form of pressure (Jolly’s) Iaw.

VolT

(6 - 6)

P1

1

= P2

2

P = const

(6 - 7)

(Vol)1T1

(Vol)2T2

=∴


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2- The temperature of a normal human body on the Kelvin sca1e is about:a) 0˚K b) 37˚K c) 100˚K d) 373˚K e) 310˚K

3- The volume of a given mass of a gas is :a) inversely proportional to its temperature at constant pressure.b) inversely proportional to its pressure at constant temperature.c) directly proportional to its pressure at constant temperature.d) directly proportional to its temperature at variable pressure.e) inversely proportional to its pressure at variable temperature.

4- The pressure of a gas at 10˚C is doubled if it is heated at constant volume to :a) 20˚C b) 80˚C c) 160˚Cd) 293˚C e) 410˚C.

5- If we press a gas slowly to half of its original volume: a) its temperature is doubled.b) its temperature is decreased to half its value.c) its pressure will be half of its original value.d) the velocity of its molecules is doubled.e) the pressure of the gas is doubled.

III) Eassy questions1- How can you show experimentally that the volume coefficient of expansion at

constant pressure is the same for all gases?2- Describe an experiment to find the pressure coefficient of a gas at constant volume

and that it is the same for all gases.3- How can you verify Boyle’s law experimentally?4- How can you show that pressure of a gas increases by raising temperature at constant

volume?


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I) Complete (Fill in the spaces) :Which phrase (a-e) completes each of the next following statements (1-3)?

a) increases by a small value.b) decreases by a small value.c) remains constant. d) doubles.e) dereases to its half value.

1- If the pressure of a gas is doubled at constant temperature. So its volume...............2- If a barometer is transferred to the top of a mountain above the sea level, the length

of mercury in the barometer .............3- If the absolute temperature of a gas is decreased to be half its original value at

constant pressure, so its volume ...............

II) Choose the correct answer:1- The increase of the temperature of a car’s tire during motion leads to :

1) an increase in air pressure inside the tire. 2) an increase of air volume inside the tire.3) a decrease of the contact area of the tire with the road.

Choose the correct letter (a-e) a) (1, 2, 3) are correct. b) (1, 2) only are correct.c) (1, 3) only are correct. d) 3 only is correct. e) 1 only is correct


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5- How can you determine experimentally the absolute zero?6- Explain the meaning of zero Kelvin and the absolute temperature scale. 7- Deduce the general gas law.

IV) Drills:1- The temperature of one liter of gas is raised from 10˚C to 293˚C at constant pressure,

find its volume. (2 liters)

2- A container containing air at 0˚C is cooled to (-91˚C). Its pressure becomes 40 cmHg. Find the pressure of the gas at 0˚C. (60 cm

Hg.)

3- The volume of a quantity of oxygen at 91˚C under 84 cm Hg is 760 cm3 (S.T.P). Findits volume at 0˚C under a pressure of 76 cm.Hg. (630 cm3)

4- A flask containing air is heated from 15˚C to 87˚C. Find the ratio between the volumeof air that goes out from it to its original volume. (25%)

5- A tire contains air under pressure 1.5 Atm at temperature (-3˚C). Find the pressure ofair inside the tire if the temperature is raised to 51˚C, assuming that the volume isconstant. (1.8 Atm)

6- An air bubble has a volume of 28cm3 at a depth of 10.13 m beneath the water surface.Find its volume before reaching the surface of the water, assuming that thetemperature at a depth of 10.13 m, is 7˚C and that at the surface is 27˚C.

(Let g = 10ms-2 , Pa = 1.013 × 105 N/m2, ρ = 1000 kg/m3) (60 cm3)


cyan magenta yellow black File: ch7 fl ˙ Æ˝ ” 159

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Avogadro’s number

Different quantities of substances - even as small as 1cm3 - contain a huge number of

atoms or molecules. It is convenient to express such numbers in terms of a unit called

mole or gram mole. It is agreed upon that a mole (or gram mole) of any substance

contains the number of atoms or molecules equal to the number of atoms in 12 gram of

carbon .It is found experimentally that 12 gram of carbon contains 6.023x1023 carbon

atoms. This is known as Avogadro’s number. NA The mole is, thus, introduced as a

measuring unit of a quantity of matter in the international system of units. Although the

original definition of mole was associated with carbon, yet the concept of the mole is

generalized to any ensemble of particles, such that one mole contains Avogadro’s number

of these particles. Thus, a mole of iron contains 6.023 x 1023 iron atom, and one mole of

water contains 6.023 x 1023 water molecules. In general, the mass of one mole of any

substance equals numerically the atomic or molecular mass (in grams) of this substance,

i.e., the mass of one mole of carbon is 12 gram, one mole of oxygen is 32 gram and one

mole of water is 18 gram. Each of these quantities contains the same number of atoms or

molecules, which is Avogadro’s number.

Thus, the mole of any substance is defined as the quantity of this substance in grams,

which equals the atomic or molecular mass of the substance. Oxygen gas has atomic mass

16, i.e the molecular mass of a mole of Oxygen is 32.

Avogadro’s law

Avogadro’s law states that:

Equal volumes of different gases contain equal number of molecules under the

same conditions of temperature and pressure. Alternatirely, Each mole of any gas at


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The KineticTheory of Gases

Overview

To study the behavior of gases and explain their different laws, one can make use of the

kinetic theory of gases. This theory is based on postulates given below:

1) A gas is composed of molecules which we shall regard as very minute perfectly elastic

spheres obeying Newton’s law of motion.

2) The intermolecular distances are relatively large, hence, the volume of the gas

molecules is negligible compared to the volume occupied by the gas itself(the volume

of the container).

3) The forces of intermolecular attraction between the gas molecules are very weak due to

the large intermolecular distances, so they are negligible. Therefore, the potential energy

of the molecules is zero. This means that the gas molecules do not interact with each

other. Thus, the mean distances which a molecule moves before colliding with another

(called mean free path) does not depend on the mass or type of molecule, and is

statistically the same for all gases under the same conditions. Therefore, a certain volume

of any gas at S.T.P. contains the same number of molecules regardless of the gas type.

4) Gas molecules are in continuous random motion due to the collisions between each

other and due to their collisions with the walls of the container. The molecules move

between any two successive collisions in straight lines.

5) The collisions between the gas molecules are perfectly elastic, i.e., the total kinetic

energy of the gas molecules remains constant before and after the collisions.

6) The gas is in thermal equilibrium state with the walls of its container.

Chapter 7


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In reality, a gas contains a huge number of molecules moving randomly. Studying the gas

on the level of the molecules is called the microscopic point of view. This has led to the

kinetic theory of gases. We start by the following postulates:

1) A gas contains a huge number of molecules in random motion.

2) The size of the molecule is much smaller than the total volume of the gas.

3) Collisions among the molecules and with the walls are elastic, and hence no energy is

lost.

4) Interactive forces among the molecules are negligible, except at collision. Hence, there

is no potential energy involved.

5) Molecules obey Newton’s laws. Consider one of the gas molecules in a box in the form

of a cube whose side is l (Fig 7-1). The mass of the molecule is m, its average velocity

is v and the x component of velocity is vx. The pressure exerted by the gas on the walls

of the box originates from the collision of the gas molecules with the walls. The

pressure P is the force per unit area P = F/A, where A= l2, and F is the force which the

molecule applies to the wall. The linear momentum is PL .The change in the linear

momentum for a molecule PL is the difference between the linear momentum before and

after collision with the wall:

Because the collision is elastic, the velocity after collision in the x direction is -vx . The changein linear momentum transmitted to the wall PL is opposite to the change in the linear

F = PL

t


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ases 0˚C and 1 Atm (S.T.P) occupies a volume of 22.4 liters. Therefore, each mole of any

gas contains the same number of molecules at S.T.P. This number is given by NA =

6.023 x 1023 molecules/Mole.

To understand this, let us say we have NA molecules of oxygen (molecular mass is 32 x

mH where mH is the mass of the hydrogen atom). The Mass of one mole of oxygen is mH

x 32 x NA. Thus, the mass is a constant (NAmH) times 32. If we have NA hydrogen

molecules, then their mass is 2 x (NAmH). In other words, 32 gram oxygen (one mole

oxygen) and 2 gram hydrogen (one mole hydrogen) have the same number of molecules

(NA). Also, at the same temperature and pressure, the interatomic or intermolecular

distances are the same on average, due to the random motion of gas molecules and non

existence of attractive forces or potential energy between them, which are the postulates of

the perfect gas. Consequently, any mole of any gas at S.T.P. occupies the same volume,

which is found experimentally to be 22.4 liters.

Gas density:

Knowing the number of molecules (N) in a given volume of gas Vol and the mass of one

molecule(m), we can calculate the density of the gas (ρ) from the relation:

Gas pressure

Our study of the properties of gases in terms of pressure, volume and temperature have

led to the deduction of the gas laws. Such a study is called the macroscopic point of view.

(7 - 1)ρ = NmV

kg/mol

3


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PL = -mvx - (mvx) = - 2mvx

The change in the linear momentum delivered to

the wall PL is opposite to the change in the linear

momentum of the molecule.

PL = 2mvx

The force with which the molecule acts on the

wall is given by :

where t , is the time of contact between the molecule and the wall upon impact. The

impulse Iimp delivered by the molecule to the wall is given by:

Iimp = F t

= PL

= 2mvx

Because the time interval t is very small and indeterminate, we can take the time

between collisions tav as a substitute measure. In this case, the force is the average force

acting all the time such that:

Fav tav = F t

where tav is the average time between for collisions of a molecule with the walls:

Number of gas molecules in cube Fig (7 – 1 )

F = PL

t=

2mvX

t

t 2

vavx

=l

l

ll

Z

Y


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23

uT = 12

mvav2

nRT = 23

nNAmvav

2

2

23

RNA

T = mvav2

232

mv2

mv2

.

where is constant for every molecule and is called Boltzmann constant(k) :

From equations (7-7) and (7-8) ,

This relation ties the macroscopic theory of a gas to the microscopic model .It is to be

noted that temperature T (a macroscopic quantity) measures the average kinetic energy of a

molecule (a microscopic quantity). As the temperature increases, the kinetic energy

increases.

It is to be noted from equation (7-9) that each direction of motion (dimension or degree

of freedom) has associated with kinetic energy kT. In fact this relation does not apply

solely to gas molecules but also to electrons in a metal , and even to any ensemble of

particles in random motion.

We might be tempted to believe that at T = 0˚K, the kinetic energy, and hence the

velocity is zero, i.e., everything stops at absolute zero. In reality, we cannot claim so,

because at absolute zero the equations of the ideal gas are no longer valid. It is known that

gases are transformed in turn to liquids at low temperatures (chapter 8). Einstein showed

that even at absolute zero, there is still energy called rest energy. In such a case, the above

equations become inapplicable.

u = RNA

= 1.3γ 10−23 J / k˚k 38× (7 - 8)J/˚K

kT (7 - 9)32 mv2

RNA

12

(7 - 7)


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(7 - 3)∴ p = 13

2 vavρP

p = 13

2Nmv

vavP Vol

(7 - 2)

Referring to equation (7-1),

where ρ is the gas density and v2 is the mean square velocity of the gas molecules.

The scientific concept of temperature :

From equation (7-2), multiplying the numerator and

denominator by 2 :

We note that the number of gas molecules N is the number

of moles times Avogadro’s number NA :

From the laws of the ideal gas, the macroscopic relation is given by :

where R is the universal gas constant = 8.314 J/mole˚K, n is the number of moles in the

substance. This relation is based on experimental observations, while the microscopic

relation is based on theoretical deduction. We must equate the right hand side of both

equations (7-4) and (7-6).

Boltzman

23

N mvav2

2PVol =

(7 - 5)

(7 - 6)

N = nNA

Pv = 23

nNAmvav

2

2

PVolmv2

(7 - 4)

Pv = nRTPVol

=

= nRPV

olT

= nRT


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and occupies 22.4 liters at S.T.P., and that Avogadro’s number equals 6.02 x 1023, Boltzmann’sconstant equals 1.38 x 10-23 J/˚K, and the atmospheric pressure is 1.013 x 105 N/m2

Solution

There are two methods to solve this problem. The first method:

=

where M is the mass of one mole of the gas and Vol (0˚C), Po(0˚C) and the values of the

volume and pressure are those at S.T.P. and ρo is the density of the gas and vo is average

velocity at S.T.P.

The second method:

P = 13

v2= 1

3MV

v2Po(0˚C)o o olρo

M V12

V = 3 x 0.76 x 13600 x 9.8 x 22.0.028

3 x 1.013 x 105 x 22.4 x 10-3

0.028= 493 m/svVo

v = 3KTN A

M = 3 x 1.38 x 10 -23 x 273 x 6.02 x 10 23

0.028

12

MN A

v 2 = 32

KT

12

m v 2 = 32

KT

NA

NA

k

kT

Vo

o

k

2

o2

= 493 m/s

3Po(0oC) (Vol)0oC

M

3Po(0oC)

ρο


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I) Essay questions :

1. State the main postulates of the kinetic theory of gases.

2. On the basis of the postulates of the kinetic theory of gases, show how to prove that the

gas pressure P is given by the relation:

where ρ is the gas density and v2 is the mean - square speed of its molecules.

3. Using the previous relation, show how to find expressions for each of the following:

a) the root - mean - square speed of the gas molecules.

b) the concept of the gas temperature.

c) the average kinetic energy of a free particle.

4. A uniform cubic vessel of side length l has gas whose molecule has mass m moving in

the x direction with velocity vx, and collides with the walls of the vessel in perfectly elastic

collisions.

a) What is the linear momentum of the molecule before collision?

b) What is the linear momentum of the molecule after collision?

c) What is the change in linear momentum of the molecule on collision?

d) What is the distance traveled by the molecule before the next collision with the walls

of the vessel?

e) What is the number of the collisions with the walls of the vessel per second made by

ρ v2 P= 13


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ases In a Nutshell

• The mole of any substance equals the molecular mass number in grams.

• Avagadro’s number is the number of molecules in one mole and equals 6.023 x 1023

• The density of a gas is given by :

where N is the number of gas molecules in a certain volume Vol and m is the mass of one

molecule.

• The pressure of a gas in a container is calculated from the relation:

where ρ is the density of the gas and v2 is the mean - square speed of the molecules.

• The average kinetic energy of one of the gas molecules is directly proportional to its

absolute temperature in ˚K and the relation between them is:

where k is Boltzmann’s constant = 1.38 x 10-23 J/˚K

ρ = NmV

kg/mol

3

vav2P= 1

3ρ

12

m v 2 = 32

KTk


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ases the molecule?

f) What is the total change in linear momentum of one molecule per second due to its

successive collisions with the walls of the vessel?

g) What does the above quantity represent?

h) If NA is the number of the gas molecules in the container, what will be the total force

acting on the internal surface of the vessel?

II) Drills:

1. Hydrogen gas in a vessel is at S.T.P. Calculate the root mean square speed of its

molecules, given that a hydrogen mole = 0.002 kg and Avogadro’s number = 6.02 x

1023, 1 Atm = 1.013 x 105N/m2 (1844 m/s)

2. What is the change in linear momentum of the hydrogen molecule in the above problem

on each impact perpendicular to the walls of the vessel? (1.224 x 10-23kg.ms-1)

3. Calculate the average kinetic energy of a free electron at 27˚C, given that Boltzmann’s

constant k = 1.38 x 10-23 J˚K-1. (6.21 x 10-21J).

4. Using the data given in the previous problem, find the root mean square speed of a free

electron if its mass is 9.1 x 10-23 kg. (1.168 x105m/s)

5. Find the ratio between the root mean square speed of the molecules of a certain gas at

temperature 6000˚K (Sun’s surface) and that at temperature 300˚ K (Earth’s surface).

(4.472)


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Mechanism of achieving low temperatures

Low temperatures may be achieved by drawing or removing energy out of the matter,This can be done in various ways. The simplest is to establish contact with anotherprecooled substance. Ice or dry ice ( solid CO2) or liquid air may be used. Temperatures of77°K ( liquid nitrogen temperature) have been widely used. Liquid helium temperature(4.2°K) has even been reached . From the concept of latent heat of vaporization, the liquidgas draws energy from the material to be cooled in order for the liquid gas to evaporate tobe gaseous again. This results in the cooling of the substancerequired.

Superfluidity

Some liquid gases have the property of superfluidity, i.e., theycan flow without resistance (or without friction) at temperaturesclose to obsolute zero. Helium liquid has this property. In otherwords, it loses viscosity completely at such low temperatures. It caneven flow upwards uninterruptedly against gravity or friction alongthe walls of its container (Fig 8–1). It also has very low specificheat and is one of the best thermal conductors.

Dewar’s Flask

It is a glass or metallic container evacuated to prevent heattransfer. It is used to store liquid gases, since it is designed toprevent heat losses by conduction, convection and radiation. Itconsists of a double walled pyrex container with silver plated wallsto minimize heat transfer by radiation. The spacing between thewalls is evacuated to prevent conduction and convection, e.g., as in

Fig (8-1)Superfluidity

Fig (8-2)Dewar’s flask

vacuum

reflectingsurfaces

hot or coldliquid

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Cryogenics (Low Temperature Physics)

Overview

Cryogenics (or low temperature physics) is a branch of physics dealing with the cases

when temperature approaches absolute zero (-237°C) or 0˚K . The temperature scale used

in low temperature physics is the Kelvin temperature scale (the absolute temperature scale)

which is based on the behavior of the ideal gas.

Van Der Waals’ Effect:

One of the postulates of the kinetic theory of gases uponwhich the ideal gas laws are based is neglecting the interactive(attractive) forces among the molecules of the gas, as well asneglecting the size or the volume of the gas molecule incomparison with the volume of the container. The properties ofa real gas differ from those of the ideal gas, as the gas densityincreases. Interaction among gas molecules can no longer beneglected. This interaction is called van der Waals’ effect . It isunlike chemical interaction between atoms leading to theformation of molecules. The attractive forces among the molecules become important asthey lead to the liquefaction of the gas under high pressure. Due to the high pressure, vander Waals’ interaction takes over, where two molecules approaching each other attracttogether, and eventually attract more molecules, until the gas switches to the condensedstate of matter (liquid or even solid).

This mechanism explains the liquefaction of gases, which has led to achieving very lowtemperatures approaching near absolute zero.

Van der Waals

Chapter 8

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s a thermos bottle (Fig 8–2). It is used to store liquid nitrogen (boiling point 77°K) and liquid

oxygen (boiling point 90°K). As to helium (boiling point 4.2° K and low specific heat), it is

stored in a double Dewar’s flask, one inside the other. The spacing between the two flasks is

filled with liquid nitrogen (due to the low specific heat and boiling point of helium).

How does a refrigerator work ?

From the law of conservation of energy, if a gas acquires thermal energy Qth it is used upin one of two ways:

1) an increase in internal energy U which is manifested by an increase in temperature.

2) work done by the gas molecules W. There are two types of heat transfer. One is at

constant temperature with the surroundings, i.e. , at constant internal energy ( U = 0).

In this case, the acquired energy is transformed in full into mechanical work done by

the gas. This is called an isothermal process. The second type is performed when the

gas is thermally isolated with its surroundings. So, it can neither acquire nor lose heat.

In this case, Qth = 0 The work done by the gas must be at the expense of its internal

energy. If W is positive, the gas does the work and the internal energy decreases ( U is

negative), i.e., the gas cools down. If work is done on the gas, then W is negative, so the

internal energy increases and its temperature rises. The process when Qth = 0 (W is

positive or negative) is called adiabatic process. A refrigerator is an application to both

isothermal and adiabatic processes , and the coolant (refrigerant) or the cryogenic liquid

used is freon (boiling point- 30°C) or its substitutes.

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sFig (8-5)Meissner's effect

Fig (8-6)Magnetically levitated train

metallic compounds) becomes very high, i.e., the electrical

resistance vanishes. This occurs at a critical (transitional)temperature (Fig 8–4). Materials having this property arecalled superconductors. If current happens to flow in asuperconductor, it continues to flow even if the voltage

difference is removed. It will continue to flow for years, as it

is met by nearly zero resistance.

Such a metal will not be heated by current flow. No

energy is consumed in compensating electrical energy

associated with an electric current, as in ordinary resistors.

Superconductors can be used to pick up weak wireless signals. Therefore, they are used

in the electric circuits of satellites. It is interesting to notice that if a permanent magnet is

placed over a disk of a superconducting material, then the current in the superconductor

generates a magnetic field, which is always repulsive with the external magnet, so the

permanent magnet remains hanging in the air. This is called Meissner effect (Fig 8 – 5).

Fig (8-4)Superconductivity

criticaltemperature

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s through a condenser (an apparatus outside the refrigerator). Heat exchange occurs in whichheat energy in the gas is radiated out to the surroundings being at a lower temperature. Thehigh pressured gas condenses and becomes a liquid at constant temperature (isothermalprocess). The liquid refrigerant is returned to the refrigerator once more. Before it entersinto the freezer compartment, the refrigerant is forced to expand in an adiabatic processthrough the expansion valve. In this case, the liquid molecules diffuse from a high pressureregion into a low pressure region. The refrigerant’s volume increases and does work indoing so against the spring in the valve. Thus, work is done at the expense of the internalenergy of the refrigerant. Since no external heat exchange is allowed (Qth= 0 or W ispositive so ∆U is negative). The internal energy of the liquid decreases so does itstemperature. Thus, the refrigerant is now back to be a liquid as it was when we started thecycle. The cycle repeats. The final result is the expulsion of thermal energy from the cabinto the condenser outside the refrigerator. Therefore, the refrigerator cools down. Of course,the refrigerator must be well insulated. It should be noted that the electric energy needed bythe refrigerator throughout the cycle is the energy consumed in operating the piston. Theinternal energy one throughout complete cycle must remain unchanged (∆Unet = 0). Thecompressor is, thus, a heat pump that transfers the heat from the refrigerator to the outsidethrough the work done by the compressor Wnet. Thus, the electric energy E required foroperation: E = Wnet = (Qth)

net

Superconductivity

In 1911, i.e., 3 years after the liquefaction of helium, Onnes and his

assistants discovered superconductivity. When the temperature

reaches a few degrees above absolute zero, the electrical conductivity

of some metals (platinum, aluminum, zinc, lead, mercury and some onnes

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Learn at Leisure

Magnetic resonance imaging ( MRI )One of the most popular and safest tools in medical diagnosis nowadays is magnetic

resonance imaging (MRI). In this method, a magnetic field affects the nuclei of hydrogen inthe body. Exciting these nuclei with an alternating magnetic field, waves are radiated fromthe excited hydrogen nuclei, which are indicative of water ( hydrogen ) localization(oedemas and tumors).An internal image of the body can be made (Fig 8–7), which helpsidentify such lumps.

Superconducting magnets are used to counteract the huge energy losses in normalmagnets, hence heating effects are reduced.

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s The reason for this is that superconductors belong to a class of materials called

diamagnetic materials in which the magnetic field inside the material is zero. Therefore,

an external magnet induces current in the superconductor which creates a magnetic field

inside the superconductor in an opposite direction, so that the net magnetic field inside

the superconductor is zero . This phenomenon has been put to use by designing a high

speed (magnetically levitated) train. The train carries coils of a superconducting material.

When the train moves, it induces current in fixed coils, which produces a magnetic field

repelling the inducing field. The train is raised above the rails for a few centimeters . This

levitation eliminates friction (Fig 8 – 6), hence increases the train velocity. The levitated

train may reach a velocity of 225 km/h . The discovery of room temperature

superconductive materials will lead to expansion in the applications of superconductivity,

since no cooling is then needed . Superconductors are also used in electric power plants

and in transmission lines, where voltage losses are eliminated due to the vanishing

resistance .

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Questions

1) Explain each of the following phenomena :

a) Van Der Waals’ effect .

b) low temperature phenomena .

c) superfluidity of some liquefied gases .

d) superconductivity .

2 ) Give reasons :

a)the use of two Dewar's flasks to store helium .

b) the spacing between the double walls in a Dewar's flask is evacuated .

c) helium can flow upwards along the walls of its container without stopping .

d) a levitated train has been designed with a very high speed (225 km/hr ) .

e) a magnet may remain hanging up above a superconductor regardless of the polarity .

3) State the most important applications for each of the following :

a) Dewar's flask .

b) superconductors .

4) Illustrate the difference between :

a)chemical reaction and Van Der Waals’ reaction .

b) the helium liquid and the nitrogen liquid .

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s In a Nutshell

• Low temperature physics deals with the study of materials at temperatures near absolute zero

• Van der Waals’ effect expresses the mutual interaction between molecules and is different

from chemical interaction, which leads to the formation of molecules.

• The mechanism for achieving very low temperatures depends on drawing energy from the

material. This may be done by putting the material to be cooled in contact with a cooler

material such as a liquefied gas.

• Superfluidity :

Some liquefied gases can flow without resistance or without friction at temperatures

close to absolute zero. Helium is a superfluid , i.e. its viscosity vanishes. It can also

flow up along the walls of the container against gravity and friction and has low

specific heat.

• Dewar's flask is a glass or metallic container evacuated to prevent heat transfer. It is used

to store liquefied gases such as nitrogen, oxygen and helium and so on.

• Superconductivity:

Some metals have excessive electrical conductivity (zero resistance) at very low

temperatures.

• Meissner effect :

If a permanent magnet is placed above a superconductor, the current induced in the

superconductor generates a magnetic field which repels the permanent magnet so the

permanent magent remains hanging in the air.

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sectional area (m2) and (ρe) is the resistivity (Ωm).The electrical conductivity of a certain

material σ (Ω-1m-1) is the reciprocal of the resistivity σ = ( ).

6) Ohm’s Law:

The current intensity in a conductor is directly proportional to the potential

difference across its terminals at a constant temperature : V = IR

7) as a convention, the direction of the electric current always goes from the positiveterminal to the negative terminal outside the source into a closed electric circuit. It isopposite to the direction of motion of electrons. It is called the conventional direction ofcurrent.

Connecting resistorsFirstly: series connection

Resistors are connected in series to obtain a higher resistance (Fig9–1). The equivalent

resistance of a group of resistors connected in series can be obtained in connecting these

resistors in an electric circuit comprising a battery,an ammeter,a rheostat (variable resistor)

and a switch (Fig 9-2). The circuit is closed and the rheostat is adjusted so that an

appropriate current I is passed. The voltage difference across each resistor is measured (V1

across R1, V2 across R2, V3 across R3) as well as the total voltage (V), which is equal to thesum of the voltage differences across the resistors in the series circuit and this is calledKirchhoff,s law

Fig (9 – 1)Connection in series

1ρe

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Secondly: Parallel connection

The purpose of connecting resistors in parallel is to obtain a small resistance out of abunch of large resistances (Fig 9 – 3). To obtain the equivalent resistance for a parallelconnection, the combination is included in an electric circuit comprising a battery, anammeter and a rheostat all connected as shown (Fig 9 – 4).

We close the circuit and adjust the rheostat to

obtain an appropriate current in the main circuit

of intensity I (A), which can be measured by the

ammeter. The total voltage difference can then

be measured across the terminals of the

resistances by a voltmeter (V). The current in

each branch is measured ( I1 in R1, I2 in R2, and

I3 in R3). In a parallel connection, the total

current is determined by the smallest resistance.

This case is similar to the flow of water in pipes.

Fig (9 – 3)Connection in parallel

Fig (9 - 4)Measuring the equivalent resistance

in a parallel connection

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V = V1 + V2 + V3

But ... V = IR

V1 = IR1

V2 = IR2

V3 = IR3

IR = IR1 + IR2 + IR3

R = R1 + R2 + R3 (9-1)

Thus, the equivalent resistance R of a group of resistors connected in series equals the sum of

these resistances. It is to be noted that the largest resistance in the combination determines the

total resistance in a series connection. If N resistances are connected in series each equal r then :

R = Nr

We conclude that if we want a large resistance out of a bunch of small resistances, wesimply connect them in series.

Fig (9 – 2)Measuring the equivalent resistance in a

series connection

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I = ER + r

VB

Ohm’s Law for a closed circuitWe know that the emf of an electric cell (battery - source) is the total work done inside

and outside the cell to transfer an electric charge of 1C in the electric circuit. If we denotethe emf of a battery by VB, the total current in the circuit by I, the external resistance by Rand the internal resistance of the cell by r, then

VB = IR + IrVB = I (R + r)

This is known as Ohm’s law for a closed circuit, from which we find that the currentintensity in a closed circuit is the emf of the total source divided by the total (external plusinternal) resistance of the circuit.Relation between emf and voltage across a source

From Fig (9 – 5), we find V = VB - Ir

From this relation, we see that as I is decreased gradually in the circuit shown (Fig 9– 5),-by decreasing the external resistance R- the voltage difference across the source increases.

When the current vanishes, the voltage difference across the source becomes equal to theemf of the source. Hence, we may define the emf of a source as the voltage differenceacross it when the current ceases to flow in the circuit.

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VR

= VR1

+ VR2

+ VR3

1R

= 1R1

+ 1R2

+ 1R3

The smallest pipe ( the highest resistance) determines the flow rate in a seriesconnection, while the widest pipe (the least resistance) determines the rate of flow in aparallel connection, since it draws most of the water current.

It is to be noted that :

where R is the equivalent resistance, and V is the voltage difference across resistorsconnected in parallel. The total current I is the sum of the branch currents. I1 + I2 + I3 .

Thus:

Hence, the reciprocal of the equivalent resistance R is the sum of the reciprocal ofresistances in the case of a parallel connection. In the case of two resistors in parallel, theequivalent resistance R is given by :

R = R1 R2R1 + R2

When N resistances are connected in parallel each equal to r,

Therefore, if we wish to obtain a small resistance out of a bunch of resistors, we simplyconnect them in parallel.

(9 - 4)

I = VR

, I 1 = VR1

, I 2 = VR2

, I 3 = VR3

1R

= Nr

(9 - 5)R = rN

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V2 = IR2 = 0.25 x 70 = 17.5V

V1 = IR1 = 0.25 x 25 = 6.25V

V3 = IR3 = 0.25 x 85 = 21.25V

2) If the resistors in the previous example are connected in parallel to the same battery,calculate:a) the current flowing in each resistor.b) the total resistance. c) the current through the circuit.

solution :a) the voltage difference across each resistor = 45V, since they are connected in parallel

and the battery is of negligible internal resistance. The current flowing through eachresistor is calculated separately as follows :

b)The total (equivalent or combined) resistance R is calculated as follows :

R = 15.14 Ωc) The current flowing through the circuit I is :

I = VR

= 4515.14

= 2.972 A

I2 = VR2

= 4570

= 0.643 A

I3 = VR3

= 4585

= 0.529 A

I1 = VR1

= 4525

= 1.8 A

1R

= 1R1

+ 1R2

+ 1R3

= 125

+ 170

+ 185

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It can be calculated also as the sum of the currents I1 , I2 , I3 flowing through allresistors:

I = 1.8 + 0.643 + 0.529 = 2.972 A

3) In the figure shown above two resistors A and B are connected in parallel. The combinationis connected in series with a resistor C and a 18 volt battery of negligble internal resistance.If the resistances of A,B and C are 3Ω,6Ω,7Ω, respectively, calculate:

a) the total resistance.

b) the current flowing through the circuit.

c) the current through each of A and B.Solution :

The equivalent resistance for the combination (A, B) is :

The equivalent resistance for the combination (A,B)and( C) is :

R = R´ + R3 = 2 + 7 = 9 Ω

The current I flowing through the circuit is :

R´=R1 R2

R1 + R2

= 3 x 63 + 6

= 2

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• In a parallel connection:

• For N equal resistances each r :

• Ohm’s law for a closed circuit:

where VB is the emf of the source, r is its internal resistance and R is the externalresistance.

R = rN

I = ER + r

VB

1R

= 1R1

+ 1R2

+ 1R3

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6) In the circuit shown :

a) the ammeter reading is .....................

b) the voltmeter reading is .....................

7) In the circuit shown

a) the ammeter reading A1 is .....................

b) the ammeter reading A2 is ......................

II) Choose the right answer:

Four lamps 6 each are connected in parallel. The combination is connected to a 12Vbattery with a negligible internal resistance:

1) The current in the battery equals..........

a) 8A b) 6A c) 4A d) 2A e) 72A

2) The total charge leaving the battery in 10s is...............

a) 80C b) 60C c) 40C d) 20C e)2C

3) The current in each lamp is .........

a) A b) 8A c) A d) 1A e) 2A

4) The voltage difference across each lamp is..........

a) 3V b) 12 V c) 6 V d) 2 V e) 4 V

5) The total resistance of the four equal lamps is...........

a) b) 24 c) d) 6 e) 12

6) If the 4 lamps are connected in series, the total resistance is.............

a) b) 24 c) d) 6 e) 12

32

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3) The circuit shown in Fig (9 – 5) consists of a 15 V battery, an external resistance 2.7and a switch. If the internal resistance of the battery is 0.3 , determine :

a) the reading of the voltmeter when the switch is open, assuming that the voltmeterresistance is infinite. (15 V)

b) the reading of the voltmeter when the switch is closed. (13.5)

4) A student wound a wire of a finite length as a resistor. Then, he made another of thesame material but half the diameter of the first wire and double the length. Find theratio of the two resistances.

5) A copper wire 30 m long and 2x10-6m2 cross sectional area has a voltage difference of3V across. Calculate the current if the copper resistivity is 1.79 x 10-8 .m

(11.17 A)

6) A 5.7 resistor is connected across the terminals of a battery of 12 emf and 0.3internal resistance. Calculate:

a) the current in the circuit . (2. A)

b) the voltage difference across the resistor. (11.4 V)

(1:8)

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Oersted

Overview

In 1819, Hans Christian Oersted- a Danish physicist-brought a compass near a wirecarrying an electric current. He noticed that the compass was deflected. When he turnedthe current off, the compass assumed its original position. The deflection of the compass-while current was flowing through the wire- indicated that it was being acted upon byan external magnetic field.This discovery started a chain of events that has helped shapeour industrial civilization.

In this unit we are going to study the magnetic field of current- carrying conductors inthe form of:

a) a straight wire. b) a circular loop. c) a solenoid.

Magnetic field due to current in a straight wire:

We can examine the pattern of the flux density surrounding a long straight wirecarrying a direct current using iron filings sprinkled on a paper surrounding the wire in avertical position.It will be noted that they become aligned in concentric circles aroundthe wire, as shown in Fig (10-1).

Fig (10 – 1)Pattern of iron filings

around a wire carryingcurrent

Magnetic Effects of Electric Current and Measuring InstrumentsChapter 10

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The figure shows that the circular magnetic flux lines are closer together near the wireand farther apart from each other as the distance from the wire increases.

As the electric current in the wire increases, the iron filings rearrange themselves aftergently tapping the board such that the concentric circles become more crowded.

This indicates that the magnetic field due to the electric current passing through astraight wire increases with increasing the current intensity and vice verse.

The magnetic flux density β measured in Weber/m2 or Tesla( where φm is themagnetic flux, A is the area) a point near a long straight wire carrying current I can bedetermined using the formula:

This relation is called Ampere's circuital law, where d is the normal distance between

the point and the wire, and µ is the magnetic permeability of the medium (in air it is 4π

x 10-7 Weber/Am). Thus, B is inversely proportional to d and directly proportional to I.

This is why it is advisable to live away from high voltage

towers.

Ampere's right hand rule:

To determine the direction of the magnetic field resulting

from an electric current in a wire, imagine that you grasp the

wire with your right hand such that the thumb points in the

direction of the current. The rest of the fingers around the wire

give the direction of the magnetic field due to the current

(Fig 10-2).

BAm= φ

B = µ I2 d

(10-1)

Fig (10 – 2)Right hand rule

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Thus circular loop carrying current may be considered as a bar magnet (Fig 10-3)

Examples:

Determine the magnetic flux density at the center of a circular loop of radius 11cmcarrying a current of 1.4 A. if the wire loop consists of 20 turns and µ

air = 4 π x 10-7

Weber/Am

solution:

= 4 x 22 x 10-7 x 20 x 1.47 x 2 x 0.11

= 16 x 10-5

B = µ NI2r

= 4 x 10-7 x 20 x 1.42 x 0.11

Fig (10 – 5)A circular loop carrying current in the direction

of screwing.

Fig (10 – 4)Right hand screw

direction of screwing.

Tesla

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To study the magnetic field due to a circular loop (or a coil),iron filings are sprinkledon the board as shown in Fig (3 -10). Tapping it gently, the filings arrange themselves asshown in figure, from which we can notice that:1. the flux lines near the center of the loop are no longer circular.2. the magentic flux density changes from point to point.3. the magnetic flux lines at the center of the loop are straight parallel lines

perpendicular to the plane of the coil. This means that the magnetic field in this regionis uniform.The flux density at the center of a circular loop of N turns and radius r carrying current

I is given by :

From this relation, the magnetic flux density at the center of a circular loop dependson three parameters:1. number of turns of the circular loop where B ∝ N.2. current intensity passing through the circular loop where B ∝ I.

3. radius of circular loop where B ∝ .

- Right-hand screw rule:To determine the direction of the magnetic field at the center of a circular loop or coil,

imagine a righthand screw being screwed to tie along the wire in the direction of the

current. The direction of fastening of the screw gives the direction of the magnetic flux at

the center of the loop (Figs.10 -4, 10 -5 )

Thus, a circular loop carrying current acts as a magnetic dipole or a bar magnet.

It is to be noted that no single poles exist in nature. They always exist in N - S pairs.

1r

B= µ N I2 r (10-2)

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Magnetic field due to current in a solenoid:

When an electric current is passed through a solenoid ( a long spiral or cylindrical coil) as

shown in Fig(10-6), the resultant magnetic flux is very similar to that as a bar magnet. As

shown in Fig(10-6A), the magnetic flux lines make a complete circuit inside and outside the

coil,i.e., each line is a closed path. The side at which the flux emerges is the north pole, the

other side where the magnetic flux reenters is the south pole. The magnetic flux density in the

interior of a solenoid carrying an electric current depends on :

1) the current intensity passing through the coil where B∝ I.

2) the number of turns per unit length where B ∝ n :

∴ B ∝ nI

B = µ nIwhere µ is the permeability of the core material. In this case, it is airThis relation may be rewritten as follow:

a) field pattern b) polarity of the field usingAmpere’s right hand rule.

Fig (10 – 6)Magnetic field due to a solenoid

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Force due to magnetic field acting on a straight wire carrying current.If we place a straight wire carrying current

between the poles of a magnet,a force resultswhich acts on the wire and is perpendicular toboth the wire and the field (Fig 10-7). Thedirection of the force is reversed if we reversethe current or the magnetic field. In all cases,the force is perpendicular to both electriccurrent and the magnetic field. In case thewire is allowed to move due to this generatedforce, the direction of motion is perpendicularto both the electric current and the magneticfield. The direction of the force with which amagnetic field acts on a current- carrying wireperpendicular to the field can be obtained byapplying Fleming’s left hand rule.

Fleming’s left hand rule

Form your left hand fingers as follows: the

pointer and thumb perpendicular to each other

and to the rest of the fingers. Make the pointer

point to the direction of the magnetic flux, and

the rest of the fingers- except the thumb- in the

direction of the current. Then, the thumb points

to the magnetic force or motion (Fig 10-8).

It is found that the force acting on a wire carrying current flowing perpendicularly to a

Fig (10 – 7)Force due to a magnetic field acting on a

straight wire carrying current, mark”x”denotes the direction into the paper.

Fig (10 – 8) Fleming's left hand rule.

the rest of the fingersare in the directionof the current.

the pointer isin the direction

of themagnetic flux

the thumbis in the

direction ofmotion or

force

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You can imagine what the direction of the force will be in different cases. Themark means out of the page, and the mark means into the page.

The force between two parallel wires each carrying current.When a current I1 passes in a wire and a current I2 passes in another parallel wire, a force results

between the two wires. This force is attractive if the two currents flow in the same direction. The forceis repulsive if the two currents flow opposite to each other. We can calculate this force as follows:

. x

Fig (10 – 10)Force between two parallel wires each carrying current

(b)

Fig (10 – 9) A wire carrying current in a direction inclinded by

an angle θ to the magnetic field.

a) the two currents are in the same direction. b) the two currents are in opposite directions.

a) the force vanishes when θ = 0(wire and magnetic field are parallel)

b) a force exists for θ other than zero

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c) top view (plan) of the rectanglewhen the magnetic dipole moment is

perpendicular to the field.

a) the coil is parallel to themagnetic field.

d) top view (plan) of the rectanglewhen the magnetic dipole moment

makes an angle θ with the field.

e) top view (plan) when the rectangleis perpendicular to the field or the

magnetic dipole moment is parallel

to the field and the couple is zero.

b) top view (plan)of the rectanglewhen the coil is parallel to the field.

Fig (10 – 11)A torque acting on a coil carrying a

current

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The essential parts of this device are shown in Fig(10-12). It consists of a rectangle ofa thin wire coil wrapped around a light aluminum frame mountend on a soft iron core.The frame is pivoted on agate bearings. The assembly rotates between the poles of a Ushaped (horse shoe) magnet. Its rotational motion is restrained by a pair of spiral controlsprings, which also serve as current leads to the coil. Depending upon the direction ofthe current being measured, the coil and pointer rotate either in clockwise orcounterclockwise direction. The permanent magnet's poles are curved so that themagnetic flux lines are radially directed. Thus, the magnetic flux density is constant andperpendicular to the side of the rectangle irrespective of the angle of the coil. thedeflection of the pointer is proportional to the current in the coil.

The current flows in the coil from the right side upwards, and emerges from the otherside. Then the magnetic force generates a torque which makes the coil rotate clockwise.The pointer deflects until it settles at a certain reading when the torque is balanced with thespring torsion which is counterclockwise. Thus, at balance, we can read the current value.When the current is reversed, the pointer deflects in the opposite direction.

The galvanometer sensitivity:

The galvanometer sensitivity is defined as the scale deflection per unit current

intensity passing through its coil i.e, sensitivity = degree/micro ampere (deg/µA) .

Direct current (DC) ammeter :

An ammeter is a device which- through calibrated scales- is used to measure directlythe electric current. A galvanometer is an ammeter of limited range due to its movingcoil sensitivity. To extend the range of the galvanometer, it is necessary to add a verylow resistance, called a shunt Rs to be connected in parallel with the galvanometer coilRg as shown in Fig (10-13).

θΙ

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Applications: Measuning InstumentsThe sensitive moving coil galvanometer

A sensutive moving coil galvanometer is an apparatus used to detect very weakcurrents in a circuit, measure their intensities and determine their polarities. Its principleof operation depends on the torque that is generated in a current -carrying coil moving ina magnetic field.

a) a simplified view of agalvanometer when the pointer is inthe middle of the graduated scale

graduatedscale

pointer spiralspring

ironcore

pointer

magnet

aluminum frame

(Fig 10 – 12)A moving coil galvanometer

b) top view

c) a galvanometer converted to a milliammeter

d) top view

radial magneticfield

soft iron core

pointer

aluminumframe

permanentmagnet

control spring

coil

falcrum

permanentmagnet

permanentmagnet

central spring

soft iron core

uniform scale

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Placing the parallel shunt assures that the ammeter as a whole will have a very lowresistance, which is necessary if the current in the circuit is to be unaltered afterconnecting the ammeter in series.

Most of the current in the circuit passes through the shunt Rs, while only a smallcurrent Ig passes in the galvanometer coil Rg. If the maximum current to be measured isI, which is the full scale deflection (FSD), then

I = Ig + IsIs = I - Ig

Because Rs and Rg are connected in parallel, the voltage difference across each is the same.

The two equations can be solved simultaneously to find Rs. Thus,

I s Rs = Ig Rg

Rs = Ig Rg

I s

.

b) use of a shunt resistance

a) a DC ammeter is a galvanometerwhose pointer deflects in one direction

Fig (10 – 13)The DC ammeter

pointermagnet coil

Rs = I g Rg

I - I g

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Ohmmeter

Measuring a resistance depends on measuring the current passing through it by anammeter and the voltage drop across it by a voltmeter. If the current is I and the voltagedrop is V, the resistance R from Ohm's law is R =V/I

If the voltage is fixed and known, we may remove the voltmeter from the circuit andcalibrate the galvanometer to give the value of the resistance directly (Fig10-15).As theresistance is increased, the current in the circuit decreases,and consequently, thegalvanometer reading.The Ohmmeter shown (Fig10-15) is actually a microammeterwhich reads 400µA as a full scale deflection (FSD).Its resistance is 250Ω connected inseries with 3000Ω, a variable resistance whose maximum value is 6565Ω, and a 1.5 Vbattery of negligible internal resistance.When we short circuit (sc) the terminals of theinstrument (RX =0), current flows in the circuit.For this current to give FSD, the resistance

in the circuit must be: Ω

The variable resistance must be adjusted to give FSD, when the variable resistance is500 since 250+3000+500=3750Ω.

Now, if the unknown resistance is introduced into the circuit, the current flowing willbe less, and the pointer will deflect short of FSD.

6565Ω

3000Ω

Rg=250Ω

Rx

Fig (10 – 15)A circuit for calibrating an ohmmeter

galvanometervariableresistance

instrumentterminals

standardresistance

battery

1.5400 x 10-6

= 3750

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voltage,it must be converted to a high-resistance instrument.The voltmeter must draw anegligible current, so that it will not affect the voltage drop to be measured.To do this,alarge multiplier resistor is connected in series with the galvanometer as shown in Fig.(10-14).The voltmeter is connected parallel across the two points between which thevoltage difference is to be measured. Let us call the resistance of the galvanometer coilRg and the multiplier resistance Rm which is connected in series parrallel with Rg. Themaximum current that passes through it is Ig, which is the current needed for the fullscale deflection (FSD) voltage V.

The voltage difference across the coil is : Vg = Ig Rg

The maximum voltage drop to be measured is: V = Ig Rg + Ig Rm = Vg + Ig Rm

Example

A galvanometer has an internal resistance of 0.1Ω and gives a full scale deflectionfor a current of 1mA. Calculate the multiplier resistance necessary to convert thisgalvanometer to a voltmeter whose maximum range is 50V.Solution

Vg = Ig Rg = 0.001 x 0.1 = 1 x 10-4 V

= 49999.9 ΩThe total resistance of the voltmeter is :

Rtotal = 49999.9 + 0.1 = 50000 Ω

Rm = V - V g

I g

(10-8)

Rm = =V - Vg

Ig

50 - 1 x 10-4

1 x 10-3

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Fig (10 – 17)Analog multimeter

Fig (10 – 18)Digital multimeter

They depend on digital electronics (Chapter 15). All the above instruments measurevoltage or current in one direction (DC). Therefore, they are called DC/multimeters. Butif the current or voltage is AC, the instrument used is called AC/ multimeters.

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Thus, we may calibrate the instrument in terms of the resistance to be measured. If Rx= 3750Ω, the current in the instrument is 200 µA, which is 1/2 the maximum current,and hence the deflection is 1/2 FSD.

If the resistance is doubled, i.e., 7500Ω., the deflection will be FSD. For three timesthe total resistance, i.e., 11250Ω, the deflection will be FSD corresponding to a currentof 100µA. It is to be noted that the graduated scale used to measure the resistance(Fig 10-16) is opposite to the graduated scale for the current .

This means that the maximum deflection corresponds to zero resistance (short circuitor sc). As the resistance increases, the deflection decreases.

It is to be noted also that the scale is not linear. The spacings between the readings ofthe scale to the right are further apart than the readings to the left.

The instruments using a point, are called analog instruments. A combined instrumentcalled multimeter can be switched around to measure voltage, curent and resistance(Fig 10-17).

Another set of instruments now exist which depend on reading numerals, denotingvoltage, current a resistance on a small LCD (liquid crystal display) without the need fora pointer. Such instruments are called digital multimeters (Fig 10-18).

131

4

IµARx(Ω)

400

200

100

0

0

3750

11250

Fig (10 – 16)An ohmmeter has a nonlinear graduated scale

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a) the length of the wire.b) the current intensity.c) the magnetic flux density.d) the angle between the wire and the direction of the magnetic field.

• A moving coil galvanometer is an instrument used to detect, measure and determinethe polarity of very weak electric currents.

• The operation of a moving coil galvanometer is based on the torque acting on a currentloop in the presence of a magnetic field.

• The sensitivity of a galvanometer is defined as the scale deflection per unit currentintensity flowing through its coil.

• The ammeter is a device which is used through a calibrated scale to measure directlythe electric current.

• To extend the range of the galvanometer, a low resistor known as a shunt is connectedin parallel with the coil of the galvanometer.

• The total resistance of the ammeter (with the shunt) is very small, therefore, it does notappreciably change the current to be measured in a closed circuit.

• The voltmeter is a device used to measure the potential difference across two points ofan electric circuit. It is basically a moving coil galvanometer having a very highresistance called a multiplier resistance connected in series with its coil.

• Since the total resistance of the voltmeter is very great, it does not affect much the flowof current through the element across which it is connected to measure its potentialdifference.

• The ohmmeter is an instrument which is used to measure an unknown resistance.• An ohmmeter is basically a microammeter connected in series with a constant cell

resistance, a variable resistance and a 1.5 volt battery. If its terminals are in contact(sc), the pointer gives full-scale deflection (FSD). If a resistor is inserted between itsterminals, the current flowing decreases. Hence, the pointer's deflection decreases,and indicates directly the value of the inserted resistor through a calibrated scale.

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In a Nutshell

- Definitions and Basic Concepts:• A megnetic field is produced around a current-carrying wire.• The intensity of the magnetic field produced around a current-carrying wire,

increases, by :a) getting closer to the wire.b) increasing the current.

• The direction of the magnetic field produced around a current-carrying straight wire isdetermined by Ampere’s right-hand rule.

• The lines of force around a current-carrying wire forming a circular loop, resemble to agreat extent those of a short bar magnet.

• The magnetic flux density at the center of a current-carrying circular loop depends on:a) the number of loop turns.b) the current intensity in the loop.c)the radius of the loop.

• The direction of the magnetic field at the center of a current-carrying loop isdetermined by the right-hand screw rule.

• The magnetic field produced by a current flowing through a solenoid (coil of severalclosely spaced loops) resembles to a great extent that of a bar magnet.

• The magnetic flux density at any point on the axis of a current-carrying a solenoiddepends on :a) the current intensity.b) the number of turns per unit length.

• Right-hand screw rule is used to determine the polarity of a solenoid carrying a current.• The unit of magnetic flux density is Web / m2, (Tesla or N/Am). • The force exerted by a magnetic field on a current-carrying wire placed in the field

depends on:

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5) What is the magnetic flux density at a point on the axis of a solenoid of length 50 cm

carrying a current of 2A and has 4000 turns? (0.02 Tesla).

6) A rectangular loop (12 x 10 cm) of 50 turns, carrying a current of 3 A, is placed in a

magnetic field of 0.4 Tesla flux density, such that the plane of the loop is parallel to

the field. Calculate the torque acting on the loop. (0.72 Nm)

7) A galvanometer's loop of 5 x 12 cm2 and 600 turns is suspended in a magnetic field of

0.1 Tesla flux density. Calculate the current required to produce a torque of 1 Nm.

(2.78 A).

8) A loop of cross-sectional area 0.2 m2 and 500 turns,carrying a current of 10 A is

placed at 30˚ between the normal to its plane and a magnetic field of 0.25 Tesla flux

density. Calculate the torque acting on the loop.

(125 Nm).

9) The coil of an ammeter is capable of carrying current up to 40 mA. If the resistance of

the coil is 0.5 , and it is desired to use the ammeter for measureing a current of 1 A,

What is the resistance value of the required shunt? (0.021 )

10) A galvanometer gives full scale deflection at current 0.02 A, and its terminal voltage

is 5 V. What is the value of the multiplier resistance required to make it valid to

measure potential differences up to 150 V? (7250 )

11) A voltmeter reads up to 150 V at full scale deflection. If the resistance of its coil is

50 and the current flowing is 4 x 10-4 A. Calculate the resistance of the potential

multiplier connected to the coil? (374950 )

12) A galvanometer reads up to 5A and has a resistance of 0.1 . If we want to increase

its reading 10 times, what is the value of the required shunt resistor? (0.0111 ).

13) An ammeter has resistance 30 . Calculate the value of the required shunt resistor to

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b) the coil of the moving coil galvanometer is attached to a pair of spiral springs.

c) when the moving coil galvanometer is used as a voltmeter, a resistor of high

resistance is connected in series with its coil.

d) an ammeter is connected in series with a circuit, but the voltmeter is connected

parallel to it.

e) connecting a constant resistor inside the ohmmeter.

f) the cell connected to the ohmmeter should have a constant emf.

9) What is meant by each of: potential multiplier and shunt? What is the use of each?

Deduce the rule related to each.

10) Explain how you can use the moving coil galvanometer to measure each of the

electric current, the electromotive force and the electrical resistance.

II) Drills:1) A coil of cross sectional area 0.2 m2 is placed normal to a regular magnetic flux of

density 0.04 Weber/m2. Calculate the magnetic flux which passes through this coil.

(0.008 Weber).

2) A wire of 10 cm length, carrying a current 5 A, is placed in a magnetic field of 1Tesla

flux density. Calculate the force acting on the wire, when:

a) the wire is at right angles to the magnetic field. (0.5 N)

b) the angle between the wire and the field is 45˚. (0.356 N)

c) the wire is parallel to the magnetic flux lines. (0)

3) A straight wire of diameter 2 mm carries a current of 5A. Find the magnetic flux

density at a distance of 0.2 m from the wire. (5x10-6 Tesla).

4) A circular loop of radius 0.1 m carries a current of 10 A. What is the magnetic flux

density at its center? (the loop has one turn). (2 x 10-5 Tesla)

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decrease the ammeter FSD to one third (decrease the sensitivity), and determine also

the total resistance of the ammeter and the shunt resistor. (15 , 10 ).

14) A galvanometer of resistance 54 , when connected to a shunt (a), the current

flowing through the galvanometer is 0.1 of the total current. But if connected to a

shunt (b), 0.12 of the total current flows through the galvanometer. Find the

resistances of a and b. (6 , 7.364 )

15) A moving coil galvanometer of resistance 50 ohms gives full scale deflection at

current 0.5A. How could it be converted to measure:

a) potential differences up to 200V? (350 in series).

b) electric currents up to 2A? (16 2/3 in parallel)

16) A milliammeter of resistance 5 has a coil capable of carrying a current of 15 mA.

It is desired to use it as an ohmmeter using an electric cell of 1.5V having internal

resistance 1 . Calculate the required standard resistor, and calculate the external

resistance needed to make the pointer deflect to 10mA? Calculate the current that

flows through it when connected to an external resistor of 400 ?

(94 , 50 , 3mA)

233

Unit 4 : Electricity D

ynamic Elictricity and Electrom

agnetism C

hapter 11: Electromagnetic Induction

the coil, a deflection of the pointer was noticed in the opposite direction. This phenomenon iscalled "electromagnetic induction". According to this phenomenon, an electromotive force andan electric current are induced in the coil, when the magnet is plunged into or removed from thecoil. As a result, Faraday concluded that the induced electromotive force and also the inducedelectric current were generatd in the circuit as a result of the time variation of the magnetic fluxlinked with the coil during the motion of the magnet.

Moreover, the action of the magnet is met by a reaction from the coil.If the magnet isplunged into the coil, the induced magnetic field acts in a way to oppose the motion of themagnet. If the magnet is pulled out, the induced magnetic field acts to retain (or keep) themagnet in. Faraday concluded that the induced emf and current were generated in thecircuit as a result of the time variation of magnetic field lines as they cut the windings ofthe coil while the magnet was in motion.

Faraday’s laws:From the above Faraday’s observations, one can conclude the following:

1) the relative motion between a conductor and a magnetic field in which there is timevariation of the magnetic flux linked with the conductor, induces an electromotive forcein the conductor. Its direction depends on the direction of motion of the conductorrelative to the field.

2) the magnitude of the induced electromotive force is proportional to the rate by which theconductor cuts the lines of the magnetic flux linked with it, i.e.,

where ∆φm is the variation in the magnetic flux intercepted by the conductor through thetime interval ∆t3) the magnitude of the induced electromotive force is proportional to the number of turns

N of the coil which cut (or link with) the magnetic flux., i.e.,emf N

Thus, from the analysis of the above mentioned results, one can conclude the following relation: ∝

t

∝emf m

(11 - 1) = - N t

emf m

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OverviewIt has been noticed that the passage of an electric current in a conductor produces a magnetic

field. Soon after Oersted's discovery that magnetism could be produced by an electric current,aquestion arose, namely, could magnetic field produce an electric current ?

This problem was addressed by Faraday through a series of experiments which led to oneof the breakthroughs in the field of physics, namely, the discovery of electromagneticinduction. On the basis of such a discovery, the principle of operation and function of mostof the electric equipment - such as the electrical generators (dynamos) and transformers -depend.

Faraday’s Experiment: Faraday made a cylindrical coil of insulated copper wire, such that the coil turns were

separated from each other. He connected the two terminals of the coil to a sensitivegalvanometer having its zero reading at the mid point of its graduated scale, as shown in Fig(11-1) . When Faraday plunged a magnet into the coil, he noticed that the pointer of thegalvanometer was deflected momentarily in a certain direction. On removing the magnet from

Fig (11-1a)The magnet is plunged into the coil

Fig (11-1b)The magnet is pulled out of the coil

Electromagnetic Induction Chapter 11

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agnetism C


This is known as Farady's law of electormagnetic induction. The negative sign in theabove relation indicates that the direction of the induced etectromotive force or the inducedcurrent tends to oppose the cause producing it. This rule is known as Lenz's rule.

Lenz’s ruleThe induced current must be in a direction such as to oppose the change producing it.Fig (11-2) illustrates a direct application of Lenz’s rule :

The direction of the induced current in a straight wire:In one of his several experiments, Faraday showed that the induced current in a straight

wire flowed in a direction perpendicular to the magnetic field. Many years later. Flemingconcluded a simple rule:

Fleming’s right hand rule Extend the thumb,pointer and the middle finger of the right hand, mutually perpendicular

to each other. Let the pointer points to the direction of the field, and the thumb in thedirection of motion, then the middle finger (with therest of the fingers) will point to the direction of theinduced current or voltage as shown in Fig (11-3).

Fig (11 - 3)Fleming’s right hand rule

thumb(motion)

point to (field)

rest of the fingers(induced current

or voltage)

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(S)

Fig (11 – 2)Lenz's law

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where M is the coefficient of mutual induction (mutual inductance) of the two coils. Itsunit is VsA-1 and is equivalent to what is calIed "Henry". Thus, the henry is the unit used tomeasure the inductance in general. The negative sign in equation (11-2) follows fromLenz's rule, namely, that the direction of the induced electromotive force (or the directionof the induced current) is such as to oppose the cause producing it. The coefficient ofmutual inductanc between two coils depends on the following factors.

1. the presence of an iron core inside the coil. 2. the volume of the coil and the number of its turns.3. the distance separating them.The transformer is considered as a clear example of mutual induction

Experiment to study mutual induction One can study experimentally the mutual induction as follows:

Connect one of the two coils in a circuit which contains a battery, a switch and a rheostat. Onecoil is called the "primary coil", while the other coil - connected to a sensitive galvanometer with itszero point at the middle of its scale - is known as the "secondary coil". Fig( 11-5). Let us do theexperiment as follows:1) Close the circuit of the primary coil, while plunging the primary coil into the secondary coil.

One notices a deflection in the galvanometer in a certain direction, indicating the generationof an induced electromotive force in the secondary coil due to the variation of the number ofmagnetic flux lines linked with the turns of the secondary coil. On taking away the primarycoil from the secondary coil, one notices that the pointer of the sensitive galvanometer isdeflected in the opposite direction.

2 = - MI 1

t(emf)

(emf)

(11 - 2)

I1

t

1

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Fig (11 - 4A)in case there is no current in the first

coil, there is no emf in the second coil.

Fig (11- 4b)at the instant of closing the ciruit of the firstcoil, an emf is generated in the second coil.

Fig (11 - 4c)after the current in the primary is steady (the flux is steady) emf in the secondary coil: 0

Mutual induction between two coils:

If the two stationary coils are arranged such that one coil surrounds the other., i.e., onecoil is plunged into the second one, or even one is placed in the neighborhood of the otheras shown in Fig.(11-4), then the variation in the intensity of the electric current in one of thetwo coils (opening and closing the switch) will induce an electromotive force in the othercoil, according to Faraday’s law. This induced electromotive force is proportional to therate of change in the magnetic flux linked with the other coil. Since the magnetic flux isproportional to the intensity of current in the first coil.

239



agnetism C


magnetic field will be in a direction as to resist the increase in the affecting magnetic field.II. The pointer of the galvanometer deflects in the opposite direction in the following cases:

a) on the withdrawal of the primary, or taking it far away from the secondary coil. b) on decreasing the intensity of the current in the primary.c) on switching off the primary circuit. In the above cases, he intensity of the magnetic field affecting the secondary coil

decreases and the magnetic flux linkage decreases. The induced emf in the secondary coildecreases as the affecting field decreases with time. The direction of the inducedelectromotive force (and the induced current) is in the forward direction, so as to produce amagnetic field in the same direction as the current in the primary. This in turn resists thedecrease in the affecting magnetic field. All these observations clarify Lenz's rule, wherethe direction of the induced current is such as to resist (or to oppose) the time variationcausing it.

Self induction of a coil:One can understand what is meant by self induction of a coil by connecting the coil of a

strong electromagnet (a coil of largenumber of turns) in series with a 6Vbattery, and a switch as shown in Fig(11-6). Current passes in the consideredcoil, due to which a strong magneticfield is formed, since each turn acts as asmall magnet. The magnetic flux linkswith the neighboring turns.

On switching off the circuit, it is noticedthat an electric spark is passed between thetwo terminals of the switch. This isexplained as follows.

Fig (11 - 6)Effect of self induction in a coil

battery switch

neon lamp

electromagnetcoil

VB

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n 2) Plunge the whole primary coil to reside in thesecondary one, then increase the intensity of thecurrent in the primary coil. Notice the deflectionof the pointer of the galvanometer in acertain direction. Decrease the current in theprimary, and notice that the deflection of thepointer takes place in the opposite direction. Thisindicates the generation of an inducedelectromotive force in the secondary coil onincreasing or decreasing the intensity of thecurrent in the primary coil.

3) With the primary coil inside the secondary one,close the circuit of the primary coil, a deflectionis noticed in the galvanometer in a certaindirection. Open the primary circuit, and noticethat the deflection is in the opposite direction.This indicates that an electromotive force isinduced in the secondary coil upon switching on or switching off the primary circuit.The analysis of the above mentioned observations leads to the following conclusions:

I. The pointer of the sensitive galvanometer deflects in a certain direction in the following cases:a) bringing the primary coil close to the secondary coil or when the primary coil is

plunged inside the secondary one.b) increasing the intensity of the current in the primary coil. c) switching on the primary circuit.In all cases above, there is a positive increase in magnetic flux linkage and the induced

emf in the secondary coil increases as the affecting magntic field increases with time. Theinduced current is in opposing direction to that in the primary. In such a case, the induced

battery

switch rheostat

primarycoil

secondarycoil

galvanometer

Fig (11 - 5)Mutual inductance between

two coils

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agnetism C


The Henry :It is the self-inductance of a coil in which an emf of one volt is induced when the current

passing through it changes at a rate of one Ampere per second (vsA)-1.The self inductance of a coil depends on:

a) its geometry.b) its number of turns.c) the spacing between the turns.d) the magnetic permeability of its core.

Among the applications of self induction isthe fluorescent lamp, where magnetic energy isstored in the coil. This energy is discharged inan evacuated tube filled by an inert gas,causing collisions of its atoms and theirsubsequent ionization and collision with thewalls of the tube.

The inner walls are coated with a fluorescent material which causes visible light to beemitted upon the collision of the inert gas ions with it.

Electromagnetic induction is also used in Ruhmkorff coil, which is used as an ignitioncoil in internal combustion engines (such as a car).

Eddy Currents:If the magnetic flux changes with time through a solid conductor ,currents will be induced

in closed paths in the conductor. Such currents are called "eddy currents". The change in theintercepted magnetic flux is effected either by moving the solid in a suitable magnetic field orby subjecting the metallic solid to an alternating magnetic field( for example field due to anAC current). The eddy currents are associated with heating effects. Thus, they are useful inmelting metals in what is called the induction furnaces.

Henry

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n

∝

L = - / t

eemf

When the coil circuit is switched off, the current ceases to pass in it, and this isassociated with a decrease of the magnetic field of the neighboring turns to zero. This inturn is accompanied by a time variation of the flux linkage, i.e., each turn cuts thediminishing lines of the magnetic flux, and thus, an induced electromotive force isgenerated in the coil.

The induced electromotive force is formed in the turns of the coil as a whole as a resultof the self induction of the coil itself. This induced electromotive force is generated due tothe self induction of the coil on switching off or switching on the circuit following Lenz'srule. Thus, an induced electric current is generated in the same direction as the originalcurrent. When the circuit is switched off, to retain the existing current, a spark is formedbetween the two terminals of the switch. When the number of turns of the coil is large, theinduced emf on switching off the circuit will be much larger than that of the battery, Thiscauses a neon lamp connected in paralle1 between the two terminals of the switch to glow(aneon lamp requires a potential difference about 180V to glow).

Since the induced electromotive force is proportional to the rate of change of the currentin the coil, then the emf induced by self induction is directly proportional to the rate ofchange of the current in the coil. That is :

where L is a constant of proportionality known as the coefficiont of self induction (selfinductance) of the coil, and the negative sign in equation (11-3) indicates that the inducedelectromotivc force opposes the change causing it (Lenz's rule).

Thus, the self inductance of a coil is defined as: It is the electromotive force induced in the coil when the current passing through it changes

at a rate equals one Ampere per second. The self inductance is measured in the unit henry.

I1

t(emf)1

= - L I 1

t(11 - 3)e(emf)1∴

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agnetism C


Alternating current generator: The AC generator (or the dynamo) is a device which converts the mechanical energy into

electrical energy. In a generator, a coil rotates in a magnetic field, and the resulting induced

current can be transferred (or transmitted) by wires for long distances.

The simple electric generator consists as shown in Fig (11-8) of four main parts :

a) a field magnet.

b) an armature.

c)two slip rings.

d) two brushes.

The field magnet may be a permanent

magnet or an electromagnet. The armature

consists of a single loop of wire or coil of

many turns suspended between the two poles

of the field magnet. A pair of slip rings are

connected, one to each end of the loop. They

rotate with the loop in the magnetic field.

The induced current in the coil passes to the

external circuit through two graphite

brushes, each touching one of the two

corresponding slip rings. Fig (11-9) shows

the direction of rotation of the armature between the poles and the direction of the induced

current at a certain instant. The loop rotates around its axis in a circle of radius r. Its linear

velocity is

v = ω r

where ω is the angular velocity equal to 2πf, (where f is the frequency). Substituting for

slip rings

directionof motion

brushes

permanent field magnetic

armature

Fig (11 - 8)A simplified schematic for an

AC generator (dynamo)

245



agnetism C


From Fig (11-10), we see that the induced currentchanges direction every half a revolution. It followsa sine wave. From figure, we can also understandthe meaning of f.

Throughout a complete revolution, the currentincreases from zero to a maximum, then decreasesto zero, then reverses direction, and increases in thenegative direction up to a negative maximum. Then,it heads back to zero. In one complete revolution,one complete oscillation has occurred. The numberof oscillations per second is the frequency f. Thefrequecy of home use power is 50Hz

Example:The coil of a simple AC generator consists of 100 turns, the cross sectional area of each

is 0.21 m2. The coil rotates with frequency 50 Hz (cycles/second) in a magnetic field ofconstant flux density B = 10-3 Weber/m2. What is the maximum induced emf generated?and what is the instantaneous value at θ = 30˚?Solution:

(emf)max = NBA ω = NBA (2 πf)

Thus, the maximum induced emf generated equals 0.6 volts.

It is worth remembering that the induced current is directly proportional to the inducedemf. Thus, the instantaneous value of the induced current is given by :

I = Imax sin (2 πf t )

= 100 x 10-3 x 0.21 x 2 x 227

x 50 = 6.6 V

graphitebrushes

slip rings

armature

Fig (11-10a)AC generator

e = max sin = 6.6 x sin 30 = 6.6 x 12

= 3.3 V˚emf = (emf)max

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n This induced current reaches its maximum value when the induced emf reaches itsmaximum value, and it vanishes as the induced emf is zero.

Effective value of the alternating current:It is worth mentioning that the average value

of an AC current equals zero, because the ACcurrent changes from (Imax) to (-Imax). Neverthless,the electric energy is consumed as thermalenergy due to the motion of electric charges,and the rate of the electric energy consumed isproportional to the square of the intensity ofthe current.

The effective value of the intensity of thealternating current is the value of the directcurrent which generates the same rate of thermaleffect in a resistance (or the same power) as thatgenerated by the considered AC current.

Ieff = 0.707 Imax

The value Ieff is called the "effective value of the alternating current". There is a similar relation for the effective electromotive force, that is :

(emf)eff = 0.707 (emf)max

Veff = 0.707 Vmax

Example:If the effective intensity of current in a circuit equals 10 A, and the effective voltage is

240 volts,what is the maximum value for current and voltage ?

Fig (11-10b) The relation between current and

angle of rotation(sine wave)

maximum positive current

maximumnegative current

coil position

current

onecomplete

revolution

(11 - 11)

(11 - 12)

θ

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agnetism C


Continuing the rotation, the brush Fl acts as a positive pole, while F2 acts as thenegative pole of the dynamo. Accordingly, the current in the external circuit will bealways in one direction as shown. It is noticed that using the commutator renders theinduced emf in Fig (11-11d) in one direction, but its value changes from zero up to amaximum value, then decreases again to zero during each half cycle of the coil rotation,but it is always in one direction.

To obtain a uni-directional current ofapproximately constant value, i.e., to obtain a nearlyDC (value), many coils separated by small angles areused. A cylinder is used which is split into a numberof segments, double the number of coils. Thus, thecurrent in the external circuit is almost constant. Thisis the way to obtain a DC generator (Fig 11-12).

The transformer: The electric transformer is a device whose

function is based on the mutual inductionbetween two coils, and is used to step up or tostep down an AC voltage. Transformers areused to transfer the electric energy fromgenerators at electric power stations. Suchtransformers are called step - up transformers,while the transformers used at the zoneswhere the energy has to be distributed among buildings are called step-down transformers.The transformer as shown in Fig (11-13) consists of two coils: a primary coil and asecondary coil. The two coils are wound around a soft iron core made of thin iron sheets

Fig (11-12)Nearly DC current

Fig (11-13a)Step UP transformer

primary coil

secondary coil

output

input

soft iron core( laminas)

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n commutator consists of two halves 1 and 2 of ahollow metallic cylinder split in between, and are wellinsultated from each other as shown in Fig(11-11).Two brushes F

1and F

2 touch the two halves

during the rotation of the coil. The external circuit isconnected to the two brushes Fl and F2. It is necessarythat the two brushes F1 and F2 touch the insulatorbetween the two halves at the moment when the planeof the coil is perpendicular to the magnetic field, i.e,at the instant when the generated electromotive forcein the coil is zero.

Let us consider that the coil starts rotation in thedirection shown (Fig.11-11c).During the first halfrotation, brush F1 touches the half cylinder (1),while brush F2 touches the other half (2) of thecylinder. The current in such a case will pass in thecoil in the direction w x y z. As a result, the currentpasses in the external circuit in the direction from Flto F2 during the first half of the cycle. In the secondhalf of the cycle, the electric current reverses itsdirection in the coil, i.e., the current passes in the coilin the direction z y x w. At the same time, brush F1 will be in contact with the half(2), while F2will be in contact with the half(1), i.e., the two halves of the commutator reverse their positionrelative to the two brushes. In such a case, the current in the external circuit passes from, F1 to F2,which is the same direction as that in the first half of the cycle.

direction ofrotation

brushes

split cylinder

Fig (11-11c) Use of a split cylinder

rectifies the current

Fig (11-11d)Unidirectional current versus θ (sine wave)

current

number ofrevolutions

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agnetism C


This equation shows the interrelation between the emf Vs in the secondary and Vp in theprimary. If Ns is larger than Np, one has a step-up transformer, where the emf in thesecondary coil will be larger than the emf in the primary one. For example, if the number ofturns of the secondary coil is twice that for the primary coil, one gets Vs = 2VP.

While, for the case when Ns is less than Np one gets a step-down transformer, where, insuch a case Vs will be less than Vp.

The relation between the current intensities in the two coils of the transformer: Let us assume that there is no loss in the electric energy in the transformer (almost zero

resistance), then according to the law of conservation of energy, the electric energy madeavailable by the source in the primary coil must equal that delivered to the load in thesecondary coil.

Vp Ip t = Vs Ist

From which the input power is equal to the output power, i.e, Vp Ip = Vs Is

Thus,From the equations (11-11) and (11-12),

This shows that the intensity of the electric current in either of the two coils is inverselyproportional to the number of its turns.

For example: if the number of turns of the secondary coil is twice that of the primary coil,then the intensity of current in the secondary coil equals half that in the primary coil.

From this argument, we see the importance of the use of the step-up transformer at the

I s

I p =

Np

Ns

V s

V p =

Ip

Is

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n (laminas) insulated from each other, to minimize the effectof eddy currents and to minimize the dissipated electricenergy. When an electric current passes in the primary coil,a magnetic field is generated. The core makes the lines ofsuch a field pass through the secondary coil.

The relation between the two emfs in the twocoils of the transformer:

When the primary coil is connectcd to a source of AC

voltage, the variation in the magnetic field linked with the primary current generates aninduced emf in the secondary coil having the same frequency. The induced emf in thesecondary is determined from the relation:

where, Ns is number of turns of the secondary coil and is the rate of change of themangetic flux linked between the primary through the secondary coil. The electromotiveforce in the primary is in turn related to the rate of change of the magnetic flux and isdetermined from the relation :

where, Np is the number of turns of the primary coil. Assume that the wasted magneticenergy is negligible, i.e., there is no considerable loss in the magnetic flux, i.e., the wholeresulting magnetic flux passes through the secondary coil (no stray lines). Dividing theabove two relations one can get the following formula :

Vs = Ns t

Vs= - t

Vp = Np t

Vp= -

Fig (11-13b)Transformer symbol

(11 - 13)V s

V p =

N s

N p

m

m

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agnetism C


Solution:

Learn at Leisure

AC/DCThere are two types of current or voltage AC and DC .In the case of DC, Ohm’s law

dictates that what determines the current is the resistance.In the case of AC, what determines the current are three elements,the resistor, the

inductor and the capacitor. Household appliances use 220 V AC of frequency 50 HZ. Often,we need to convert this to a lower DC voltage, as in the case of the mobile charger andsome other appliances.To do this, we use a down transformer and a rectifier. It is to benoted that a low AC current is more hazardous to man than a low DC current (why?).

η= x100

η= x x100Vs NpVp Ns

80 = x x1008 1100220 Ns

Ns = 50

IsIp

= NpNs

Is0.1

= 110050

Is = 2.2 A

turns

Vs IsVp Ip

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n an audio signal (Fig 11-16). The same thing happens in the hard disk in the computer,where data is stored by magnetization. In this way, the data is not lost from the hard diskwhen the power of the computer is switched off.

Examples:1- A trandformer connected to a 240 V AC power source gives 900 V output emf with

current intensity 4A. What is the intensity of the source current assuming that the efficiencyof the transformer is 100%?Solution:

2) An electric bell is connected to a transformer of efficiency 80% which gives 8 V output,while the input household voltage is 220 volts. What is the number of turns of the secondarycoil if the number of turns of the primary coil is 1100 ? and what is the intensity of current inthe secondary coil if the current in the primary coil is 0.1 A ?

. . .Vs

Vp

= Ip

I s

I p = 900 x 4240

= 15 A

900240

= Ip

I s4

Fig (11-13b)Use of electromagnetic induction in recording

input audio

unmagnetizedtape

iron core

magnetized tape

magnetic field

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agnetism C


Operation of a DC motor through one complete revolution:Starting from a position at which the plane of the coil is parallel to the lines of the

magnetic flux, and the brush F1

- connected to the positive terminal of the battery - touchesthe half cylinder x, while F

2 - connected to the negative terminal of the battery - touches the

half cylinder y as shown in Fig (11-17). Thus, current passes in the coil in the direction dcba.Applying Fleming's left hand rule, one concludes that the wire ab is affected by a force inthe upward direction, while the wire cd is affected by a force in the downward direction. Thetwo produced forces (couple) form a torque, and the coil begins to rotate in the directionshown in the figure. As the coil rotates, the moment of the couple decreases gradually till itvanishes, when the coil plane becomes perpendicular to the lines of the magnetic flux. Butthe coil having gained a momentum will continue motion due to its inertia, which in turnpushes the coil to the other side. The two halves x and y of the commutator interchangeposition, such that the half cylinder x will be in touch with the brush F2,while the brush F

1will touch to other half cylinder y. Thus, the current in the coil will reverse direction andpass in the direction abcd. Applying "Fleming's left hand rule" for the new position of thecoil shows that the force acting on the wire ab will be downward, while the force acting onthe wire cd will be upwards. The obtained torque enables the coil to continue rotation in thesame circular direction. The torque increases gradually to its maximum value when the planeof the coil becomes parallel to the lines of the magnetic flux. Then, it decreases to zero whenthe plane of the coil is perpendicular to the lines of magnetic flux. The inertia of the coilthen causes it to continue rotating to the other side. This permits the two halves tointerchange positions and with respect to the two brushes F1 and F2, and thus, the current inthe coil is reversed once more. The coil continues rotating in the same circular directionmaking one complete revolution, and so on.

In order to increase the power of the motor, a number of coils may be used with equal

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n DC motor:It is a device which converts electric energy to

mechanical energy. It operates on a DC source(battery) (Fig 11-17). It consists in its simplestform of a rectangular coil abcd comprising a largenumber of turns of insulated copper wire woundaround a soft iron core made of thin insulatedsheets to cut down on eddy currents.

The core and the coil can rotate between thetwo poles of a strong horseshoe (U-shaped) fieldmagnet. The two terminals of the coil areconnected to two halves of a split cylinder(commutator). The two halves (x,y) are insulated from each other and capable of rotatingaround the axis of the coil.

The plane separating the two halves is perpendicular to the plane of the coil and the lineconnecting the two brushes is parallel to the lines of magnetic flux.

To operate the motor, the two brushes must be connected to the battery.

The motor and the galvanometer:The principle of operation of the electric motor and that of the moving coil galvanometer

are alike. The main difference is that the electric motor must rotate continuously in thesame direction. The design of the electric motor necessitates that the two halves x,y of thecylinder must interchange positions relative to the two brushes F1 and F2 each half cycle.As a result, the electric current passing in the motor must reverse direction in the coil eachhalf revolution.

Fig (11 - 17)DC motor

ficld magnet

brushes

variable resistance

splitcylinder

259



agnetism C


Learn at Leisure

The microphone and the loud speakerThe operation of a moving coil microphone depends

on the vibration of an armature according to the soundwaves. The magnetic field in an iron core changes,which results in the generation of an emf in a coilwound around the iron core. This emf is of variableamplitude and frequency according to the individualsound. Thus, a sound signal (mechanical wave) isconverted to an electrical (audio) signal.

In a moving coil loud speaker, the reverse takesplace.

Fig (11 - 19)A microphone

Learn at Leisure

Search for Metals A metal detector is used in the search for

metals. Its operation depends on measuring

the change in the self inductance L of a coil

due to its proximity to a metal. The current

in the detector changes giving away the

hidden matal (Fig. 11-18).

Fig (11 - 18)A metal detector

magnet

coil

Soundwaves

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n angles between their planes. The two terminals, of each coil are connected to two oppositesplits of a cylinder. The cylinder is split into a number of segments twice that of the numberof the coils. During rotation, each two opposite segments touch the two brushes F1 and F2

when their corresponding coil is in position of largest torque.

Learn at Leisure

Motor and generator at the same time:While operating the motor, its coil cuts the line of magnetic flux of the field magnet.

There is a rate of change of cutting magnetic lines. Therefore, an emf is induced oppositeto the source, reducing the current, and hence, the speed.This back emf in the motor coilacts to the stabilize the speed of rotation of the coil. If the speed of the coil tends toincrease, the back emf increases. The difference between the back emf and the externalsource is the voltage drop across the coil resistance. Therefore, as the back emf increases,the current decreases, and so does the speed of rotation. Conversely, if the coil speed tendsto decrease, the back emf decreases, and the current increases. So the speed of rotation ofa DC motor remains constant.But the speed can be changed by changing the source(battery) voltage. It should be noted that if we try to stop the motor by force while it isconnected to the source, the motor coil burns out, because the back emf would disappearand the battery voltage is applied in full across the small coil resistance so it burns out.Also, if a transformer works on no load (secondary is open circuited), the secondarycurrent is zero and the primary current should be zero. However, a back emf in the primaryalmost balances out with the input voltage due to self-induction. A small current in theprimary exists even at no load to produce the flux linkage. So, an ideal transformer doesnot really exist. However, at full load, we may consider - as an approximation - that theideal transformer model works.

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agnetism C


Fig (11 - 21b)A section in ignition circuit components

Fig (11 - 21a)A schematic for the ignition circuit in a car

copacitor

point contact

platinumpoint contacts car battery

primary coil

secondary coil

cam

iron core

spark plug

distributer

spark

rotating distributer

discharge arm

ignition coil

point contact

contact

spark plug

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n The variable audio (electrical) signal producesvariations in the coil current. The coil isconnected to a diaphragm which vibrates dueto the force generated in the presence of amagnetic field. Mechanical (sound) wavesresult, resembling the original audio signal.

Thus, sound is heard back (Fig 11-20).

paper core

soft iron cylinder

movingcoil

soft ironsheet

permanentmagnet

flexible wires tothe coil

diaphragm

Fig (11 - 20)A loud speaker

Learn at Leisure

lgnition circuit in a carThe ignition coil (Fig 11-21) consists of two coils one inside the other, both wound

around a soft iron core. The primary coil and the core comprise an electromagnet. theprimary circuit is opened regularly by a distributer cam as it rotates, thus, opening andclosing the point contacts. The secondary coil contains thousands of turns. A large emf isgenerated from time to time at the same rate of opening the primary circuit. This large emfgenerates a spark across the air gap across the spark plugs. The spark plugs are connectedalternately to the secondery coil as the distributer rotates. A capacitor is used to protect thepoints from corrosion due to the spark.

Electronic ignition system works on the same principle, but the cam is replaced bytransistors as a switch (Chapter 15).

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agnetism C


• Self-induction: It is the electromagnetic effect induced in the same coil when theintensity of the current increases or decreases.This effect acts to resist such a change inthe intensity of current.

• Coefficient of self-induction : It is measured numerically by the electromotive forcegenerated by induction in the coil when the intensity of the current passing through itchanges at a rate of 1A/s.

• The unit of measuring the self induction (Henry): It is the self induction of a coil inwhich an emf of 1V is induced when a current passes through it which changes at a rateof 1A/s.

• The self-induction of a coil depends on :a) its geometry. b) its number of turns.c) the spacing between its turns. d) the magnetic permeability of its core.

• The Dynamo (AC Generator): It is a device used to convert the mechanical energy toelectric energy(AC current and voltage) when its coil rotates in a magnetic field.The simple dynamo (AC generator) consists of :a) field magnet (strong magnet).b) a coil of insulated copper wire suspended between the two poles of the magnet.c) two metallic rings in contact with two graphite brushes connected to an external

circuit.• A commutator: (cylinder split into a number of insulated segments) is used to obtain aDC current and voltage (DC generator).• The alternating current: It is current which changes periodically its intensity and

direction with time according to a sinusoidal curve. • The electric transformer: It is an electric device used to step up or step down an emf

through mutual electromagnetic induction.

1H 1V.SA

=s

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n In a Nutshell

Definitions and Basic Concepts:- Electromagnetic induction : It is a phenomenon in which an induced electromotiveforce and also an induced current are generated in the coil on plunging a magnet intoorwithdrawing a magnet out of a coil.

• The presence of a soft iron core inside a coil concentrates the lines of magnetic flux thatlink with the coil. This in turn increases the induced electromotive force and also theinduced current.

• Faraday's law for the induced emf : The induced emf generated in a coil byelectromagnetic induction is proportional to the time rate by which the conductor cutsthe lines of magnetic flux and is also proportional to the number of turns of the coil.

• Lenz's rule: the direction of the induced current generated by induction is such thatto oppose the change in the magnetic flux producing it.

• Fleming's right hand rule: Place the thumb, the pointer and the middle finger(withthe rest of the fingers) of the right hand mutually at right angles. If the pointerpoints in the direction of the magnetic field and the thumb in the direction ofmotion then the middle finger (with the rest of the fingers) will point in thedirection of the induced current.

• Mutual induction: It is the electromagnetic interaction between two coils kept close toeach other (or one inside the other).An electric current with time varying intensitypassing in one coil (primary coil)will produce in the second one (secondary coil) aninduced current in a direction such that to oppose the variations of the current intensity inthe primary coil.

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n • The efficiency of the transformer: It is the ratio between the output electric energygiven in the secondary and that available to the primary.• The electric motor: It is an electric device used to convert the electric energy intomechanical energy .

Basic laws:• The induced emf genrated in a coil of N turns as a result of time variation of magnetic

flux φm linked with the coil in an interval of time is given by the relation:

The nagative sign indicates that the direction of the induced emf (and thus the current) issuch as to oppose the cause producig it.• The emf induced in a secondary coil due to the time variation in the lines of magnetic flux

resulting from a primary coil linking with the secondary coil in a time interval t is givenby the relation :

emf = where M is the coefficient of mutual induction.

• The emf induced by self induction as a result of the current ∆I passing through the coil ina time ∆t is given by the relation :

where M is the coefficient of self induction of coil.

= - N t

vVemf

- M

emf = - L

It

It

∆∆

∆

∆

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4) A current passes in the primary coil, then this coil is plunged into a secondary coilwhose terminals are connected to a galvanometer. The deflection of its needle will be ina direction:a) opposite to the current in the primary coil.b) points to zero readingc) increasing.d) same as the current in the primary coile) variable

5) Opening the primary circuit while the primary coil is inside the secondary one, leads tothe generation of :a) an induced forward current.b) an electric fieldc) an induced back current.d) an AC current.e) a magnetic field.

6) The slow rate of growth of the current in the solenoidal coil is due to the:a) production of forward current.b) production of a magnetic field.c) production of a back induced current opposing (resisting ) the original one.d) production of a magnetic flux.e) production of an electric field.

7) The ohmic resistors are made of double wound wires:a) to decrease the resistance of the wire.b) to increase the resistance of the wire.

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I) Put ( ) against the right answer:1) The pointer of a galvanometer whose terminals are connected to a solenoidal coil will be

deflected if one withdraws the magnet quickly from the coil because: a) the number of the coil turns is very large.b) the coil intercepts the lines of the magnetic flux.c) the number of the turns of the coil is small.e) the number of turns of the coil is suitable.

2) The needle of the galvanometer whose terminals are connected to a solenoidal coildeflects on the withdrawal of the magnet in a direction opposite to that which occurs onplunging the magnet into the coil because:a) an induced current is generated in a direction opposite to that on plunging the magnet.b) an electric current is generated.c) the number of the lines of magnetic flux decreases.d) the number of the lines of the magnetic flux changes.e) the number of flux lines remains constant.

3) The emf induced in a coil on plunging a magnet into or withdrawing it out of a coildiffers according to the difference in :a) [the intensity of the current - the length of the wire - the number of the lines of flux]. b) [magnet strength - the velocity with which the magnet moves- the number of turns of

the coil].c) [the cross sectional area of the coil - the mass of unit length - the material from which

the wire is made]. d) [the length of the wire - the number of turns - the type of the magnet].e) [the magnetic flux density - time - the intensity of the current].

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c) several magnetsd) an insulated copper wire. e) a current rectifier.

12) The ratio between the electric energy in the secondary to that in the primary is called:a) the lost energy. b) the given energy.c) the efficiency of the transformer.d) the working strength of the transformer.e) the gained energy.

II) Define the following :1- Electromagnetic induction.2- Faraday's law of induction3- Lenz's rule.4- Fleming 's right hand rule.5- Mutual induction.6- Unit of measuring the mutual inductance.7- Self induction.8- Coefficient of self induction.9- The Henry.10- The induction coil.11- The AC current.12- The dynamo. 13- The electric motor.14 - The transformer.15- The efficiency of the transformer.16- The back emf in the motor.

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n c) to avoid self-induction.d) to eliminate the resistance of the wire.e) to facilitate the connection process.

8) The direction of the current produced in the dynamo coil can be determined using:a) Fleming's left hand rule. b) Lenz's rule. c) Fleming's right hand rule.

9) The rate with which the coil intercepts the lines of magnetic field in the dynamo ismaximum when: a) the plane of the coil is perpendicular to the flux lines.b) the plane of the coil is inclined to the lines by an angle 30˚ c) the face area of the coil is minimum.d) the face area of the coil is maximum. e) the plane of the coil is parallel to the lines of the magnetic flux.

10) The intensity of the current in the two coils of the transformer is : a) directly proportional to the number of the turns.b) inversely proportional to the number of the turns. c) depending on the temperature of the wire.d) depending on the substance of the wire. e) depending on the temperature of the air (ambient temperature).

11) The power of an electric motor to rotate increases on using:a) larger number of turns. b) several coils with angles between their planes.

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IV) Give reasons 1) The core of an electic transformer is made of thin sheets insulated from each other.2) A bar of soft iron will not be magnetized if a double wound wire carrying a current is

wound around it.3) A wire free to move in a magnetic field moves when a current passes through it.4) The transformer is not suitable to convert DC voltage.5) The electric motor rotates with uniform velocity. 6) The induced current dies out in a straight wire faster than in a coil with air core, and

in a coil with air core faster than in a coil wound around an iron core.7) The metallic cylinder used to obtain a unidirectional current in the dynamo is split into

two halves completely insulated from each other.

V) Drills 1) A coil of 80 turns, and cross sectional area 0.2 m2 is suspended in a perpendicular

position to a uniform magnetic field. The average induced emf is 2 V when it rotates1/4 revolution through 0.5 s. Find the magnetic flux density.

(0.0625T)2- If the magnetic flux density between the two poles of the magnet of a dynamo is 0.7

Tesla, and the length of its coil is 0.4 m, find the velocity of motion in such a field toobtain an induced emf in the wire equal to 1V. (3.57m/s)

3) A coil of a dynamo consists of 800 turns each of face area 0.25 m2. It rotates at a rateof 600 revolutions per minute, in a field of magnetic flux density 0.3 Tesla. Calculatethe induced emf when the angle made between the normal to the coil and the magneticflux is 30˚.

4) A rod of copper of length 30 cm moves with at velocity 0.5 m/s in a perpendicular directionto a magnetic field of density 0.8 Tesla. Calculate the emf induced in such a rod.

(1885v)

(0.12v)

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n III) Essay questions: 1) What are the factors on which the emf induced in a conductor depends ? Mention the

relation between the emf. and such factors. 2) State Faraday's law of the emf induced in a coil, then show how to verify this practically?3) What is meant by mutual induction between two coils? and what is meant by the

coefficient of mutual induction? How - using the mutual induction - one can verifyLenz's rule?

4) If a current passes through a coil, deduce an equation relating the induced emf in the coiland the rate of change of the current in the coil. From this, deduce a definition for thecoefficent of self induction and the Henry.

5) When does the emf induced in a coil become maximum ? and when does it become zero?6) Explain an experiment to show the conversion of the mechanical energy into electrical

energy, and another experiment to show the opposite conversion. Then, state the ruleused to define the direction of the current in the first case and the direction of motion inthe second case.

7) Deduce the relation by which one can evaluate the instantaneous emf induced in an ACgenerator.

8) What are the modifications introduced to the AC generator to render it a unidrectionalgenerator ?

9) Describe the structure of the electric transformer ? then explain the principle of itsopertion. What is meant by saying that the efficiency of the transformer is 80%?.

10) What is meant by the efficiency of the transformer? What are the factors which lowersuch an efficiency and how to deal with them?

11) Draw a labelled diagram showing the structure of the motor and explain its operation.

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n 5) An antenna of length one meter fixed in a motor car, which moves at velocity80km/hour in a direction perpendicular to the horizontal component of the Earth’smagnetic field. An emf of 4 x 10-4 V is induced in the antenna. In such a case,calculate the magnetic flux density of the considerd horizontal field.

(18 x 10-6T)6) Calculate the coefficient of self-induction for a coil in which an emf of 10 V is

induced if the passing current changes at a rate of 40 A/s (0.25 Henry)

7) The mutual induction between two faces of opposite coils is 0.1 Henry and theintensity of current in one of them is 4 A. If this intensity drops to zero in 0.01s, findthe emf induced in the other coil.

(40V)8) A rectangular coil of dimensions 0.4m x 0.2m and of 100 turns rotates with a uniform

velocity 500 revolutions per minute in a uniform field of magnetic flux density 0.1Tesla. The axis of rotation in the plane of the coil is perpendicular to the field.Calculate the emf induced in the coil.

(41.89 V.)9) A step-down transformer of efficiency 90% has a primary coil voltage of 200 V and

that of the secondary is 9 V. If the intensity of the electric current in the primary is 0.5A, and the number of turns of the secondary is 90 turns, what is the intensity of thecurrent of the secondary coil, and what is the number of turns of the primary?

(10 A, 1800 turns )10) A step-down transformer connected to an AC power source of 2500 V gives a

current of 80 A.The ratio between the number of turns of the primary and thesecondary coils is 20:1 Assuming that its efficiency is 80%, find the emf inducedacross the two terminals of the secondary, and find also the current in the primary coil.

(100V,4A)

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OverviewAll what we have studied so far can be lumped under the title of classical physics. By

classical, we do not mean outdated or obsolete. In fact, classical physics explainseverything in our daily life and our common experiences. The present unit, however,entails some of the basic concepts of modern physics and a general view of a quantumphysics. This branch of physics (modern or quantum) deals with a great collection ofscientific phenomena which might not be directly observed in our daily life, but treat anumber of situations in the universe which classical physics cannot explain, especiallywhen we deal with atomic and subatomic systems, i.e, down to the subatomic scale .

Also, this kind of physics explains all phenomena involved in electronics which isthe basis for all modern electronic and communication systems. It also explainschemical reactions on the level of the molecule. Some of such reactions werephotographed by Ahmed Zewail using a high speed laser camera. Such work entitledhim to earn the Noble Prize in chemistry in1999.

Blackbody Radiation:We are content so far to regard light as waves. Waves have common features, i.e,

UV visible light

wavelength (m)

Fig (12-1)Electromagnetic spectrum

Chapter 12 Wave Particle Duality

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reflection, refraction, interference and diffraction. We know also that visible light is but a

small portion of the electromagnetic (em) spectrum (Fig 12-1). Electromagnetic waves may

differ in frequency, and hence, in wavelength, but they propagate in free space at a constant

speed c = 3 x 108 m/s. Electromagnetic waves do not need necessarily a medium to

propagate in. We all observe that hot bodies emit light and heat. An example is the Sun (Fig

Fig (12-2)The Sun as a source

of em radiationFig (12-3)

A burnig charcoal emitsem radiation

Fig (12-4a)A glowing incandescentlamp emits em radiation

Fig (12-4b)A lamp emitting less

em radiation

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wave length (nm)nanometer)

Fig(12-5)The wavelength at the peak is

inversely proportional to temperature

UV visable light IR

12-2) and other stars, a burning charcoal (Fig 12-3) and a glowing incandescent lamp (Fig

12-4). We also note that the dominant color of light emitted from these sources varies.

Hence,an em source does not emit all wavelengths equally, but the intensity of radiation

varies with wavelength. The distribution of the radiation intensity with wavelength is called

Planck’s distribution (Fig 12-5). It was also found that the wavelength λm at which the peak

of the curve occurs is inversely proportional to temperature. This is known as Wien’s law.

Therefore, the higher the temperature,

the smaller the wavelength of the peak .

We also note that as the wavelength

tends to infinity (very large)or to zero

(very small ) the intensity of radiation

tends to zero. For example, the

temperature at the surface of the Sun is

6000˚K. Hence, the wavelength at the

peak is 5000˚A ( 0.5 µm). This is within

the visible range. Thus, almost 40% of

the total energy emitted by the Sun is in

the visible range and almost 50% is heat

(infrared radiation), while the rest is distributed over the remaining spectrum. We

practically obtain the same shape of radiation intensity distribution for a glowing

incandescent lamp, except that the temperature is now 3000˚K which puts the wavelength

at the peak at 1000 nm = 10-6 m = 10000˚A = 1 Micron. From such lamps we get nearly 20

% as visible light and most of the rest as heat.We cannot explain these observations using classical physics. It can be argued from

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tomography (tumor detection) (Fig 12-11), inembryology and in criminology, since the heat radiatedfrom a person lingers for a while even after the personhas left. All these applications are called remotesensing. Egypt has been a pioneer in this field. Howcan we explain the bell shape of radiation? Planck in1900 came up with the answer.

Planck called this phenomenon black body radiation.

The reason for naming it so is that a black body absorbs

all radiation falling on it, regardless of the wavelength.

It is, thus, a perfect absorber. It then re-emits this

radiation wholly. It is therefore a perfect emitter.

If we imagine an enclosed cavity with a small hole,

the inside of the cavity appears black because all of the

radiation within the cavity remains trapped due to multiple reflections. Only a small part

of it leaks out, which is called blackbody radiation (Fig 12-12).

Planck managed to explain this blackbody phenomenon with an interpretation that

Fig (12-10)An image taken by a night vision system

Fig (12-9)A night vision system

Fig (12-8)An image of southern Sinaitaken by Land sat satellites

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lity classical physics that since the radiation is an em wave, the intensity of radiation increases

with frequency. Why then should the intensity of radiation go down at the high frequencyend, (Fig 12-6)? This curve is repeated forall hot bodies which emit continuousradiation not only the Sun but also theEarth, and all bodies even living creatures.But the Earth- being a non glowing body -it absorbs the radiation from the Sun andreemits it. But its temperature is far lessthan that of the Sun. Therefore, we find thewavelength at the peak to be nearly 10Micron ,which is within the infrared region(Fig 12-7).There are satellites, and airborneas well as terrestrial equipment which mapand photograph the surface of the Earth,using different regions of the spectrumincluding the infrared radiation emitted bythe surface of the Earth ,in addition to thereflected visible light (Fig 12-8). Also,microwaves are used for the same purposein radars. Scientists analyze such images todetermine possible natural Earth resources.This technique is also used for military purposes such as night vision systems, whichdetect and image moving objects in the dark due to the heat radiation which these objectsre- emit (Figs 12-9,12-10). Thermal imaging is also used in medicine, particularly in

λ µm

Fig (12-6)Radiation decreases with increasing

frequency in disagreement withclassical expectations

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Fig (12-7)Radiation from the Earth

and from the Sun

em radiationfrom the Sun

em radiationfrom the Earthra

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tomography (tumor detection) (Fig 12-11), inembryology and in criminology, since the heat radiatedfrom a person lingers for a while even after the personhas left. All these applications are called remotesensing. Egypt has been a pioneer in this field. Howcan we explain the bell shape of radiation? Planck in1900 came up with the answer.

Planck called this phenomenon black body radiation.

The reason for naming it so is that a black body absorbs

all radiation falling on it, regardless of the wavelength.

It is, thus, a perfect absorber. It then re-emits this

radiation wholly. It is therefore a perfect emitter.

If we imagine an enclosed cavity with a small hole,

the inside of the cavity appears black because all of the

radiation within the cavity remains trapped due to multiple reflections. Only a small part

of it leaks out, which is called blackbody radiation (Fig 12-12).

Planck managed to explain this blackbody phenomenon with an interpretation that

Fig (12-10)An image taken by a night vision system

Fig (12-9)A night vision system

Fig (12-8)An image of southern Sinaitaken by Land sat satellites

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(a)

(d)

(b)

(e)

(c)

(f)Fig (12-13)

An image where each shot has a differentnumber of photons in increasing order from(a) to(f)

image taken for an object for different numbers of photons. It is worth mentioning though

that the human eye is so sensitive that it can detect as little as one photon falling on it.

Photoelectric Effect:A metal contains positive ions and free electrons which can move around inside the

metal but cannot leave it, due to the attractive forces of the surface which may berepresented by a surface potential barrier. But some of these electrons can escape ifgiven enough energy in the form of heat or light (Fig 12-14).

This is the idea behind the cathode ray tube (CRT), which is used in TV andcomputer monitors (Fig 12 -15).

This tube consists of metal surface called the cathode, which is heated by a filament.Electrons are, thus, emitted by the so called electron gun (E-gun). Due to heat, someelectrons may overcome the forces of attraction at the surface. These electrons are thenfreed (liberated) from the metal and are then picked up by the screen, which is connected

Photoelectric Effect and thermoionic effect:

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lity sounded weird at the time. He proposed that radiation was

made up of small units (or packets) of energy, each he

called quantum (or photon). Therefore, we may consider

radiation from a glowing object as a flux of emitted

photons. The photons’ energy increases with frequency,

but their number decreases with increasing energy.

The photons emanate from the vibrations of atoms. The

energy of these vibrating atoms is not continuous but

quantized (discrete or discontinuous) into levels. These

energy levels take values E=nhν, where h is Planck's

constant h=6.625x10-34 Js, and ν is the frequency (Hertz

- Hz). The atom does not radiate as long as it remains in

one energy level. But if the vibrating atom shifts from a

high energy level to a lower energy level, it emits a

photon whose energy E = hν. Thus, photons with high

frequency have high energy and those with low frequency

have low energy. Radiation consists

of billions upon billions of these

photons. We do not see separate

photons, but we observe the features

of the stream of photons as a whole.

These features express in, the stream

of photons represent the classical

properties of radiation Fig (12-13) shows an

Fig (12-11)A thermal image for the

face and neck

Fig (12-12a)Radiation inside the cavity istrapped so it appears black

Fig (12-12b)A small part of energy leaks out of the

hole which is called blackbody radiation

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(a)

(d)

(b)

(e)

(c)

(f)Fig (12-13)

An image where each shot has a differentnumber of photons in increasing order from(a) to(f)

image taken for an object for different numbers of photons. It is worth mentioning though

that the human eye is so sensitive that it can detect as little as one photon falling on it.

Photoelectric Effect:A metal contains positive ions and free electrons which can move around inside the

metal but cannot leave it, due to the attractive forces of the surface which may berepresented by a surface potential barrier. But some of these electrons can escape ifgiven enough energy in the form of heat or light (Fig 12-14).

This is the idea behind the cathode ray tube (CRT), which is used in TV andcomputer monitors (Fig 12 -15).

This tube consists of metal surface called the cathode, which is heated by a filament.Electrons are, thus, emitted by the so called electron gun (E-gun). Due to heat, someelectrons may overcome the forces of attraction at the surface. These electrons are thenfreed (liberated) from the metal and are then picked up by the screen, which is connected

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Fig (12-14c)A more tightly bound electronneeds higher energy to escape

fluorescent screen

a photon a freedelectron

energy

Fig (12-15)Light spot on a fluorescent screen(emits photons when struck by

electrons)

E-beam

E-gun

cathode grid anode plate Xplate Y lightspot

filamentheater

to a positive pole called the anode, thus causing current in the external circuit. When theelectrons hit the screen, they emit light which varies in intensity from point to point on thefluorescent screen, depending on the intensity of the electrical signal transmitted. Such asignal controls the intensity of the electron beam emitted from the E -gun through a negativegrid in its way.

The E -beam can be controlled by electric or magnetic fields to sweep the screen point by

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Fig (12-14a)Electrons may be freed from a metal

if given sufficient energy

Fig (12-14b)Minimum energy needed to free an

electron is called work function

uv radiation

zinc plate

freedelectrons

a photonAn electron barely

escaping

energy

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Fig (12-14c)A more tightly bound electronneeds higher energy to escape

fluorescent screen

a photon a freedelectron

energy

Fig (12-15)Light spot on a fluorescent screen(emits photons when struck by

electrons)

E-beam

E-gun

cathode grid anode plate Xplate Y lightspot

filamentheater

to a positive pole called the anode, thus causing current in the external circuit. When theelectrons hit the screen, they emit light which varies in intensity from point to point on thefluorescent screen, depending on the intensity of the electrical signal transmitted. Such asignal controls the intensity of the electron beam emitted from the E -gun through a negativegrid in its way.

The E -beam can be controlled by electric or magnetic fields to sweep the screen point by

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Einstein put forth an interpretation for all this, which led him to Nobel prize in 1921. Heproposed that a photon with ν > νc falling on a metallic surface , has energy hν , while theenergy needed to free an electron ( called the work function) is Ew = hνc ( Fig 12-14).

Thus, the photon is barely able to free an electron, if it has energy hν=hνc= Ew. If thephoton energy exceeds this limit, the electron is freed and the energy difference

hν -Ew is carried by the electrons as kinetic energy, i.e., it moves faster as hν increases.Whereas if hν<Ew, the electron would not be emitted at all, no matter how intense thelight might be. Also, the emission is instantaneous. There is no need for time to collectenergy. The emission takes place instantly, once hν > hνc .

It is to be noted that νc and Ew vary for different materials, and do not depend on thelight intensity, the exposure time or the voltage difference between the anode and the cathode.

Fig (12-17a)Photocurrent versus light

intensity for ν < νc

ph

otoc

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light intensity

ph

otoc

urr

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light intensity

Fig (12-17b)Photocurrent versus light

intensity for ν > νc

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lity point generating the picture,so called raster until the frame

is completed (Fig 12-15).When light falls on a cold cathode instead of heating a

filament, a current flows in the circuit too. This meanselectrons have been freed due to light. The emission ofsuch electrons due to light falling on a metallic surface is aphenomenon called photoelectric effect (Fig 12-16). Thisphenomenon cannot be explained by the classical theory oflight. Considering light as a wave, part of the light fallingon the surface of the metal is absorbed, giving someelectrons enough energy to escape. We are then up aganistcertain difficulties with the classical theory. If we attemptusing the classical model, the current intensity or theemission of such electrons (called photoelectrons) shoulddepend on the intensity of the incident wave, regardless ofits frequency. Also, the kinetic energy (or velocity) of theemitted electrons should increase with increasing intensityof the incident radiation. Even in the case of low lightintensity, giving sufficient time should give some electronsenough energy to be freed, regardless of the frequency of the incident light. But thepractical observations are contrary to these classical expectations. It has been observedthat the emission of electrons depends primarily on the frequency of the incident light noton its intensity. Such electrons are not emitted if the frequency is under a threshold(critical value) νc no matter how intense light may be. If the frequency exceeds νc,photocurrent increases with the intensity of light (Fig 12-17). Also, the kinetic energy (orvelocity) of the emitted electrons depends on the frequency of the incident wave not itsintensity.In addition, the emission of electrons occurs instantly as long as ν > νc. Theelectrons do not need time to collect energy if the light intensity is low, provided ν > νc .

Fig (12-16)Photoelectric current

achieved by absorbingphotons on a metal surface

incident light

emittedphotoelectrons

vacuum

ammeter

voltmeter

battery

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Einstein put forth an interpretation for all this, which led him to Nobel prize in 1921. Heproposed that a photon with ν > νc falling on a metallic surface , has energy hν , while theenergy needed to free an electron ( called the work function) is Ew = hνc ( Fig 12-14).

Thus, the photon is barely able to free an electron, if it has energy hν=hνc= Ew. If thephoton energy exceeds this limit, the electron is freed and the energy difference

hν -Ew is carried by the electrons as kinetic energy, i.e., it moves faster as hν increases.Whereas if hν<Ew, the electron would not be emitted at all, no matter how intense thelight might be. Also, the emission is instantaneous. There is no need for time to collectenergy. The emission takes place instantly, once hν > hνc .

It is to be noted that νc and Ew vary for different materials, and do not depend on thelight intensity, the exposure time or the voltage difference between the anode and the cathode.

Fig (12-17a)Photocurrent versus light

intensity for ν < νc

ph

otoc

urr

ent

light intensity

ph

otoc

urr

ent

light intensity

Fig (12-17b)Photocurrent versus light

intensity for ν > νc

)Photo electeric cell(

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Thus, Vs serves as a measure for KEmax. If the

photon energy is hν, we have:

hν = Ew + KEmax

KE max = hν - Ew

Thus, KEmax is directly proportional to hν,

regardness of light intensity φL (light flux is the

number of photons/s). If ν becomes νc , we have

hν=Ew, then KEmax = 0 and Vs = 0, i.e., no stopping

voltage is needed to stop the current (Fig 12-19).

constant lightintensity

constantcurrent

Fig (12-19a)Measuring KEmax for different

frequencies at constant photon flux

Fig (12-19b)A linear relation between

KEmax and ν

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1e (12-1)

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Interpretation of the photo electric effect:

To measure the velocity of photoelectrons(and their KE), we apply a negativeretarding voltage between the anode and thecathode. The magnitude of the voltage.which causes the photocurrent to cease iscalled the stopping voltage Vs. At thisvoltage, electrons barely make it to theanode.Vs is the lowest voltage that does that.The kinetic energy of electrons at the anodebecome zero. The kinetic energy at thecathode which would enable electrons tohardly reach the anode is the maximumkinetic energy at the cathode (most energeticelectrons), and hence, is called the maximumkinetic energy KEmax where e is the electroncharge since the total energy at the cathodeequals the total energy at the anode.

-eVs + KEmax

= 0

Vs = KEmax

ν > νc

constant light of

constantcurrent

stopping voltage

constant light of

Fig (12-18a)A circuit for measuring

photocurrent versus voltage

anodecathode

light

φL2

φL1constantcurrent

Fig (12-18b)Photocurrent versus voltage

for different light intensity and constantfrequency ν > νc

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Thus, Vs serves as a measure for KEmax. If the

photon energy is hν, we have:

hν = Ew + KEmax

KE max = hν - Ew

Thus, KEmax is directly proportional to hν,

regardness of light intensity φL (light flux is the

number of photons/s). If ν becomes νc , we have

hν=Ew, then KEmax = 0 and Vs = 0, i.e., no stopping

voltage is needed to stop the current (Fig 12-19).

constant lightintensity

constantcurrent

Fig (12-19a)Measuring KEmax for different

frequencies at constant photon flux

Fig (12-19b)A linear relation between

KEmax and ν

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Compton Effect

It was observed that when a photon ( X or γ rays ) collided with a free electron, thephoton frequency decreased and changed its direction. Also, the electron velocity increasedand it changed its direction (Fig 12-21). This observation could not be explained by thewave (classical) theory of light. It can be argued based on Planck,s hypothesis thatelectromagnetic radiation consists of photons which can collide with electrons as billiardballs collide. In this collision, linear momentum must be conserved (law of conservation oflinear momentum), i.e., the linear momentum before collision must equal the linearmomentum after collision. Also, the law of conservation of energy must apply, i.e., the thesum of the energy of the photon and the electron after collision must equal the sum of theenergy of the photon and the electron before collision . We must, therefore, consider aphoton as a particle with a linear momentum, i.e., it has mass and velocity as much as theelectron is a particle which has mass and velocity, and hence a linear momentum.

Photon Properties A photon is a concentrated packet of energy which has mass, velocity and linear

momentum. Its energy E = hν, it always moves at the speed of light c regardless of itsfrequency. Einstein showed that mass and energy were equivalent E = mc2.A loss of mass

Fig (12-21)

Compton effect

incident photon

scattered electron electron

scattered photon

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Fig (12-20a)Relation of photocurrent

with voltage for material A

Fig (12-20b)Relation of photocurrent with

voltage for material B

high light intensity

low light intensity

low light intensity

high light intensity

Fig (12-20c)Relation between KEmax with ν

for different materials

ν ν ν

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Compton Effect

It was observed that when a photon ( X or γ rays ) collided with a free electron, thephoton frequency decreased and changed its direction. Also, the electron velocity increasedand it changed its direction (Fig 12-21). This observation could not be explained by thewave (classical) theory of light. It can be argued based on Planck,s hypothesis thatelectromagnetic radiation consists of photons which can collide with electrons as billiardballs collide. In this collision, linear momentum must be conserved (law of conservation oflinear momentum), i.e., the linear momentum before collision must equal the linearmomentum after collision. Also, the law of conservation of energy must apply, i.e., the thesum of the energy of the photon and the electron after collision must equal the sum of theenergy of the photon and the electron before collision . We must, therefore, consider aphoton as a particle with a linear momentum, i.e., it has mass and velocity as much as theelectron is a particle which has mass and velocity, and hence a linear momentum.

Photon Properties A photon is a concentrated packet of energy which has mass, velocity and linear

momentum. Its energy E = hν, it always moves at the speed of light c regardless of itsfrequency. Einstein showed that mass and energy were equivalent E = mc2.A loss of mass

Fig (12-21)

Compton effect

incident photon

scattered electron electron

scattered photon

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(12-2)2pcPw

c2 ( ) φLhν

=

is translated to released energy as in the atomicbomb (Fig 12-22). Nuclear fission is associatedwith a small loss of mass which is converted tolarge amount of energy due to the c2(c2 = 9 x1016 m2/s2) factor. Therefore, the law ofconservation of mass and the law of theconservation of energy blend into the law ofconservation of mass and energy. Thus, aphoton whose energy is hν has a mass of hν/c2,while in motion . Since it is moving at velocityc, its momentum which is the product of massand velocity becomes hν/c . If a beam ofphotons is incident on a certain surface at the rate of φL (photons/s,), then each photonimpinges on the surface and bounces off, and hence, suffers a change in linear momentum2mc. The force which a beam of photons applies to the surface is the change in linearmomentum per second:

F = 2mcφL

F =

where Pw is the power in watts of the light incident on the surface. This force is toosmall to be noticed. But it is appreciable if it affects a free electron instead, due to its smallmass and size, so it throws it off. This is the explanation of Compton effect. In themicroscopic model, we can image a phaton as a sphere whose radius is roughly equal to λand oscillates at frequency ν. The stream of photons collectively has a magnetic field andan electric field. These two fields are perpendicular to one another and to the direction ofpropagation.Both oscillate at ν. The photon flux (or stream) carries the energy of the wave.The wave properties are ,thus, manifested by the photon stream as a whole. The wave

Fig (12-22)Atomic bomb

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eye nasalcavity

ear

earcavityskull

braintissue

Fig (12-23b)A CT scan image of the head

Fig (12-23d)A CT scan image of the

abdomen

Fig (12-23c)An image of blood vessels

using X- rays and a dye

intestines

kidneyspine

lever

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Thus, the wavelength is Planck’s constant divided by the linear momentum PL. It

should be noted that when photons fall on a surface, a comparison is made between λ and

the interatomic distance of the surface. If λ is greater than the interatomic distance, these

photons sense the surface as a continuous one and get reflected from it as in wave theory.

If the interatomic distance is comparable to λ, photons penetrate through the atoms. This

is what happens in the case of X- rays.

ExampleCalculate the photon mass and linear momentum if λ = 380 nm

Solution

= 7.89 x1014 Hz

= 5.81x10-36 kg

= 1.74 x10-27 kgm/s

Wave properties of a particle In the universe, there is a great deal of symmetry. If waves have particle nature, could

it be that particles might have wave properties ? a question posed by De Broglie in 1923led to a hypothesis of wave particle duality applying to particles. The wavelength of aparticle must be in analogy with a photon

λ = h/PL

where pL is the linear momentum of the particle.

(6.625 x 10-34 Js)(380) (1x10-9m)

PL = h/λ =

(3x108 m/s)(380) (1x10-9m)

ν = c/λ =

(6.625 x 10-34 Js) (7.89x1014 s-1)(3x108m/s)2m= E/c2 = hν/c2 =

(12 − 4)

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Magnetic Ressonance Imaging (MRI) is another method of tomography. Instead ofusing X- ray with their possibly harmful side effects, radio(RF) waves are used. It has theability to detect tumors, and it depends also on making computerized image slices. Thepatient lies on a moving bed surrounded by a strong (superconductive) magnet. Areceiving detector is used to receiving RF waves from hydrogen nuclei in the body . Thestrong magnet orients the spins of the nuclei, RF waves produced by a source disturb thisspin orientation . Such waves are then stopped. As nuclei relax to their original state, theyemit RF waves which are received by the detector. The computer reconstructs the imagesshowing the concentration of hydrogen, and hence water collections, indicating tumors(Fig 12-24). Superconducting magnets are useful in reducing the heat due to eddy currents.

ExampleCalculate the force applied by a beam of light whose power is 1W on the surface of a wall.

Solution

This force is too diminutive to affect the wall

Relation between photon wavelength and its linear momentumλ = c/ν

Multiplying the numerator by h

λ = =

PL = mc

= c

=

∴ λ =

F = = = 0.67 x 10-8 N2 x 13 x 108

2 Pwc ∴

hchν

hhν/c

hνc2

hνc

(12-3)

hPL

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Thus, the wavelength is Planck’s constant divided by the linear momentum PL. It

should be noted that when photons fall on a surface, a comparison is made between λ and

the interatomic distance of the surface. If λ is greater than the interatomic distance, these

photons sense the surface as a continuous one and get reflected from it as in wave theory.

If the interatomic distance is comparable to λ, photons penetrate through the atoms. This

is what happens in the case of X- rays.

ExampleCalculate the photon mass and linear momentum if λ = 380 nm

Solution

= 7.89 x1014 Hz

= 5.81x10-36 kg

= 1.74 x10-27 kgm/s

Wave properties of a particle In the universe, there is a great deal of symmetry. If waves have particle nature, could

it be that particles might have wave properties ? a question posed by De Broglie in 1923led to a hypothesis of wave particle duality applying to particles. The wavelength of aparticle must be in analogy with a photon

λ = h/PL

where pL is the linear momentum of the particle.

(6.625 x 10-34 Js)(380) (1x10-9m)

PL = h/λ =

(3x108 m/s)(380) (1x10-9m)

ν = c/λ =

(6.625 x 10-34 Js) (7.89x1014 s-1)(3x108m/s)2m= E/c2 = hν/c2 =

(12 − 4)

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Magnetic Ressonance Imaging (MRI) is another method of tomography. Instead ofusing X- ray with their possibly harmful side effects, radio(RF) waves are used. It has theability to detect tumors, and it depends also on making computerized image slices. Thepatient lies on a moving bed surrounded by a strong (superconductive) magnet. Areceiving detector is used to receiving RF waves from hydrogen nuclei in the body . Thestrong magnet orients the spins of the nuclei, RF waves produced by a source disturb thisspin orientation . Such waves are then stopped. As nuclei relax to their original state, theyemit RF waves which are received by the detector. The computer reconstructs the imagesshowing the concentration of hydrogen, and hence water collections, indicating tumors(Fig 12-24). Superconducting magnets are useful in reducing the heat due to eddy currents.

ExampleCalculate the force applied by a beam of light whose power is 1W on the surface of a wall.

Solution

This force is too diminutive to affect the wall

Relation between photon wavelength and its linear momentumλ = c/ν

Multiplying the numerator by h

λ = =

PL = mc

= c

=

∴ λ =

F = = = 0.67 x 10-8 N2 x 13 x 108

2 Pwc ∴

hchν

hhν/c

hνc2

hνc

(12-3)

hPL

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source ofelectrons

screenFig (12-25b)Calculation of the path difference between two

e-rays through a double slit

double slitsource ofelectrons

screen

intensity distribution

Fig (12-25a)Diffraction of electrons through a double slit

But what does this mean? Weconsider light as a huge stream ofphotons. Photons collectively have awave property accompanying them,thus, manifesting reflection,refraction, interference anddiffraction.The wave intensitydescribes the photon concentractionas if a photon carries the genes oflight, regarding frequency, speed andwavelength. By the same token, an electron ray (e-beam) is a huge stream of electrons.Collectively, there must be a wave accompanying them. An electron carries the genes ofthe stream, regarding charge, spin and linear momentum. The accompanying wave haswavelength λ The intensity of the accompanying wave describes the electronconcentration. Such a wave can disperse, reflect, refract, interfere and diffract, just as lightdoes (Fig 12-25). But does this mean we can use an electron ray as much as we use a lightray in a microscope? The answer is yes. This answer is verified by the discovery of theelectron microscope.

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path which has an integral multiple of λ , or else the

path over which a standing wave is formed (Fig

12-27), or the path over which ψ2 is maximum (Fig

12-26 b).

Electron Microscope

Electron microscope is an important labinstrument which depends in its operation onthe wave nature of electrons. It resembles anoptical microscope in many ways. Theimportant difference is in the resolvingpower. The e-microscope has a highresolving power, because the electrons cancarry a high kinetic energy, and hence veryshort λ (equation 12-3). Thus, itsmagnification is so high that it can detectvery small objects, so small that an ordinaryoptical microscope fails to observe(Fig 12-28).

The optical microscope uses light, whilethe e-microscope uses an electron beam. Theelectron beam might have a wavelength 1000times or more shorter than visible light.

Therefore, the electron-microscope candistinguish fine details. The lenses used ine-microscope are usually magnetic. Theselenses focus the e-beam. Their design fallsunder the topic of electron optics.

Fig (12-27c)An orbit as a standing wave

formed over a string fixed at both ends

opticalmicroscope

electronmicroscope

source

lens

object

objectiveimage

image

projectionlens

screen orphotographic

plate

Fig (12-28a)Electron microscope

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with the nucleus is zero (so the electron does not fall on the nucleus or else the universewould vanish). Also, the probability for an electron to exist infinitely away from the nucleusis zero, or else the atom is ionized by itself. Ionization needs external energy. We concludethat the energy of the electron when trapped in an atom is less than that of a free electron bythe magnitude of the ionization energy. Therefore, an electron remains trapped in the atom,unless acted upon by an external stimulus. Heisenberg showed also that we could notdetermine an exact path (orbit) for an electron in an atom. But we can say that an orbit is the

Fig (12-27a)An orbit is an integer of λ as a traveling wave ina closed path whose end coincides with its start

Fig (12-27b)The order of the orbit is

determined by the integer value

Neuclus

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path which has an integral multiple of λ , or else the

path over which a standing wave is formed (Fig

12-27), or the path over which ψ2 is maximum (Fig

12-26 b).

Electron Microscope

Electron microscope is an important labinstrument which depends in its operation onthe wave nature of electrons. It resembles anoptical microscope in many ways. Theimportant difference is in the resolvingpower. The e-microscope has a highresolving power, because the electrons cancarry a high kinetic energy, and hence veryshort λ (equation 12-3). Thus, itsmagnification is so high that it can detectvery small objects, so small that an ordinaryoptical microscope fails to observe(Fig 12-28).

The optical microscope uses light, whilethe e-microscope uses an electron beam. Theelectron beam might have a wavelength 1000times or more shorter than visible light.

Therefore, the electron-microscope candistinguish fine details. The lenses used ine-microscope are usually magnetic. Theselenses focus the e-beam. Their design fallsunder the topic of electron optics.

Fig (12-27c)An orbit as a standing wave

formed over a string fixed at both ends

opticalmicroscope

electronmicroscope

source

lens

object

objectiveimage

image

projectionlens

screen orphotographic

plate

Fig (12-28a)Electron microscope

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Quantum Mechanics

The interpretation of previous observations has paved the way to a new set of laws of

mechanics, namely, Quantum Mechanics. This branch of science is based on the following

assumptions formed by Schrodinger:

1) An electron in an atom has energy values which belong to a set of allowable values

called energy levels. The atom does not emit energy unless it falls from a high level to a

lower level.

2) Such emission is in the form of a photon whose energy hν is equal to the difference

between the two energy levels. This process is called relaxation.

3) The absorption of energy by an atom occurs if the photon energy is exactly equal to the

energy difference between two levels . In this case, the atom is excited by having its

electron move up in energy to the higher level. This process is called excitation .

4) If the photon energy is greater than the ionization energy of the atom, an electron is

totally freed from the parent atom, and the atom becomes ionized (ion).

5) Relaxation and excitation are simultaneous processes. At thermal equilibrium, the atom

is stable due to the balance and simultaneity of these processes.

6) There is a function which is always positive that describes the electron in the atom. This

functions tends to zero at the nucleus and at infinity (at the border of the atom).

Therefore, the electron remains trapped within the atom due to nuclear attraction

without falling onto the nucleus. To explain this, we may say that as the electron draws

near the nucleus, its velocity increases so much that it flies away (back off). It was also

found that the assumptions of quantum mechanics agree with experimental observations

in all cases when electrons are tightly bound in a limited size. However, if the size is

extensive, then classical mechanics may be used.

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In a Nutshell

• Classical physics cannot explain many phenomena, particularly those in which light ( orem radiation) interacts with electrons or atoms.

• Light or any em radiation consists of a huge collection of photons, each photon havingenergy hν, where h is Planck’s constant and ν is the frequency.

• An evidence for photons is the photoelectric effect, where photocurrent depends on theintensity of incident light as long as the frequency is greater than a critical value νc. Butif the frequency is less than νc , no photocurrent flows. The kinetic energy of theelectron freed by the photoelectric effect depends on the frequency not on the lightintensity.

• A photon has a mass, a linear momentum and a constant speed which is the speed oflight. It has a size denoted by the wavelength. If a photon falls on a wall, it applies asmall force on it, but if it falls on an electron, the electron will be thrown off due to itssmall mass and size.

• Compton effect proves the particle nature of photons, where a photon has mass, speedand linear momentum.

• A wave describes the collective behavior of photons.• The wavelength of a photon is Planck’s constant divided by the linear momentum. The

same relation applies to a free particle, where the wavelength describes the wave natureof the particle ,i.e., the wave accompanying the particle.

• The electron microscope proves de Broglie relation for particles. It is used to detectdiminutive particles.

• Quantum mechanics is based on assumptions which agree with experimentalobservations, for the cases when an electron is trapped within a limited confinement.While classical physics applies when the electron is free to move or when the continingsize is extensive.

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Fig (12-28b) Head of a fly as seen by

an e-microscopeFig (12-28c)

Uranium atoms as seen by a specialtype of e-microscopes

Fig (12-28d)Rubella virus as seen by an

e-microscope (white spots are on thesurface of the infected cells)

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Quantum Mechanics

The interpretation of previous observations has paved the way to a new set of laws of

mechanics, namely, Quantum Mechanics. This branch of science is based on the following

assumptions formed by Schrodinger:

1) An electron in an atom has energy values which belong to a set of allowable values

called energy levels. The atom does not emit energy unless it falls from a high level to a

lower level.

2) Such emission is in the form of a photon whose energy hν is equal to the difference

between the two energy levels. This process is called relaxation.

3) The absorption of energy by an atom occurs if the photon energy is exactly equal to the

energy difference between two levels . In this case, the atom is excited by having its

electron move up in energy to the higher level. This process is called excitation .

4) If the photon energy is greater than the ionization energy of the atom, an electron is

totally freed from the parent atom, and the atom becomes ionized (ion).

5) Relaxation and excitation are simultaneous processes. At thermal equilibrium, the atom

is stable due to the balance and simultaneity of these processes.

6) There is a function which is always positive that describes the electron in the atom. This

functions tends to zero at the nucleus and at infinity (at the border of the atom).

Therefore, the electron remains trapped within the atom due to nuclear attraction

without falling onto the nucleus. To explain this, we may say that as the electron draws

near the nucleus, its velocity increases so much that it flies away (back off). It was also

found that the assumptions of quantum mechanics agree with experimental observations

in all cases when electrons are tightly bound in a limited size. However, if the size is

extensive, then classical mechanics may be used.

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whose mass is 10 kg , what happens if the object is an electron and why ?

II) Essay questions

1) Show why the wave theory failed to explain the photoelectric effect, and how Einstein

managed to interpret the experimental results of this phenomenon.

2) Show how to verify the particle nature of light from the blackbody radiation .

3) Explain the Compton effect and show how it proves the particle nature of light ?

0.67x10-3N

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Can you identify the contribution of each of the following scientists to modern physics ?

Schrodinger

Planck Einstein

Heisenberg

de Broglie

Compton

Bohr

Thompson

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I)Drills

1) Calculate the energy of a photon whose wavelength is 770 nm and find its mass and

linear momentum?

(2.58x10-19J , 0.29x10-35kg , 0.86x10-27kgm/s)

2) Calculate the mass of an X- ray photon and a γ ray photon if the wavelength of X-ray is

100 nm , and that of γ-ray is 0.05 nm

(mX=2.2 X10-35kg , mγ=4.4x10-32kg)

3) Calculate the wavelength of a ball whose mass is 140 kg which moves at velocity 40

m/s. Also, calculate the wavelength of an electron if it has the same velocity.

(λ=1.18x10-37m , λe=1.8 x10-5m)

4) A radio station emits a wave whose frequency is 92.4 MHz. Calculate the energy of

each photon emitted from this station. Also, calculate the rate of photons φL if the

power of the station is 100 kW.

(E=612.15x10-28J , φL=16.3 x1029 s-1)

5) An electron is under a potential difference 20 kV. Calculate its velocity upon collision

with the anode from the law of conservation of energy. The electron charge is 1.6 x 10-19C,

its mass is 9.1 x 10-31 kg. Then calculate λ and PL.

(v=0.838x108m/s , λ=0.868x10-11m , PL=7.625x10-23kgm/s)

6) If the least distance detected with an electron microscope is 1nm, calculate the velocity

of the electrons and the potential of the anode.

(velocity=0.725x106m/s , V=1.5Volt)

7) Calculate the force by which an e-beam whose power is 100 kW affects an object

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whose mass is 10 kg , what happens if the object is an electron and why ?

II) Essay questions

1) Show why the wave theory failed to explain the photoelectric effect, and how Einstein

managed to interpret the experimental results of this phenomenon.

2) Show how to verify the particle nature of light from the blackbody radiation .

3) Explain the Compton effect and show how it proves the particle nature of light ?

0.67x10-3N

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spectra of the atoms of all elements would have been continuous. This is contrary to allexperimental observations.The spectra of the elements have a discrete nature, and arecalled line spectra, i.e., occurring at wavelengths characteristic of the element.

Fig (13 – 4a )Apparatus for studying the spectra of the elements

Fig (13 – 4b )Spectra of some elements

gas slit prism screen

potentialdifference

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Bohr’s Model (1913)

Bohr studied the difficulties faced by Rutherford’s model,and proposed a model for the hydrogen atom building onRutherford’s findings :1) At the center of the atom there is a positively charged

nucleus .2) Negatively charged electrons move around the nucleus in

shells. Each shell (loosely often called orbit) has an energyvalue. Electrons do not emit radiation as long as they remainin each shell (Fig 13 – 5).

3) The atom is electrically neutral, since the number ofelectrons around the nucleus equals the number ofpositive charges in the nucleus.

Fig ( 13-5a)Bohr’s Model

first shell

second shell

En

ergy

free electron levelcontinuous levels

Bohr

Fig (13-5b)Energy levels

1

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OverviewThe word atom goes back to a Greek origin, meaning the indivisible. Different models forthe atom have been put forth since then by many great scientists based on manyexperimental evidences.

a) Thompson’s Atom (1898) 1 – After Thompson conducted several experiments leading to the discovery of theelectron and the determination of the ratio for the electron, he put forth a model of asolid positively charged substance in which negative electrons were immersed (Fig13–1).2 – Since the atom is neutral, the sum of the negative charge is equal to the sum of thepositive charge.

b) Rutherford’s Atom (1911)Rutherford performed his well known experiment based on which he formulated a modelfor the structure of the atom and showed that it was not solid.In his experiment, Rutherford bombarded a thin gold plate (10-4cm) with a beam of alphaparticles (4He2) (Fig 13 – 2 a, b).

Atomic SpectraChapter 13

Fig (13-1)Thompson’s

atomic model Rutherford

eme

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Emission of Light from Bohr’s Atom.

1) When hydrogen atoms are stimulated (given energy) not all of them are excited the sameway. Thus, electrons in different atoms move from the first level K (n = 1) to differenthigher levels (n = 2, 3, 4..)

2) Electrons remain in excited levels (or states) only for a short period of time ,calledlifetime (nearly 10-8s), then they revert to the lowest level (ground state).

3) In going down from level E2 to level E1 , the electron emits a photon whose energyhν = E2 - E1 : where ν is the frequency of the photon and its wavelength is :

4) The line spectrum of hydrogen consists of a particular energy value, and hence aparticular frequency.

Fig (13 – 7)Standing waves

Fig (13 – 6)Electron transitions

between atomic levels

cνλ =

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He then added three more postulates:1) If an electron moves from an outer shell of energy E2 to an inner shell of energy E1 (E2 > E1 ), an amount of energy E2 – E1 is released in the form of a photon, whoseenergy hν = E2 – E1, where ν is the frequency of the emitted photon (Fig 13 – 6).

2) The electric (Coulomb’s) forces and mechanical (Newton’s) forces are at work in theatom.3) We can estimate the radius of the shell by considering that the wave accompanying theelectron forms a standing wave (Fig 13 – 7 ).(calculate the orbit radius for n = 1, 2, 3,)

Fig (13-5c)Absorption of photons

ener

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emittedphoton

absorbedphoton unabsorbed

photon

Fig (13 - 5d)Emissin of photons

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Different series of atomic spectral lines for hydrogen are produced, and are arranged asfollows (Fig 13 – 8):

1) Leyman’s series: where the electron moves down tolevel K (n = 1) from higher levels. This series liesin the ultraviolet range (short wavelengths andhigh frequencies).

2) Balmer’s series: where the electron moves down to

Fig (13 – 8 b)Atomic model for

hydrogen spectrum spect

Fig (13 – 8 a)Atomic spectral series for hydrogen

Pfund’sseries

Brackett’sseries

Paschen’sseries

Balmer’sseries

Lyman’s series

Leyman’sseries

Balmer’sseries

K

ultraviolet

IR

paschen’s

series

P

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N

M

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paschen’sseries

n= n=6

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Fig (13 – 9b)Spectrometer schematic

level L (n = 2) from higher levels. This series lies in the visible range. 3) Paschen’s series: where the electron moves down to level M (n = 3) from higher

levels. This series lies in the infrared (IR) range.4) Bracket’s series: where the electron moves down to level N (n = 4) from higher

levels. This series lies in the IR range.5) Pfund’s series: where the electron moves down to level O (n = 5) from higher levels.

This series lies in the far IR and is the longest wavelengths ( the lowest frequencies)among the line spectrum of hydrogen.

SpectrometerTo obtain a pure spectrum, a spectrometer is

used (Fig 13 – 9). It consists of 3 parts :1) a source of rays : a light source in front of

which there is a slit whose width can beadjusted by a screw. This slit is at the focalpoint of a convex lens.

sourceslit

prism

violet

red

yellow

Fig (13 – 9a)Spectrometer

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Different series of atomic spectral lines for hydrogen are produced, and are arranged asfollows (Fig 13 – 8):

1) Leyman’s series: where the electron moves down tolevel K (n = 1) from higher levels. This series liesin the ultraviolet range (short wavelengths andhigh frequencies).

2) Balmer’s series: where the electron moves down to

Fig (13 – 8 b)Atomic model for

hydrogen spectrum spect

Fig (13 – 8 a)Atomic spectral series for hydrogen

Pfund’sseries

Brackett’sseries

Paschen’sseries

Balmer’sseries

Lyman’s series

Leyman’sseries

Balmer’sseries

K

ultraviolet

IR

paschen’s

series

P

Q

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M

L

paschen’sseries

n= n=6

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Fig (13 – 9b)Spectrometer schematic

level L (n = 2) from higher levels. This series lies in the visible range. 3) Paschen’s series: where the electron moves down to level M (n = 3) from higher

levels. This series lies in the infrared (IR) range.4) Bracket’s series: where the electron moves down to level N (n = 4) from higher

levels. This series lies in the IR range.5) Pfund’s series: where the electron moves down to level O (n = 5) from higher levels.

This series lies in the far IR and is the longest wavelengths ( the lowest frequencies)among the line spectrum of hydrogen.

SpectrometerTo obtain a pure spectrum, a spectrometer is

used (Fig 13 – 9). It consists of 3 parts :1) a source of rays : a light source in front of

which there is a slit whose width can beadjusted by a screw. This slit is at the focalpoint of a convex lens.

sourceslit

prism

violet

red

yellow

Fig (13 – 9a)Spectrometer

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2) a turntable on which a prism is placed.3) a telescope consisting of two convex lenses (objective and eye

piece).To use the spectrometer for obtaining a pure spectrum, the slit is lit

with bright light falling from the slit onto the prism at the minimumangle of deviation. The telescope is directed to receive the lightpassing through the telescope.The objective focuses the raysbelonging to the same color at the focal plane of the lens . That ishow we obtain a sharp (pure) spectrum.

From studying the line spectra of different elements whose atoms are excited , wenotice different types of spectra (continuous and line) :- the spectrum consisting of all wavelengths in a continuous manner is called the

continuous spectrum.- the spectrum occurring at specified frequencies and not continuously distributed is called

the line spectrum. Alternatively, they may be divided as emission and absorption spectra :- the spectrum resulting from the transfer of excited atoms from a high level to lower level

Fraunhofer

Fig (13-9c)Use of a spectrometer to measure the temperature

of the stars and their gases

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is called the emission spectrum.- It was found experimentally that when white light passes through a certain gas, some

wavelengths in the continuous spectrum are missing. These wavelengths are the same asthose which appear in the emission spectrum of the gas (Fig 13 – 9) . This type ofspectrum is called the absorption spectrum. Fraunhofer lines in the solar spectrum areexamples of the absorption spectrum of the elements in the Sun, basically helium andhydrogen.

X-raysWhat are X-rays ?

They are invisible electromagnetic waves of short wavelength (10-13 – 10-8m) betweenuv and gamma rays. They were first discovered by Rontgen. He called it so (the unknownrays) because he did not know what they were .

Properties of X-rays:- They can penetrate media easily .- They can ionize gases .- They diffract in crystals . - They affect sensitive photographic plates .

Fig (13 – 10)Emission line spectra for some elements

atomichydrogen

barium

mercury

sodium

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2) a turntable on which a prism is placed.3) a telescope consisting of two convex lenses (objective and eye

piece).To use the spectrometer for obtaining a pure spectrum, the slit is lit

with bright light falling from the slit onto the prism at the minimumangle of deviation. The telescope is directed to receive the lightpassing through the telescope.The objective focuses the raysbelonging to the same color at the focal plane of the lens . That ishow we obtain a sharp (pure) spectrum.

From studying the line spectra of different elements whose atoms are excited , wenotice different types of spectra (continuous and line) :- the spectrum consisting of all wavelengths in a continuous manner is called the

continuous spectrum.- the spectrum occurring at specified frequencies and not continuously distributed is called

the line spectrum. Alternatively, they may be divided as emission and absorption spectra :- the spectrum resulting from the transfer of excited atoms from a high level to lower level

Fraunhofer

Fig (13-9c)Use of a spectrometer to measure the temperature

of the stars and their gases

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is called the emission spectrum.- It was found experimentally that when white light passes through a certain gas, some

wavelengths in the continuous spectrum are missing. These wavelengths are the same asthose which appear in the emission spectrum of the gas (Fig 13 – 9) . This type ofspectrum is called the absorption spectrum. Fraunhofer lines in the solar spectrum areexamples of the absorption spectrum of the elements in the Sun, basically helium andhydrogen.

X-raysWhat are X-rays ?

They are invisible electromagnetic waves of short wavelength (10-13 – 10-8m) betweenuv and gamma rays. They were first discovered by Rontgen. He called it so (the unknownrays) because he did not know what they were .

Properties of X-rays:- They can penetrate media easily .- They can ionize gases .- They diffract in crystals . - They affect sensitive photographic plates .

Fig (13 – 10)Emission line spectra for some elements

atomichydrogen

barium

mercury

sodium

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Coolidge TubeThis is used to produce X-rays. When the filament is

heated, electrons are produced and directed at the targetunder the influence of the electric field,which gives themhigh energy, depending on the voltage difference betweenthe target and the hot filament. When an electron collideswith the tungsten target, part- if not all- of its energy isconverted to X-rays (Fig 13 – 11).

Spectrum of X-raysAnalyzing a beam of X-rays generated from a target to

components of different wavelengths, we find that the

spectrum consists of two parts :

a) the continuous spectrum of all wavelengths (within a

certain range) regardless of the target material.

b) the line spectrum corresponding to certain wavelengths

characteristic of the target material, called the

characteristic X-ray radiation.

Interpretation of X-ray generation

a) characteristic radiation

The line spectrum is generated when an electron collides with an electron close to thenucleus of the target material atom. If the latter electron receives sufficient energy, itjumps to a higher level, or leaves the atom altogether, and is replaced by another electron

Fig(13 –11)Coolidge tube

cooling fins

copper rod

vacuum tube

high dcvoltage

X rays hotfilament

heating source

targe

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target

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Coolidge TubeThis is used to produce X-rays. When the filament is

heated, electrons are produced and directed at the targetunder the influence of the electric field,which gives themhigh energy, depending on the voltage difference betweenthe target and the hot filament. When an electron collideswith the tungsten target, part- if not all- of its energy isconverted to X-rays (Fig 13 – 11).

Spectrum of X-raysAnalyzing a beam of X-rays generated from a target to

components of different wavelengths, we find that the

spectrum consists of two parts :

a) the continuous spectrum of all wavelengths (within a

certain range) regardless of the target material.

b) the line spectrum corresponding to certain wavelengths

characteristic of the target material, called the

characteristic X-ray radiation.

Interpretation of X-ray generation

a) characteristic radiation

The line spectrum is generated when an electron collides with an electron close to thenucleus of the target material atom. If the latter electron receives sufficient energy, itjumps to a higher level, or leaves the atom altogether, and is replaced by another electron

Fig(13 –11)Coolidge tube

cooling fins

copper rod

vacuum tube

high dcvoltage

X rays hotfilament

heating source

targe

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target

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Fig (13 – 13)Use of X-rays in studying crystals

energy continually due to the braking effect of the surrounding electrons, giving rise to

electromagnetic radiation covering all different possible wavelengths, since the electron

loses energy gradually. This is the origin of the continuous radiation of X-rays.

Important Applications of X-rays1) One of the important features of X-rays is diffraction, as they penetrate materials. That

is why X-rays are used in studying the crystalline structure of materials (Fig 13 – 13).The atoms in the crystal act as a diffraction grating (which is a generalization of

diffraction from a double slit). Bright and dark fringes form, depending on the

difference in the optical path.

X-ray tube anode

high DCvoltage

X-rays

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2) X- rays have a great penetrating power.

This is why they are used to detect defects in metallic

structures.3) X- rays are used in imaging bones and fractures and

some other medical diagnosis (Fig 13 – 14).

Fig (13 – 14) An X-ray image for the chest

rib spinal cord

chest heart lung

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Fig (13 – 13)Use of X-rays in studying crystals

energy continually due to the braking effect of the surrounding electrons, giving rise to

electromagnetic radiation covering all different possible wavelengths, since the electron

loses energy gradually. This is the origin of the continuous radiation of X-rays.

Important Applications of X-rays1) One of the important features of X-rays is diffraction, as they penetrate materials. That

is why X-rays are used in studying the crystalline structure of materials (Fig 13 – 13).The atoms in the crystal act as a diffraction grating (which is a generalization of

diffraction from a double slit). Bright and dark fringes form, depending on the

difference in the optical path.

X-ray tube anode

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2) X- rays have a great penetrating power.

This is why they are used to detect defects in metallic

structures.3) X- rays are used in imaging bones and fractures and

some other medical diagnosis (Fig 13 – 14).

Fig (13 – 14) An X-ray image for the chest

rib spinal cord

chest heart lung

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In a Nutshell

·• Bohr’s postulates and model of the hydrogen atom : When an electron jumps from a high level to a lower level, it produces radiation in the

form of a photon of frequency ν and energy hν, which is equal to the differencebetween the two levels

hν = E2 – E1, E2 > E1 .

·• The line spectrum of hydrogen consists of 5 series. Each line corresponds to a definiteenergy difference, frequency and wavelength

Lyman uvBalmer visiblePaschen IR (infrared)Brackett IRPfund far IR

·• The spectrometer is an apparatus used to decompose light to its components (visibleand invisible)

·• X-rays are an invisible radiation of short wavelengths, first discovered by Rontgen(1895).He called them the unknown (X) rays

·• X-ray diffraction is used in studying the crystalline structure, and also in the industrialand medical applications.

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Fig (14-1)Spontaneous emission

Excitation by absorption ofenergy from an external source

Relaxation to a lower level after alifetime and release of excitation

energy

Chapter 14 Laser

OverviewRarely has any discovery left an impact on applied science as the discovery of laser has

done. Soon after its discovery, laser has been introduced into optics, biology, chemistry,medicine and engineering especially communications.

The word laser is an acronym for Light Amplification by Stimulated Emission ofRadiation. In 1960, Maiman built the first laser out of chromium-doped Ruby. Later,He-Ne laser was manufactured along with other types of lasers.

Spontaneous Emission and Stimulated EmissionThe atom has energy levels, the lowest of which is called ground state(E1) in which the

atom initially exists. The atom may be excited to one of higher states E2, E3 etc.

If we shine a photon with energy hν = E2– E1 on the atom, the atom absorbs this photon

and gets excited to E2. Soon enough after a lifetime (nearly 10-8 s), the atom gets rid of this

excitation energy in the form of a photon and goes back to its original state (Fig 14 -1).

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Laser

This type of radiation is called spontaneous radiation. It is the type of radiation common

in ordinary light sources. The emitted photon has the same frequency and energy as the

photon that caused the excitation . But the phase and direction are arbitrary. In 1917,

Einstein showed that in addition to spontaneous radiation, there is another type of

radiation, called stimulated emission (the dominant emission in lasers). If a photon of

energy E2-E1 falls on an excited atom at level E2 before the lifetime is over, this photon

pushes the atom back to the ground state, and hence, the atom radiates the excitation

energy in the form of a photon of the same frequency, phase and direction of the falling

photon. (Fig 14–2).

Thus, throughout stimulated radiation, there are two types of photons; the stimulatingand the stimulated photons moving together at the same frequency, phase and direction.

The emission of photons from the atoms of the material in this way renders thesephotons coherent and collimated for long distances. They are highly concentrated, and

Fig (14-2)Stimulated emission

Relaxation to a lower leveldue to an external photonbefore its lifetime is over

A photon passes by an

excited atom

incident photon

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- occurs where an external photonstimulates excited atoms to emitthe energy difference is the formof a photon before the lifetimeinterval is over.

- The emitted photons are monochromatic(single) wavelength.

- The emitted photons are coherentand propagate in one direction as acollimated parallel beam.

- The intensity remains constant over longdistances contrary to the inversesquare law. It has been possible tosend a laser beam to the Moon andreceive it back, without much loseses,despite the long distance involved.Spreading effect is nil and limitedscattering takes place.

- This is the dominant radiation inlaser sources.

- occurs when the atom relaxes froman excited state to a lower state,emitting spontaneously the energydifference in the form of a photonwithout the effect of an externalphoton. It occurs after the lifetimeinterval is over.

- The emitted photons have awide range of wavelengths.

- The emitted photons propagaterandomly

- The intensity of photonsdecreases according to theinverse square law. This iscalled spreading. Whilecollisions with particles iscalled scattering. In ordinarylight sources both spreadingand scattering occur.

- This is the dominant radiationin ordinary light sources.

1

2

3

4

5

Spontaneous emission Stimulated emissions

remain unspread and unscattered, unlike photons emitted spontaneously.The following table gives a comparison between spontaneous and stimulated emissions :

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This type of radiation is called spontaneous radiation. It is the type of radiation common

in ordinary light sources. The emitted photon has the same frequency and energy as the

photon that caused the excitation . But the phase and direction are arbitrary. In 1917,

Einstein showed that in addition to spontaneous radiation, there is another type of

radiation, called stimulated emission (the dominant emission in lasers). If a photon of

energy E2-E1 falls on an excited atom at level E2 before the lifetime is over, this photon

pushes the atom back to the ground state, and hence, the atom radiates the excitation

energy in the form of a photon of the same frequency, phase and direction of the falling

photon. (Fig 14–2).

Thus, throughout stimulated radiation, there are two types of photons; the stimulatingand the stimulated photons moving together at the same frequency, phase and direction.

The emission of photons from the atoms of the material in this way renders thesephotons coherent and collimated for long distances. They are highly concentrated, and

Fig (14-2)Stimulated emission

Relaxation to a lower leveldue to an external photonbefore its lifetime is over

A photon passes by an

excited atom

incident photon

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- occurs where an external photonstimulates excited atoms to emitthe energy difference is the formof a photon before the lifetimeinterval is over.

- The emitted photons are monochromatic(single) wavelength.

- The emitted photons are coherentand propagate in one direction as acollimated parallel beam.

- The intensity remains constant over longdistances contrary to the inversesquare law. It has been possible tosend a laser beam to the Moon andreceive it back, without much loseses,despite the long distance involved.Spreading effect is nil and limitedscattering takes place.

- This is the dominant radiation inlaser sources.

- occurs when the atom relaxes froman excited state to a lower state,emitting spontaneously the energydifference in the form of a photonwithout the effect of an externalphoton. It occurs after the lifetimeinterval is over.

- The emitted photons have awide range of wavelengths.

- The emitted photons propagaterandomly

- The intensity of photonsdecreases according to theinverse square law. This iscalled spreading. Whilecollisions with particles iscalled scattering. In ordinarylight sources both spreadingand scattering occur.

- This is the dominant radiationin ordinary light sources.

1

2

3

4

5

Spontaneous emission Stimulated emissions

remain unspread and unscattered, unlike photons emitted spontaneously.The following table gives a comparison between spontaneous and stimulated emissions :

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an ordinary light source isscattered during propagation

laser light travels in parallel rays for longdistances without much scattering

ordinary light source

Fig (14-4a)Scattering of an ordinary light source and a laser

Fig (14-4b)Launching a laser beam from the Earth to a reflector on the

surface of the Moon, 380000 km away

laser source

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Properties of a laser beam

1) Monochromaticity: Each line in the visible spectrum in ordinary light sources includesa band of wavelengths (this is why the ordinary color appears to have different shades tothe naked eye). The intensity of each wavelength in this band width is shown inFig (14–3a). A laser source emits one spectral line with a very limited bandwidth andthe intensity is concentrated at the wavelength of that spectral line Fig (14–3b), hence itis called monochromatic.

Fig (14-3a)Spectral width for an ordinary

monochromatic light source Fig (14-3b)Spectral width for

a laser source

ligh

t in

tens

ity

ligh

t in

tens

ity

(φL)max

φLφL

λ

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an ordinary light source isscattered during propagation

laser light travels in parallel rays for longdistances without much scattering

ordinary light source

Fig (14-4a)Scattering of an ordinary light source and a laser

Fig (14-4b)Launching a laser beam from the Earth to a reflector on the

surface of the Moon, 380000 km away

laser source

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2) Collimation : In ordinary light sources, the diameter of the emitted light beam increaseswith distance , where in lasers, the diameter stays constant for long distances withoutmuch unscattering. Thus ,energy is transmitted without much losses .

3) Coherence: Photons of ordinary light sources propagate randomly or incoherently.They emanate at different instants of time, and have inconsistent and varying phase. Inlasers, however, photons emanate coherently both in time and place, since they comeout together at the same time sequence, and maintains the same phase differencethroughout, during propagation over long distances. This makes radiation intense andfocused.

4) Intensity: Light produced by ordinary sources is subject to the inverse square law, since theintensity of radiation falling on unit area decreases, the further away from the light source,due to spreading (Fig 14-4a). The laser rays falling on a unit surface are unspread. Theymaintain a constant intensity and are not subject to the inverse squarelaw.

Fig (14-4c)Measuring astronomical

distances by a laser beam

Fig (14-4d)Measuring the distance between the Moonand the Earth by the reflection of a laser

beam from a reflector on the lunar surface

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Theory of the Laser Action:

Laser action depends on driving the atoms or molecules of the active medium into a

state of population inversion, while maintaining a form of dynamic equilibrium. In this

state, the number of atoms in the excited state exceeds the number of atoms in the lower

The intensity of ordinary lightdecreases with distance from the

source due to the inverse square law

incoherent light

coherent light

Fig (14-5)Coherence

Fig (14-6)Laser light maintains the same

intensity as it propagates

low lightintensityhigh light

intensity

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2) Collimation : In ordinary light sources, the diameter of the emitted light beam increaseswith distance , where in lasers, the diameter stays constant for long distances withoutmuch unscattering. Thus ,energy is transmitted without much losses .

3) Coherence: Photons of ordinary light sources propagate randomly or incoherently.They emanate at different instants of time, and have inconsistent and varying phase. Inlasers, however, photons emanate coherently both in time and place, since they comeout together at the same time sequence, and maintains the same phase differencethroughout, during propagation over long distances. This makes radiation intense andfocused.

4) Intensity: Light produced by ordinary sources is subject to the inverse square law, since theintensity of radiation falling on unit area decreases, the further away from the light source,due to spreading (Fig 14-4a). The laser rays falling on a unit surface are unspread. Theymaintain a constant intensity and are not subject to the inverse squarelaw.

Fig (14-4c)Measuring astronomical

distances by a laser beam

Fig (14-4d)Measuring the distance between the Moonand the Earth by the reflection of a laser

beam from a reflector on the lunar surface

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Theory of the Laser Action:

Laser action depends on driving the atoms or molecules of the active medium into a

state of population inversion, while maintaining a form of dynamic equilibrium. In this

state, the number of atoms in the excited state exceeds the number of atoms in the lower

The intensity of ordinary lightdecreases with distance from the

source due to the inverse square law

incoherent light

coherent light

Fig (14-5)Coherence

Fig (14-6)Laser light maintains the same

intensity as it propagates

low lightintensityhigh light

intensity

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state. Thus, when stimulated emission occurs, it will be amplified as photons are increased

in number going back and forth in the active medium, due to multiple reflections between

two enclosing mirrors. In so doing, more and more excited atoms are poised to generate

stimulated emission, which is further amplified and so on. This is the origin of

amplification of the laser (Fig 14–7), called laser action .

Main Components of a Laser

Despite the variations in size, type and frequency, three common elements must exist in

any laser:

1) Active medium: This can be a crystalline solid (e.g. ruby), semiconductor (chapter15) a

liquid dye, gas atoms (e.g. He – Ne laser), ionized gases (e.g. Argon laser), or

molecular gases (e.g. CO2 laser).

2) Sources of energy responsible for exciting the active medium as follows :

(a) excitation by electrical energy, either by using radio frequency (RF) waves or by

using electric discharge under high DC voltage gas lasers:( HeNe – Ar – CO2).

(b) excitation by optical energy, also known as optical pumping, which can be done

either by flash lamps (e.g. in ruby laser) or using a laser beam as a source of energy

(liquid dye laser).

(c) thermal excitation, by using the thermal effects resulting from the kinetic energy of

gases to excite the active material (e.g. in He-Ne laser).

(d) excitation by chemical energy as chemical reactions between giving gases energy to

stimulate atoms toward lasing (e.g. the reaction between hydrogen and fluorine or

the reaction between Deuterium fluoride and CO2 ) .

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3) Resonant cavity is the container and the activating catalyst for amplification . It can be

one of two types :

(a) external resonant cavity in the form of two parallel mirrors enclosing the active

medium permitting multiple reflections leading to amplification as in gas lasers

(Fig 14 – 7a).

b) internal resonant cavity where the ends of the active material are polished so as to act

as mirrors as in ruby laser (Fig 14 – 7b). One of the two mirrors is semitransparent

to allow some of the laser radiation to leak out (Fig 14 – 8).

two reflectingmirrors

Fig (14-7a)External resonant cavity

the two polished ends ofthe active medium act as

mirrors

Fig (14-7b)Internal resonant cavity

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state. Thus, when stimulated emission occurs, it will be amplified as photons are increased

in number going back and forth in the active medium, due to multiple reflections between

two enclosing mirrors. In so doing, more and more excited atoms are poised to generate

stimulated emission, which is further amplified and so on. This is the origin of

amplification of the laser (Fig 14–7), called laser action .

Main Components of a Laser

Despite the variations in size, type and frequency, three common elements must exist in

any laser:

1) Active medium: This can be a crystalline solid (e.g. ruby), semiconductor (chapter15) a

liquid dye, gas atoms (e.g. He – Ne laser), ionized gases (e.g. Argon laser), or

molecular gases (e.g. CO2 laser).

2) Sources of energy responsible for exciting the active medium as follows :

(a) excitation by electrical energy, either by using radio frequency (RF) waves or by

using electric discharge under high DC voltage gas lasers:( HeNe – Ar – CO2).

(b) excitation by optical energy, also known as optical pumping, which can be done

either by flash lamps (e.g. in ruby laser) or using a laser beam as a source of energy

(liquid dye laser).

(c) thermal excitation, by using the thermal effects resulting from the kinetic energy of

gases to excite the active material (e.g. in He-Ne laser).

(d) excitation by chemical energy as chemical reactions between giving gases energy to

stimulate atoms toward lasing (e.g. the reaction between hydrogen and fluorine or

the reaction between Deuterium fluoride and CO2 ) .

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3) Resonant cavity is the container and the activating catalyst for amplification . It can be

one of two types :

(a) external resonant cavity in the form of two parallel mirrors enclosing the active

medium permitting multiple reflections leading to amplification as in gas lasers

(Fig 14 – 7a).

b) internal resonant cavity where the ends of the active material are polished so as to act

as mirrors as in ruby laser (Fig 14 – 7b). One of the two mirrors is semitransparent

to allow some of the laser radiation to leak out (Fig 14 – 8).

two reflectingmirrors

Fig (14-7a)External resonant cavity

the two polished ends ofthe active medium act as

mirrors

Fig (14-7b)Internal resonant cavity

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a

b

c

d

e

Fig (14-8a)Stimulated emission by an external photon

relaxing electron

emitted photon

incident photon

after excitation

incident photon

excitedelectron

before excitation

higher level

ground statenormal condition

inverted population

a photon approacheswhich causes excitation

stimulated emission is generated

recurrence of stimulated emission

Fig (14-8b)Laser action

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unexcited condition

excited condition

metastable state

incident photon hν =E2 - E1

incident photon

emitted photon

Fig (14-8c)Population inversion through a third

metastable state

a

b

c

d

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a

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c

d

e

Fig (14-8a)Stimulated emission by an external photon

relaxing electron

emitted photon

incident photon

after excitation

incident photon

excitedelectron

before excitation

higher level

ground statenormal condition

inverted population

a photon approacheswhich causes excitation

stimulated emission is generated

recurrence of stimulated emission

Fig (14-8b)Laser action

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unexcited condition

excited condition

metastable state

incident photon hν =E2 - E1

incident photon

emitted photon

Fig (14-8c)Population inversion through a third

metastable state

a

b

c

d

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mirror glass tube excited atomsemitransparent

mirror

Fig (14-8e)Amplification by

multiple reflections

Fig (14-8f)Output radiation from the semitransparent mirror

Fig (14-8d)Multiple reflections between the two mirrors

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Helium – Neon (He – Ne) laserThese two elements have been selected due to the

near equality of the values of the same metastable

excited energy levels in these two elements.

(a) Construction of He-Ne laser :1) A quartz tube including a mixture of helium and

neon in the ratio 10 : 1 at a low pressure of nearly 0.6

mm Hg (Fig 14 – 9).

2) At both ends of the tube there are two plane or concave

parallel mirrors which are perpendicular to the tube axis.

One has a reflection coefficient of nearly 99.5%, while

the other mirror is semitransparent with a reflection

coefficient of 98%.

3) High frequency electric field feeding the tube from the

outside to excite the helium and neon atoms, or a high

DC voltage difference inside the tube causing electric

discharge.

(b) Operation :1) The voltage difference inside the tube leads to the excitation of the helium atoms to

higher levels (Fig 14 – 10).

2) The excited helium atoms collide with the unexcited neon atoms inelastic collisions.

Thus, energy is transferred from the excited helium atoms to the neon atoms due to the

near equality of the excited levels in both atoms. Neon atoms are, thus, excited.

Fig (14-9a)He – Ne laser schematic

mirror laser beamvacuum tube

Fig (14-9b)He – Ne laser

window

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mirror glass tube excited atomsemitransparent

mirror

Fig (14-8e)Amplification by

multiple reflections

Fig (14-8f)Output radiation from the semitransparent mirror

Fig (14-8d)Multiple reflections between the two mirrors

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Helium – Neon (He – Ne) laserThese two elements have been selected due to the

near equality of the values of the same metastable

excited energy levels in these two elements.

(a) Construction of He-Ne laser :1) A quartz tube including a mixture of helium and

neon in the ratio 10 : 1 at a low pressure of nearly 0.6

mm Hg (Fig 14 – 9).

2) At both ends of the tube there are two plane or concave

parallel mirrors which are perpendicular to the tube axis.

One has a reflection coefficient of nearly 99.5%, while

the other mirror is semitransparent with a reflection

coefficient of 98%.

3) High frequency electric field feeding the tube from the

outside to excite the helium and neon atoms, or a high

DC voltage difference inside the tube causing electric

discharge.

(b) Operation :1) The voltage difference inside the tube leads to the excitation of the helium atoms to

higher levels (Fig 14 – 10).

2) The excited helium atoms collide with the unexcited neon atoms inelastic collisions.

Thus, energy is transferred from the excited helium atoms to the neon atoms due to the

near equality of the excited levels in both atoms. Neon atoms are, thus, excited.

Fig (14-9a)He – Ne laser schematic

mirror laser beamvacuum tube

Fig (14-9b)He – Ne laser

window

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3) An accumulation of excited neon atoms

ensues. The excited level of a neon atom has arelatively long lifetime (nearly 10-3s). Such alevel is called metastable state. Hence,population inversion occurs in neon atoms.

4) A group of neon atoms that are excited relaxto a lower excited state. In so doing, they emitspontaneous photons, which have energyequal to the difference in energy levels. Then,photons propagate randomly in all directionsinside the tube.

5) Photons which propagate along the axis of thetube are reflected back by one of the two

He Ne

collisionsof atoms

rapiddecay rapid

decay

collisions with thewalls of the container

excitation ofelectrons

ener

gy

Fig (14-10b)Transitions between energy levels in He-Ne laser

ground state

Fig (14-10a)He – Ne laser energy levels

metastable state

laserbeam

rapiddecay

excitationby

collisions

energytransfer

bycollisionsbetweenHe and

Ne atoms

groundstateNeHe

ener

gy

energy

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mirrors in its way, they bounce off inside the tube and cannot get out.

6) During the propagation of these photons inside the tube between the two mirrors, they

may well collide with some neon atoms in the excited metastable state, well before

lifetime is over. Thus, they stimulate the neon atoms to emit photons of the same energy

and direction as the colliding photon. Thus, the number of photons moving inside the

tube multiplies.

7) The new stream of photons repeat the excursion, and thus, they remultiply by the lasing

action. This is how amplification takes place .

8) When radiation inside the tube reaches a certain level, we let it out partially through the

semitransparent mirror, while the rest of the radiation remains trapped inside the tube.

The stimulated emission and the lasing action go on.

9) As to the neon atoms which have relaxed to a lower level, soon enough they lose further

whatever left of their energy in different forms, and finally go back to the ground state.

Helium atoms collide again with neon atoms, and the cycle repeats.

10) As to the helium atoms which have lost their energy by collision, they regain energy

through the electric discharge and so on.

Laser applicationsToday there are different types and sizes of lasers. Laser light covers different regions of

the electromagnetic spectrum from visible to uv and IR. Some laser systems can focus a

laser beam in a small spot, where energy might get so high as to melt - and even evaporate

- iron, or pierce diamond. There are lasers which may have enough energy to destroy

missiles and planes in what is termed Star War. Some applications of lasers also include

holography (Fig 14 - 11) and medical applications.

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3) An accumulation of excited neon atoms

ensues. The excited level of a neon atom has arelatively long lifetime (nearly 10-3s). Such alevel is called metastable state. Hence,population inversion occurs in neon atoms.

4) A group of neon atoms that are excited relaxto a lower excited state. In so doing, they emitspontaneous photons, which have energyequal to the difference in energy levels. Then,photons propagate randomly in all directionsinside the tube.

5) Photons which propagate along the axis of thetube are reflected back by one of the two

He Ne

collisionsof atoms

rapiddecay rapid

decay

collisions with thewalls of the container

excitation ofelectrons

ener

gy

Fig (14-10b)Transitions between energy levels in He-Ne laser

ground state

Fig (14-10a)He – Ne laser energy levels

metastable state

laserbeam

rapiddecay

excitationby

collisions

energytransfer

bycollisionsbetweenHe and

Ne atoms

groundstateNeHe

ener

gy

energy

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mirrors in its way, they bounce off inside the tube and cannot get out.

6) During the propagation of these photons inside the tube between the two mirrors, they

may well collide with some neon atoms in the excited metastable state, well before

lifetime is over. Thus, they stimulate the neon atoms to emit photons of the same energy

and direction as the colliding photon. Thus, the number of photons moving inside the

tube multiplies.

7) The new stream of photons repeat the excursion, and thus, they remultiply by the lasing

action. This is how amplification takes place .

8) When radiation inside the tube reaches a certain level, we let it out partially through the

semitransparent mirror, while the rest of the radiation remains trapped inside the tube.

The stimulated emission and the lasing action go on.

9) As to the neon atoms which have relaxed to a lower level, soon enough they lose further

whatever left of their energy in different forms, and finally go back to the ground state.

Helium atoms collide again with neon atoms, and the cycle repeats.

10) As to the helium atoms which have lost their energy by collision, they regain energy

through the electric discharge and so on.

Laser applicationsToday there are different types and sizes of lasers. Laser light covers different regions of

the electromagnetic spectrum from visible to uv and IR. Some laser systems can focus a

laser beam in a small spot, where energy might get so high as to melt - and even evaporate

- iron, or pierce diamond. There are lasers which may have enough energy to destroy

missiles and planes in what is termed Star War. Some applications of lasers also include

holography (Fig 14 - 11) and medical applications.

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a) Holography:Images of objects are formed by collecting rays reflected from them. An image

represents variations in the intensity of light from point to point. But is light intensity all

there is to it in the information about an image? If we have two rays leaving off an

illuminated object at two points on it, there is a difference in intensity alright (proportional

to the square of the amplitude of the wave). But in addition, there is a path difference

between the two lit points and the corresponding points on the photographic plate where

the image is recorded due to the topology of the object. Thus, the waves leaving off the

object carry information in both amplitude and phase (phase difference = x path

difference). The photographic plate records only the intensity (square of the amplitude) and

does not record the phase. That is why a 2D image does not carry the 3D detail. In other

words, a plane image has only half the truth (only the intensity). In 1948, a Hungarian

scientist Gabor (Nobel prize laurette) proposed a method to obtain the component that is

missing from the information in the image and retrieve it from the beam, using another

beam of the same wavelength called the reference beam. A laser beam is split into two

beams. One is used to illuminate the object, and the other is used as the reference beam.

The reflected beam and the reference beam meet at the photographic plate, and interference

takes place. After the photographic plate is developed, resulting interference fringes appear

coded, and we call such an image a hologram. Illuminating a hologram with a laser of the

same wavelength and looking through it with the naked eye, we see an identical 3D image

of the object without using any lenses. The full information (intensity and phase) is now

retrieved due to the coherence nature of the laser. Fig (14 – 12) shows the optical system

used to obtain a hologram using a laser beam. Tens of photos may be stored in one

hologram. We may also obtain 3D images in holograms of moving objects.

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Types of hologramsA hologram is a kind of diffraction grating which is a

generalization of a double slit, where interference occurs

between the penetrating waves. To make a hologram, the

object is illuminated with a laser light. The reflected rays

are recorded on the holographic plate, while at the same

time the reference beam is recorded. Interference pattern is

formed and a hologram is developed the same way as a

photographic plate. To read a hologram, a laser beam is

used in the same direction as the laser beam during

recording. The light rays read out the patterns formed on the

hologram, giving an imge as if the object is seen from that

angle, Looking through the hologram in the direction

opposite to the reference beam, a virtual image is seen as if the object lay behind the

hologram, i.e., on the beam side. We can also see a real image in the direction opposite to

the reference beam, .i.e.,on the same side of the observer, if a screen or smoke is used,

where a 3D image may be formed in space (Fig 14–11). What we described above is the

transmission hologram, which is lit from behind (Fig 14–12). It may be lit also by an

ordinary light source, but the image will have many colors. There are yet other types of

holograms such as the reflection hologram, which is lit up front, in which ordinary light may also

be used. There is also embossed hologram. Like the reflection hologram, it may be lit up front,

i.e., on the observer side, and uses ordinary light. It may be considered as a transmission hologram

Fig (14-11)Hologram generates

a 3D image

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a) Holography:Images of objects are formed by collecting rays reflected from them. An image

represents variations in the intensity of light from point to point. But is light intensity all

there is to it in the information about an image? If we have two rays leaving off an

illuminated object at two points on it, there is a difference in intensity alright (proportional

to the square of the amplitude of the wave). But in addition, there is a path difference

between the two lit points and the corresponding points on the photographic plate where

the image is recorded due to the topology of the object. Thus, the waves leaving off the

object carry information in both amplitude and phase (phase difference = x path

difference). The photographic plate records only the intensity (square of the amplitude) and

does not record the phase. That is why a 2D image does not carry the 3D detail. In other

words, a plane image has only half the truth (only the intensity). In 1948, a Hungarian

scientist Gabor (Nobel prize laurette) proposed a method to obtain the component that is

missing from the information in the image and retrieve it from the beam, using another

beam of the same wavelength called the reference beam. A laser beam is split into two

beams. One is used to illuminate the object, and the other is used as the reference beam.

The reflected beam and the reference beam meet at the photographic plate, and interference

takes place. After the photographic plate is developed, resulting interference fringes appear

coded, and we call such an image a hologram. Illuminating a hologram with a laser of the

same wavelength and looking through it with the naked eye, we see an identical 3D image

of the object without using any lenses. The full information (intensity and phase) is now

retrieved due to the coherence nature of the laser. Fig (14 – 12) shows the optical system

used to obtain a hologram using a laser beam. Tens of photos may be stored in one

hologram. We may also obtain 3D images in holograms of moving objects.

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Types of hologramsA hologram is a kind of diffraction grating which is a

generalization of a double slit, where interference occurs

between the penetrating waves. To make a hologram, the

object is illuminated with a laser light. The reflected rays

are recorded on the holographic plate, while at the same

time the reference beam is recorded. Interference pattern is

formed and a hologram is developed the same way as a

photographic plate. To read a hologram, a laser beam is

used in the same direction as the laser beam during

recording. The light rays read out the patterns formed on the

hologram, giving an imge as if the object is seen from that

angle, Looking through the hologram in the direction

opposite to the reference beam, a virtual image is seen as if the object lay behind the

hologram, i.e., on the beam side. We can also see a real image in the direction opposite to

the reference beam, .i.e.,on the same side of the observer, if a screen or smoke is used,

where a 3D image may be formed in space (Fig 14–11). What we described above is the

transmission hologram, which is lit from behind (Fig 14–12). It may be lit also by an

ordinary light source, but the image will have many colors. There are yet other types of

holograms such as the reflection hologram, which is lit up front, in which ordinary light may also

be used. There is also embossed hologram. Like the reflection hologram, it may be lit up front,

i.e., on the observer side, and uses ordinary light. It may be considered as a transmission hologram

Fig (14-11)Hologram generates

a 3D image

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with a mirror behind. It is a cheap alternative to a hologram. There is also pulse hologram,which uses powerful laser pulses. Holograms can be made of people and moving objects atsuccessive times, which may lead to the future 3D movies (Fig 14 – 13).

Fig (14-12a)Hologram formation

Fig (14-12b)Hologram as a grating

referencerays

referencerays

mirror

object

hologramreal image virtual image

hologram

Fig (14-13)Successive stationary shots giving

an illusion of motion

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b) Lasers in medicine:The retina contains light sensitive cells. In case of

retinal detachment, part of the retinal loses its function.

Unless quickly treated, the eye may lose sight

completely. In early stages, the eye may be treated by

reconnecting the detached part with the layer underneath.

This used to be a strenuous and delicate operation.

Nowadays, lasers are used for that purpose Fig (14 – 14).

The operation takes less time and efford than before. The

thermal heat from the laser cauterizes the points of

detachment (endothermy). Lasers are also used to treat

cases of far and near sightedness, so the patient can

dispose with glasses Fig (14-15). Other applications of

lasers in medicine include endoscopy, where lasers with

optical fibers are used for diagnosis and even operative

surgery (Fig 14-16).

Other applications of laserc) communications , where optical fibers carry information - loaded laser beam instead of

a wire carring electrical signals.

d) industry, particularly fine industries.

e) military applications include precision guidance , smart bombs and laser radar

(LADAR).

f) CD recording (Fig 14 – 17).

Fig (14-14) Use of a laser beam in

treating retinal detachment

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with a mirror behind. It is a cheap alternative to a hologram. There is also pulse hologram,which uses powerful laser pulses. Holograms can be made of people and moving objects atsuccessive times, which may lead to the future 3D movies (Fig 14 – 13).

Fig (14-12a)Hologram formation

Fig (14-12b)Hologram as a grating

referencerays

referencerays

mirror

object

hologramreal image virtual image

hologram

Fig (14-13)Successive stationary shots giving

an illusion of motion

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b) Lasers in medicine:The retina contains light sensitive cells. In case of

retinal detachment, part of the retinal loses its function.

Unless quickly treated, the eye may lose sight

completely. In early stages, the eye may be treated by

reconnecting the detached part with the layer underneath.

This used to be a strenuous and delicate operation.

Nowadays, lasers are used for that purpose Fig (14 – 14).

The operation takes less time and efford than before. The

thermal heat from the laser cauterizes the points of

detachment (endothermy). Lasers are also used to treat

cases of far and near sightedness, so the patient can

dispose with glasses Fig (14-15). Other applications of

lasers in medicine include endoscopy, where lasers with

optical fibers are used for diagnosis and even operative

surgery (Fig 14-16).

Other applications of laserc) communications , where optical fibers carry information - loaded laser beam instead of

a wire carring electrical signals.

d) industry, particularly fine industries.

e) military applications include precision guidance , smart bombs and laser radar

(LADAR).

f) CD recording (Fig 14 – 17).

Fig (14-14) Use of a laser beam in

treating retinal detachment

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g) laser printing where a laser beam is used to carry information

from the computer to a drum coated by a photosensitive

material. A toner is used to print off from the drum onto paper

(Fig 14-18).

h) arts and laser shows (Fig 14-19).

i) surveying (determining dimensions and areas).

j) space research.

Fig (14-15)Cornea treatment by a

laser

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Fig (14-16)Use of lasers in endoscopy

Fig (14-17a)Use of a laser in writing on CDs

pit

pitless arealaser

lensback side

mirror

lensdetector

glass plate

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g) laser printing where a laser beam is used to carry information

from the computer to a drum coated by a photosensitive

material. A toner is used to print off from the drum onto paper

(Fig 14-18).

h) arts and laser shows (Fig 14-19).

i) surveying (determining dimensions and areas).

j) space research.

Fig (14-15)Cornea treatment by a

laser

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Fig (14-16)Use of lasers in endoscopy

Fig (14-17a)Use of a laser in writing on CDs

pit

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lensback side

mirror

lensdetector

glass plate

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Fig (14-17b)CDs

Fig (14-18)Use of a laser in printing

(Fig (14-19)Laser show

scanning with laser drum covered with alight sensitive material

informationstart

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In a Nutshell• Spontaneous emission:

It is the emission from one excited atom as it relaxes from a high energy level to a low

energy level after its lifetime interval is over and under no external stimulus.

• Stimulated emission:

It is the emission from one excited atom as a result of a collision with an external

photon, which has the same energy as the one that caused it to be excited. Photons at the

end , come out in coherence ,i.e.,having the same phase, (direction and frequency).

• Properties of a laser beam :

1 ) spectral purity (monochromatic).

2 ) collimation (parallel rays).

3 ) coherence (same phase and direction).

4 ) concentration (high intensity and small diameter).

• Laser action :

1) the active medium must be in the state of population inversion .

2) emission of radiation for the excited atom through the stimulated emission.

3) amplification of stimulated emission through the resonant cavity

• Basic elements of a laser :

1 ) an active medium.

2 ) a source of energy (pumping).

3 ) a resonant cavity.

• He - Ne laser is a gas laser:

in which the active medium is a mixture of helium and neon in the ratio 10 : 1

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Fig (14-17b)CDs

Fig (14-18)Use of a laser in printing

(Fig (14-19)Laser show

scanning with laser drum covered with alight sensitive material

informationstart

laser

light intensitycontroller

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In a Nutshell• Spontaneous emission:

It is the emission from one excited atom as it relaxes from a high energy level to a low

energy level after its lifetime interval is over and under no external stimulus.

• Stimulated emission:

It is the emission from one excited atom as a result of a collision with an external

photon, which has the same energy as the one that caused it to be excited. Photons at the

end , come out in coherence ,i.e.,having the same phase, (direction and frequency).

• Properties of a laser beam :

1 ) spectral purity (monochromatic).

2 ) collimation (parallel rays).

3 ) coherence (same phase and direction).

4 ) concentration (high intensity and small diameter).

• Laser action :

1) the active medium must be in the state of population inversion .

2) emission of radiation for the excited atom through the stimulated emission.

3) amplification of stimulated emission through the resonant cavity

• Basic elements of a laser :

1 ) an active medium.

2 ) a source of energy (pumping).

3 ) a resonant cavity.

• He - Ne laser is a gas laser:

in which the active medium is a mixture of helium and neon in the ratio 10 : 1

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• Laser applications:

1 ) 3D photography (holography).2 ) medicine (e.g. treating retinal detachment).3 ) communications.4 ) industry.5 ) military applications.6) CD recording7) printing8) arts and shows9) surveying10) space research

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1- What is meant by laser ?2- Compare between spontaneous emission and stimulated emission operation - wise and

feature - wise. 3- Laser light has special characteristics which distinguish it from ordinary light .

Discuss this statement . 4- Discuss clearly the laser action .5- What is meant by optical pumping and population inversion?6- What is the role of the resonant cavity in laser operation ?7- Lasers have 3 main components, what are they ?8- On what basis have helium and neon been chosen as an active medium in He - Ne

laser ?9- What is the role of helium in He - Ne laser ? 10- Explain clearly how a laser beam is generated in He - Ne laser .11- Explain how holography works using lasers . 12- Lasers are used extensively in medicine. Discuss one of its applications . 13- Lasers play an important role in missile guidance in modern warfare. Why is laser

used as such?

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• Laser applications:

1 ) 3D photography (holography).2 ) medicine (e.g. treating retinal detachment).3 ) communications.4 ) industry.5 ) military applications.6) CD recording7) printing8) arts and shows9) surveying10) space research

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1- What is meant by laser ?2- Compare between spontaneous emission and stimulated emission operation - wise and

feature - wise. 3- Laser light has special characteristics which distinguish it from ordinary light .

Discuss this statement . 4- Discuss clearly the laser action .5- What is meant by optical pumping and population inversion?6- What is the role of the resonant cavity in laser operation ?7- Lasers have 3 main components, what are they ?8- On what basis have helium and neon been chosen as an active medium in He - Ne

laser ?9- What is the role of helium in He - Ne laser ? 10- Explain clearly how a laser beam is generated in He - Ne laser .11- Explain how holography works using lasers . 12- Lasers are used extensively in medicine. Discuss one of its applications . 13- Lasers play an important role in missile guidance in modern warfare. Why is laser

used as such?

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Overview:The world witnesses a tremendous mushrooming in the field of electronics and

communication to the point where they have become an insignia for this era. Electronics

and communication are now indispensible in our life. TV, cellular (mobile) phone ,

computer, satellites and other systems are evidences for the vast progress in the

applications of electronics and communications, whether in business, e-government,

information technology(IT), entertainment or culture. They have become also an essential

ingredient in modern warfare. Weapons do not fare from the point of view of fire power

only, but guidance, surveillance, monitoring jamming and deception ,called electronic

counter measures (or ECM) play an important role in combat. Also, in medicine whether in

diagnois, prognosis, or operations, electronics plays a key role. In short, there is no single

field in all walks of life where electronics has no part, starting from e –games to e– warfare.

Therefore, you must attain a certain level of awareness about electronics – simplified as it

may be, yet essential regardless of the prospective career you might end up with.

Origin of electronics:The word electronics stems from the electron. Electronics describes the behavior of electrons.

There are two states for an electron: a free electron and a bound electron. The free electron – as

in the case of CRT- is subject to classical physics. A bound electron – however – is subject to

quantum physics. The binding of an electron might be within an atom, a molecule or the bulk of

matter. Matter has different forms : gas, liquid, solid or plasma (when the gases are ionized as

in the fluorescent lamp). Matter in each form consists of molecules. What distinguishes states of

Modern ElectronicsChapter 15

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level and the excited level. If the electron goes back to a lower level, it emits energy in the

form of a photon. The probability of finding an electron in a particular excited level

decreases as the energy of that level increases. There is a balance between the process of

excitation and the process of relaxation, noting that the electron tends to go back to the

ground state.

Pure Semiconductors:There are three types of materials from the point of view of

electrical conductivity. Conductors conduct electricity and heat

easily (as in metals). Insulators do not conduct electricity and heat

(as in wood and plastics). Semiconductors are in between. At

absolute zero, they act as insulators, whereas as temperature

increases ,their conductivity increases (as in silicon).

Silicon is one of the important and common elements in the

universe. It exists in sand (SiO2) and rocks of the Earth’s crust. But

crystals of pure silicon consist of silicon atoms bound together in covalent bonds. A crystal is a

regular arrangement of atoms in the solid state. A silicon atom has four electrons in the

outermost shell (Fig 15 – 1). Therefore, each silicon atom shares 4 electrons with 4 neighboring

atoms, so that the outer shell of each is complete on sharing basis to contain 8 electrons each

(Fig 15 – 2 a,b). We must distinguish here between two types of electrons in silicon. The first

type is the innermost (tightly bound) electrons, which are strongly attracted to their parents

atoms. The second type is the valence electrons, which have more freedom to move across

interatomic distances. They exist in the outermost shell. At low temperatures (Fig 15 - 2c), all

bonds in the crystal are intact (unbroken).

In this case – unlike metals – there are no free electrons. But as temperature increases,

Fig (15-1)A silicon atom

Core

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Fig (15-3b)As temperature increasesmore bonds are broken

Fig (15-3a)Breaking a bond requires

energy

generation ofan electronhole pair

recombinationof an electron

hole pair

thermal energy

freeelectron

thermalenergy

Fig (15-2a)Each atom shareselectrons with its

neighbors

Fig (15-2b)Covalent bonds. We may

represent a Si atom (-14 e)around (+14 e) nucleus as a core

(+4e) and (-4e ) in the outer shell

+4e Core

Fig (15-2c)Silicon crystal at T=0˚K

all bonds are intact

some bonds, are broken and electrons are freed. Such an electron leaves behind a vacancy

in the broken bond.This vacancy is called a hole (Fig 15 – 3). Because the atom is neutral,

then the absence of an electron entails the appearance of a positive charge. We, thus, say

that the hole has a positive charge. We do not call a silicon atom which loses an electron

from its bond an ion, because soon enough, this atom may capture a free electron or an

electron from another bond to fill its own vacancy. Then, the atom returns neutral, and the

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matter apart is the intermolecular distance. In the case of a solid, this distance is very small. In

the case of a gas, this distance is large. In the case of a liquid, it is somewhere in between. If we

consider the solid state, the atoms or molecules of matter get close enough to each other within a

certain distance due to the forces of attraction between them. If we imagine that they are made to

get close, then the forces of repulsion act in to prevent further proximity. Thus, the interatomic

distance represents a point of equilibrium (or balance) between the forces of attraction and the

forces of repulsion among the atoms. It is to be noted that these atoms oscillate around their

equilibrium positions due to heat. But they are separated by space. We cannot see this space by

our naked eye, because the interatomic distance is much smaller than the wavelength of the

photons of visible light to which our eyes are sensitive.

An electron in an atom:An electron in an atom is considered a bound electron. It cannot depart on its own. It

needs energy to do that. This energy is called the ionization energy, i.e., the energy of an

electron in bondage is less than its energy when free by this amount. That is why the

electron remains in bondage in the first place. This energy is called the binding energy. It is

the cause of keeping the atom stable. The electron in the atom has a set of discrete energy

levels according to Bohr’s model. It occupies one of the allowable levels and cannot have

an energy value in between. The electron in the atom is governed by the laws of quantum

mechanics. That is why the probability of having an electron fall onto the nucleus, or

having the electron outside the atom (without external help) is zero. What binds the electron

to the nucleus is the electric force of attraction.

As long as the electron remains in one energy level, it does not gain or lose energy. But if

the electron acquires energy by absorption, it is excited to a higher energy level, provided

the energy absorbed is exactly equal to the energy difference between the original (ground)

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level and the excited level. If the electron goes back to a lower level, it emits energy in the

form of a photon. The probability of finding an electron in a particular excited level

decreases as the energy of that level increases. There is a balance between the process of

excitation and the process of relaxation, noting that the electron tends to go back to the

ground state.

Pure Semiconductors:There are three types of materials from the point of view of

electrical conductivity. Conductors conduct electricity and heat

easily (as in metals). Insulators do not conduct electricity and heat

(as in wood and plastics). Semiconductors are in between. At

absolute zero, they act as insulators, whereas as temperature

increases ,their conductivity increases (as in silicon).

Silicon is one of the important and common elements in the

universe. It exists in sand (SiO2) and rocks of the Earth’s crust. But

crystals of pure silicon consist of silicon atoms bound together in covalent bonds. A crystal is a

regular arrangement of atoms in the solid state. A silicon atom has four electrons in the

outermost shell (Fig 15 – 1). Therefore, each silicon atom shares 4 electrons with 4 neighboring

atoms, so that the outer shell of each is complete on sharing basis to contain 8 electrons each

(Fig 15 – 2 a,b). We must distinguish here between two types of electrons in silicon. The first

type is the innermost (tightly bound) electrons, which are strongly attracted to their parents

atoms. The second type is the valence electrons, which have more freedom to move across

interatomic distances. They exist in the outermost shell. At low temperatures (Fig 15 - 2c), all

bonds in the crystal are intact (unbroken).

In this case – unlike metals – there are no free electrons. But as temperature increases,

Fig (15-1)A silicon atom

Core

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broken bond is mended, and the hole shifts somewhere else, and so on.

As the temperature increases, the number of free electrons and holes increases, noting

that the number of free electrons equals the number of free holes in a pure semiconductor.

But a state of dynamic equilibrium is reached (called thermal equilibrium) at which only a

small percentage of bonds are broken. The number of bonds broken per second will be

equal to the number of bonds mended per second, so that a fixed number of free electrons

and free holes remains constant at every temperature. But not the same electrons and same

holes remain free.They reshuffle ,but their number stays constant.

Free electrons (a class of valance electrons) represent a third type of electrons in silicon.

Such electrons in fact are still confined, but they are confined to the full size of the crystal

itself, i.e., are limited by the so called surface of the crystal. Breaking a bond requires a

minimum energy (thermal or optical). In the case of mending a bond (called

recombination), energy is released (thermal or optical).

As the electrons move in a random motion ,so do the holes, since electrons in the bond move

around randomly to fill in vacancies (voids) within the broken bonds (Fig 15 – 4 ).

Fig (15-4a)Holes move randomly between bonds

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Fig (15-4b)Motion of holes is equivalent to motion of

electrons within bonds (in the opposite direction)Fig (15-4c)

At a certain temperature, thenumber of free electrons and

holes is constant

Doping:Semiconductors are known to be sensitive to impurities and to temperature. Since silicon

is tetravalent, the addition of an element as phosphorus (P) or antimony (Sb) or any other

pentavalent element will cause such an impurity atom to replace a silicon atom in the

crystal (Fig 15 – 5 a). Then, the phosphorus atom will try to do the same bonding with the

neighbors as the silicon atom would do.

Fig (15-5a)An antimony atom (pentavalent)

replaces a silicon atom

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Fig (15-3b)As temperature increasesmore bonds are broken

Fig (15-3a)Breaking a bond requires

energy

generation ofan electronhole pair

recombinationof an electron

hole pair

thermal energy

freeelectron

thermalenergy

Fig (15-2a)Each atom shareselectrons with its

neighbors

Fig (15-2b)Covalent bonds. We may

represent a Si atom (-14 e)around (+14 e) nucleus as a core

(+4e) and (-4e ) in the outer shell

+4e Core

Fig (15-2c)Silicon crystal at T=0˚K

all bonds are intact

some bonds, are broken and electrons are freed. Such an electron leaves behind a vacancy

in the broken bond.This vacancy is called a hole (Fig 15 – 3). Because the atom is neutral,

then the absence of an electron entails the appearance of a positive charge. We, thus, say

that the hole has a positive charge. We do not call a silicon atom which loses an electron

from its bond an ion, because soon enough, this atom may capture a free electron or an

electron from another bond to fill its own vacancy. Then, the atom returns neutral, and the

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broken bond is mended, and the hole shifts somewhere else, and so on.

As the temperature increases, the number of free electrons and holes increases, noting

that the number of free electrons equals the number of free holes in a pure semiconductor.

But a state of dynamic equilibrium is reached (called thermal equilibrium) at which only a

small percentage of bonds are broken. The number of bonds broken per second will be

equal to the number of bonds mended per second, so that a fixed number of free electrons

and free holes remains constant at every temperature. But not the same electrons and same

holes remain free.They reshuffle ,but their number stays constant.

Free electrons (a class of valance electrons) represent a third type of electrons in silicon.

Such electrons in fact are still confined, but they are confined to the full size of the crystal

itself, i.e., are limited by the so called surface of the crystal. Breaking a bond requires a

minimum energy (thermal or optical). In the case of mending a bond (called

recombination), energy is released (thermal or optical).

As the electrons move in a random motion ,so do the holes, since electrons in the bond move

around randomly to fill in vacancies (voids) within the broken bonds (Fig 15 – 4 ).

Fig (15-4a)Holes move randomly between bonds

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Because the impurity atom has 5 electrons, four of them willtake part in the bonding scheme, sparing one valence extra(excess) electron. The force of attraction on the excess electronwhich is left out is weak. Hence, it can easily be detached fromits parent atom, which becomes a positive ion.This extra electronjoins the stock of the free electrons in the crystal . In otherwords, the crystal has an added source of free electrons besidesbroken bonds, namely, impurity atoms. Such impurity atoms arecalled donors (givers). At thermal equilibrium, the sum of thepositive charge equals the sum of the negative charge.

n = p + ND+

where ND+ is the positive donor ion concentration, n is the free electron density and p is

the hole density. In this case, n > p and the material is called n–type. Conversely, if we add

aluminum (Al) or boron (B) or any trivalent element, to

pure silicon, the impurity atom replaces a silicon atom.

Since the impurity atom now has 3 electrons in the

outershell, it detaches an electron from a neighboring

bond to complete its own bond creating an extra hole,

becoming a negative ion. At thermal equilibrium ,

p= NA- + n

where NA- is the negative impurity concentration.

Thus, p>n. Such an atom is called acceptor (taker). In all

cases, we have np = ni

2

(Fig 15-5b)Doping with a pentavalent atomprovides an extra free electron.A pentavalent atom has a core

(+5 e) and 5 electrons

Fig (15-6a)A boron atom replaces

a silicon atom

(15 - 2)

(15 - 1)

(15 - 3)

an excess electron

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n = p + ND+









p= NA- + n




2




a silicon atom

(15 - 2)

(15 - 1)

(15 - 3)

an excess electron

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Fig (15-4b)Motion of holes is equivalent to motion of

electrons within bonds (in the opposite direction)Fig (15-4c)

At a certain temperature, thenumber of free electrons and

holes is constant

Doping:Semiconductors are known to be sensitive to impurities and to temperature. Since silicon

is tetravalent, the addition of an element as phosphorus (P) or antimony (Sb) or any other

pentavalent element will cause such an impurity atom to replace a silicon atom in the

crystal (Fig 15 – 5 a). Then, the phosphorus atom will try to do the same bonding with the

neighbors as the silicon atom would do.

Fig (15-5a)An antimony atom (pentavalent)

replaces a silicon atom

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n = p + ND+









p= NA- + n




2




a silicon atom

(15 - 2)

(15 - 1)

(15 - 3)

an excess electron

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n = p + ND+









p= NA- + n




2




a silicon atom

(15 - 2)

(15 - 1)

(15 - 3)

an excess electron

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n = p + ND+









p= NA- + n




2




a silicon atom

(15 - 2)

(15 - 1)

(15 - 3)

an excess electron

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n = p + ND+









p= NA- + n




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a silicon atom

(15 - 2)

(15 - 1)

(15 - 3)

an excess electron

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where ni is the electron or hole concentration in pure silicon,i.e., if n increases, p decreases and vice versa. This is called lawof mass action. As an approximation, we may say :

in case of n-type

n = ND+

p = ni2/ND

+

In case of p-type,

p = NA-

n = ni2/NA

-

Electronic Components and DevicesElectronic components and devices are the building blocks for all electronic systems (Fig

15 – 7). Some of these components are simple, e.g., resistor (R), inductor (L), capacitor

(C). Some are more complex, such as pn junction (diode), transistor. There are also other

specialized devices, such as optoelectronic and control devices. Semiconductors from

which most of these devices are made are known to be sensitive to environmental

conditions, such as light, heat, pressure, radiation and chemical pollution. That is why they

are used as sensors or means for measuring external stimulii. Using these sensors, we can

measure the intensity of incident light, temperature, pressure, humidity, pollution,

radiation,etc.

Fig (15-6b)Doping with a trivalent atom

provides an extra hole. Atrivalent atom has a core (+3e)

and 3 electrons

(15 - 4)

(15 - 5)

(15 - 6)

(15 - 7)

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Fig (15-7a)Resistors

Fig (15-7b)Diodes and transistors

Fig (15-7c)Inductors

Fig (15-7d)Capacitors

Fig (15-7e)Transformers

Fig (15-7f)Switches

Fig (15-7g)A different set of components and devices

(Can you recognize some?)

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where ni is the electron or hole concentration in pure silicon,i.e., if n increases, p decreases and vice versa. This is called lawof mass action. As an approximation, we may say :

in case of n-type

n = ND+

p = ni2/ND

+

In case of p-type,

p = NA-

n = ni2/NA

-

Electronic Components and DevicesElectronic components and devices are the building blocks for all electronic systems (Fig

15 – 7). Some of these components are simple, e.g., resistor (R), inductor (L), capacitor

(C). Some are more complex, such as pn junction (diode), transistor. There are also other

specialized devices, such as optoelectronic and control devices. Semiconductors from

which most of these devices are made are known to be sensitive to environmental

conditions, such as light, heat, pressure, radiation and chemical pollution. That is why they

are used as sensors or means for measuring external stimulii. Using these sensors, we can

measure the intensity of incident light, temperature, pressure, humidity, pollution,

radiation,etc.

Fig (15-6b)Doping with a trivalent atom

provides an extra hole. Atrivalent atom has a core (+3e)

and 3 electrons

(15 - 4)

(15 - 5)

(15 - 6)

(15 - 7)

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Fig (15-7a)Resistors

Fig (15-7b)Diodes and transistors

Fig (15-7c)Inductors

Fig (15-7d)Capacitors

Fig (15-7e)Transformers

Fig (15-7f)Switches

Fig (15-7g)A different set of components and devices

(Can you recognize some?)

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pn junction:A pn junction (Fig 15 – 8) consists of an n–type

region and a p-type region. The name pn stands for p-region and n-region not positive and negative. Alsop,n regions are not two regions glued together but ann-material is converted in part to p-material or viceversa. Holes in the p–type region have high concentration, while holes in the n–type regionhave low concentration. Therefore, some holes diffuse from the p-type region to the n–typeregion. Also, some electrons diffuse from the n–type region (high concentration forelectrons) to the p–type region (low concentration forelectrons). Since each region is neutral (the sum ofpositive charge equals the sum of negative charge), thetransfer of some electrons from the n–type regionuncovers an equal number of positive donor ions, andthe transfer of some holes from the p–type regionuncovers an equal number of negative acceptor ions.This results in a middle region composed of positive ionson one side, and negative ions on the other, while noelectrons or holes exist in this region. This region iscalled transition (depletion) region. In such a region, anelectric field is set up, directed from the positive ions tothe negative ions. This electric field causes a driftcurrent to flow in a direction opposite to the diffusioncurrent. At equilibrium, the forward current is balancedwith a reverse current, so that the net current is zero (Fig 15 – 9).If we apply an external voltage such that the p-typeregion is connected to the positive terminal of the battery

Fig (15-8)A pn Junction

Fig (15-9a)Electrons diffuse from

n to p and holes from p to n

Fig (15-9b)Transition region depleted from

electrons and holes, only ions exist

Transition†(depletion) re-

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and the n-type region to the negative terminal of the battery, the field due to the battery isopposite to the internal field.in the transition region, and therefore, it weakens it. If wereverse the battery, then the two fields will aid each other. In the first case (forward bias), anet current will flow, and in the second case (reverse bias) current is almost zero (Fig15-12). The action of the pn junction is like a switch, which is closed in the forwarddirection (conducting) and open (non conducting) in the reverse direction (Fig 15-13). Wecan make sure that the pn diode is functioning by using an ohmmeter, since the diodeshould have a small resistance in the forward direction and a large resistance in the reverse

-region -region

external potential difference

-region -regiontransition region

barriar voltage

-region

Fig (15-10a)Forward Bios

Fig (15-10b)Motion of electrons and holes

due to forward bias

-region

Fig (15-11a)Diode in reverse bias


due to reverse bias

Fig (15-12)I - V characteristic in a pn diode

reverse voltageforwardvoltage

curr

ent

-regiontransition regionp-region

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pn junction:A pn junction (Fig 15 – 8) consists of an n–type

region and a p-type region. The name pn stands for p-region and n-region not positive and negative. Alsop,n regions are not two regions glued together but ann-material is converted in part to p-material or viceversa. Holes in the p–type region have high concentration, while holes in the n–type regionhave low concentration. Therefore, some holes diffuse from the p-type region to the n–typeregion. Also, some electrons diffuse from the n–type region (high concentration forelectrons) to the p–type region (low concentration forelectrons). Since each region is neutral (the sum ofpositive charge equals the sum of negative charge), thetransfer of some electrons from the n–type regionuncovers an equal number of positive donor ions, andthe transfer of some holes from the p–type regionuncovers an equal number of negative acceptor ions.This results in a middle region composed of positive ionson one side, and negative ions on the other, while noelectrons or holes exist in this region. This region iscalled transition (depletion) region. In such a region, anelectric field is set up, directed from the positive ions tothe negative ions. This electric field causes a driftcurrent to flow in a direction opposite to the diffusioncurrent. At equilibrium, the forward current is balancedwith a reverse current, so that the net current is zero (Fig 15 – 9).If we apply an external voltage such that the p-typeregion is connected to the positive terminal of the battery

Fig (15-8)A pn Junction

Fig (15-9a)Electrons diffuse from

n to p and holes from p to n

Fig (15-9b)Transition region depleted from

electrons and holes, only ions exist

Transition†(depletion) re-

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and the n-type region to the negative terminal of the battery, the field due to the battery isopposite to the internal field.in the transition region, and therefore, it weakens it. If wereverse the battery, then the two fields will aid each other. In the first case (forward bias), anet current will flow, and in the second case (reverse bias) current is almost zero (Fig15-12). The action of the pn junction is like a switch, which is closed in the forwarddirection (conducting) and open (non conducting) in the reverse direction (Fig 15-13). Wecan make sure that the pn diode is functioning by using an ohmmeter, since the diodeshould have a small resistance in the forward direction and a large resistance in the reverse

-region -region

external potential difference

-region -regiontransition region

barriar voltage

-region

Fig (15-10a)Forward Bios


due to forward bias

-region

Fig (15-11a)Diode in reverse bias


due to reverse bias

Fig (15-12)I - V characteristic in a pn diode

reverse voltageforwardvoltage

curr

ent

-regiontransition regionp-region

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reverse bias forward bias

cathode

anode

diode

diode

Fig (15-13b)Ideal I-V characteristic

Fig (15-13a)Diode symbol

Fig (15-13c)In forward bias the diode is like a closed switch

Fig (15-13d)In reverse bias the diode is like an open switch

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direction. This is in contrast with a linear resistor, where the magnitude of the current is thesame, whether or not the voltage polarity is reversed (symmetrical characteristic).

A pn diode is important in rectification. It is used in charging car batteries, and mobilebatteries, where AC is converted to DC (Fig 15- 14).

Learn at Leisure

How to convert AC to DCTo convert AC to DC several steps may be followed. First a diode may be used as a half wave rectifier (HWR) (Fig 15 - 14a), using a resistor

and a diode (Fig 15-14b). Four diodes may be used in a bridge (Fig 15- 14 c,d) for a full

diode

Ou

tpu

t vo

ltag

e

Fig (15-14a)Waveform of a rectified half wave

Fig (15-14b)A simple half wave rectifier

Fig (15-14d)A full wave rectifier inthe negative half cycle

Fig (15-14c)A full wave rectifier inthe positive half cycle

V

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reverse bias forward bias

cathode

anode

diode

diode

Fig (15-13b)Ideal I-V characteristic

Fig (15-13a)Diode symbol

Fig (15-13c)In forward bias the diode is like a closed switch

Fig (15-13d)In reverse bias the diode is like an open switch

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direction. This is in contrast with a linear resistor, where the magnitude of the current is thesame, whether or not the voltage polarity is reversed (symmetrical characteristic).

A pn diode is important in rectification. It is used in charging car batteries, and mobilebatteries, where AC is converted to DC (Fig 15- 14).

Learn at Leisure

How to convert AC to DCTo convert AC to DC several steps may be followed. First a diode may be used as a half wave rectifier (HWR) (Fig 15 - 14a), using a resistor

and a diode (Fig 15-14b). Four diodes may be used in a bridge (Fig 15- 14 c,d) for a full

diode

Ou

tpu

t vo

ltag

e

Fig (15-14a)Waveform of a rectified half wave

Fig (15-14b)A simple half wave rectifier

Fig (15-14d)A full wave rectifier inthe negative half cycle

Fig (15-14c)A full wave rectifier inthe positive half cycle

V

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Fig (15-14e)Waveform of a rectified full wave

Fig (15-14f)Waveform of a capacitor input filter

Fig (15-14g)Capacitor input filter

input Output

wave rectifier (FWR) (Fig 15- 14e). Also, we may obtain a nearly constant current (Fig15-14f) by using a capacitor input filter (Fig 15- 14g).

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Learn at Leisure

Electronic tuningTo tune up a TV or radio onto a certain station, we need to

adjust the value of a capacitor to set the frequency of thereceiver to the frequency of the selected broadcast station. Thiscondition is called resonance. In modern receivers, the capacitoris replaced by a reverse biased pn diode . The width of thetransition region increases with increasing reverse bias (Fig 15 -15). The increase of the width of the transition region entails anincrease of the fixed ionic charge on both sides of the transitionregion with reverse voltage. This is tantamount to capacitoraction. Thus, we can change the value of the capacitor bycontrolling the revese voltage. This is called electronic tuning(and the device is called a varactor).

Transistor:The transistor was cenceived in 1955 by Bardeen,

Schockley and Brattain. There are many types of transistors,

but we focus here on bipolar junction transistor (BJT), i.e.,

pnp or npn. Such a transistor consists of a p-region followed

by an n-region then a p-region (pnp), or an n-region followed

by a p-region then an n-region (npn) (Fig 15- 16). The three

regions are called emitter (E) -base (B) and collector (C).

Consider an npn transistor. The first junction (np) is forward

biased. The second (pn) junction is reverse biased. In this case, electrons are emitted from the

Bardeen, Schochley and Brattain

Fig (15-15)The width of the transition region

increases with increasing reverse bias

forward bias

reverse bias

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Fig (15-14e)Waveform of a rectified full wave

Fig (15-14f)Waveform of a capacitor input filter

Fig (15-14g)Capacitor input filter

input Output

wave rectifier (FWR) (Fig 15- 14e). Also, we may obtain a nearly constant current (Fig15-14f) by using a capacitor input filter (Fig 15- 14g).

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Learn at Leisure

Electronic tuningTo tune up a TV or radio onto a certain station, we need to

adjust the value of a capacitor to set the frequency of thereceiver to the frequency of the selected broadcast station. Thiscondition is called resonance. In modern receivers, the capacitoris replaced by a reverse biased pn diode . The width of thetransition region increases with increasing reverse bias (Fig 15 -15). The increase of the width of the transition region entails anincrease of the fixed ionic charge on both sides of the transitionregion with reverse voltage. This is tantamount to capacitoraction. Thus, we can change the value of the capacitor bycontrolling the revese voltage. This is called electronic tuning(and the device is called a varactor).

Transistor:The transistor was cenceived in 1955 by Bardeen,

Schockley and Brattain. There are many types of transistors,

but we focus here on bipolar junction transistor (BJT), i.e.,

pnp or npn. Such a transistor consists of a p-region followed

by an n-region then a p-region (pnp), or an n-region followed

by a p-region then an n-region (npn) (Fig 15- 16). The three

regions are called emitter (E) -base (B) and collector (C).

Consider an npn transistor. The first junction (np) is forward

biased. The second (pn) junction is reverse biased. In this case, electrons are emitted from the

Bardeen, Schochley and Brattain

Fig (15-15)The width of the transition region

increases with increasing reverse bias

forward bias

reverse bias

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negative emitter (n) diffusing to the base (p), where they wander around in the base untilpicked up by the positive collector (n).A portion of electrons gets recombined with holes. Ifthe emitted electorn current is IE and the portion that reaches the collector Ic is Ic = αe IE,then the protion lost in the base by recombination with holes is IB = (1-αe)IE. This must bethe base current supplying holes to the base to make up for the losses due to therecombination process. Therefore, the ratio of the collector current to the base current is:

β αα

ααe

C

B

e E

e E

e

e

II

I(1- I

= = =−) 1

transistor symbolpnp

Fig (15-16a) A pnp transistor

Fig (15-16b) A pnp transistor

Fig (15-16c)An npn transistor

Fig (15-16d)An npn transistor

(15 - 8)

npn Transistorsymbol

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Transistor as a switch:Considering the collector circuit, we have

VCC = VCE + ICRC

where VCC is the collector battery, and vCE is

the voltage difference between the collecttor and

the emitter, IC is the collector current and RC is

the collector resistance. As IC increases, VCE

decreases, until it reaches a value as low as 0.2V

for a high base current. Considering the base as

the input ,the collector as the output and the

emitter as common (ground), we note that as the

input increases, (or positive) the transistor is ON,

and the output decreases and vice versa. The

circuit behaves as an inverter, for positive

voltage in the base (high), current flows in the

collector, and the output voltage is very small

(low). If the base voltage is small (or negative) or

(low). The transistor is OFF and the current in the

collector ceases, and the output voltage on the

collector increases (high). The transistor as such

operates as a switch (Fig 15-18).

Fig (15-18a)Transistor as a switch (ON condition)

Fig (15-18b)Transistor as a switch (OFF condition)

Fig (15-18c)Inverter characteristic

(15-9)

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Digital Electronics:All electronic systems deal with natural quantities and convert them to electrical signals.

As an example, a microphone converts sound to an electrical signal. A video camera

converts an image to electrical signals. In TV, the image (video) and sound (audio) are

transformed into electrical signals, then into electromagnetic waves. All this occurs at the

transmitter. At the receiver, the em signal is transformed back into electrical (video and

audio) signals. The electronics which deals with natural quantities is called analog

electronics. A new branch of electronics has developed, namely, digital electronics. In this

case, the electrical signal is not transmitted continuously (all values are allowed), but is

coded, such that the signal is in terms of one of two possible values representing two states

0 or 1. So, if we want to represent 3, it can be written as 112, where subscript 2 denotes the

binary system (not eleven).

3 = 1x20+1x21

as we may express 17 in decimal system as

17 = 7x100+1x101

similarly in the binary system, we use the weights of 20, 21, 22 … instead of 100, 101, 102,… .Thus, each numeral, symbol and alphabet is coded with a binary code. Analog quantities

may be encoded by an analog – digital converter (ADC). At the reciever, digital quantities are

decoded into analog quantities using a digital to analog converter (DAC). Why do all this? In

nature, there are unwanted spurious signals, called electrical noise. Noise is caused by the

random motion of electrons. Electrons are charged particles. As they move randomly, they

cause minute randomly varying currents. These currents interfere with and disturb the

information - bearing signals. We notice that in weak radio stations, noise appears as a hiss,

and in weak TV stations (or with a bad antenna an aerial) noise appears as spots (salt and

pepper). Electrical noise marrs the useful signals, and is difficult to get rid of. In case of digital

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Transistor as a switch:Considering the collector circuit, we have

VCC = VCE + ICRC

where VCC is the collector battery, and vCE is

the voltage difference between the collecttor and

the emitter, IC is the collector current and RC is

the collector resistance. As IC increases, VCE

decreases, until it reaches a value as low as 0.2V

for a high base current. Considering the base as

the input ,the collector as the output and the

emitter as common (ground), we note that as the

input increases, (or positive) the transistor is ON,

and the output decreases and vice versa. The

circuit behaves as an inverter, for positive

voltage in the base (high), current flows in the

collector, and the output voltage is very small

(low). If the base voltage is small (or negative) or

(low). The transistor is OFF and the current in the

collector ceases, and the output voltage on the

collector increases (high). The transistor as such

operates as a switch (Fig 15-18).

Fig (15-18a)Transistor as a switch (ON condition)

Fig (15-18b)Transistor as a switch (OFF condition)

Fig (15-18c)Inverter characteristic

(15-9)

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Digital Electronics:All electronic systems deal with natural quantities and convert them to electrical signals.

As an example, a microphone converts sound to an electrical signal. A video camera

converts an image to electrical signals. In TV, the image (video) and sound (audio) are

transformed into electrical signals, then into electromagnetic waves. All this occurs at the

transmitter. At the receiver, the em signal is transformed back into electrical (video and

audio) signals. The electronics which deals with natural quantities is called analog

electronics. A new branch of electronics has developed, namely, digital electronics. In this

case, the electrical signal is not transmitted continuously (all values are allowed), but is

coded, such that the signal is in terms of one of two possible values representing two states

0 or 1. So, if we want to represent 3, it can be written as 112, where subscript 2 denotes the

binary system (not eleven).

3 = 1x20+1x21

as we may express 17 in decimal system as

17 = 7x100+1x101

similarly in the binary system, we use the weights of 20, 21, 22 … instead of 100, 101, 102,… .Thus, each numeral, symbol and alphabet is coded with a binary code. Analog quantities

may be encoded by an analog – digital converter (ADC). At the reciever, digital quantities are

decoded into analog quantities using a digital to analog converter (DAC). Why do all this? In

nature, there are unwanted spurious signals, called electrical noise. Noise is caused by the

random motion of electrons. Electrons are charged particles. As they move randomly, they

cause minute randomly varying currents. These currents interfere with and disturb the

information - bearing signals. We notice that in weak radio stations, noise appears as a hiss,

and in weak TV stations (or with a bad antenna an aerial) noise appears as spots (salt and

pepper). Electrical noise marrs the useful signals, and is difficult to get rid of. In case of digital

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electronics, the information does not lie in the absolute value of the signal (which might be

contaminated by noise), but lies in the code in terms of 0 or 1. It does not matter if the valuecorresponding to 0 or to 1 has some noise superimposed on it. What matters is the state (0 or 1).This is the main advantage of digital electronics. For this reason, it has permeated our modernlife extensively, as in cellular (mobile) telephony, digital satellite TV, and CDs. What hasincreased the importance of digital electronics is the advent of the computer. Everythingthat is entered into the computer-whether numbers or letters-must be transformed into abinary code. Even images are divided into small elements, each called a pixel (pictureelement). These too must be encoded. The computer performs all arithmetic and logicoperations using binary (Boolean) algebra. It also stores information in the binary codetemporarily in the RAM (Random Access Memory) or permanently in the hard disk, bymagnetizing in one direction for 0 and in the opposite direction for 1.

Logic Gates:Modern applications of electronics, such as computer circuits and modern communication

systems depend on digital circuits, called logic gates. These are the circuits that perform logic

Fig (15-19a)Not gate symbol

Fig (15-19b)States of a NOT gate

Fig (15-19a)An equivalent drawing for a NOT

gate. When the switch is closed (ON)the lamp is (OFF) and vice versa

input output

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operations, such as inversion (NOT), simultaneity or coincidence (AND) and optionality (OR) asfollows :1) Inverter (NOT Gate) has one input and one output, and has the following truth table:

input output1 00 1

2) AND Gate: has two inputs or more and one output and has the following truth table: input output

00 001 010 011 1

input Ainput B

output

Fig (15-20a)AND gate symbol

Fig (15-20c)An equivalent drawing for an AND gate. The lamp

does not glow until both switches are closed

lamp

Fig (15-20b)States of an AND gate

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electronics, the information does not lie in the absolute value of the signal (which might be

contaminated by noise), but lies in the code in terms of 0 or 1. It does not matter if the valuecorresponding to 0 or to 1 has some noise superimposed on it. What matters is the state (0 or 1).This is the main advantage of digital electronics. For this reason, it has permeated our modernlife extensively, as in cellular (mobile) telephony, digital satellite TV, and CDs. What hasincreased the importance of digital electronics is the advent of the computer. Everythingthat is entered into the computer-whether numbers or letters-must be transformed into abinary code. Even images are divided into small elements, each called a pixel (pictureelement). These too must be encoded. The computer performs all arithmetic and logicoperations using binary (Boolean) algebra. It also stores information in the binary codetemporarily in the RAM (Random Access Memory) or permanently in the hard disk, bymagnetizing in one direction for 0 and in the opposite direction for 1.

Logic Gates:Modern applications of electronics, such as computer circuits and modern communication

systems depend on digital circuits, called logic gates. These are the circuits that perform logic

Fig (15-19a)Not gate symbol

Fig (15-19b)States of a NOT gate

Fig (15-19a)An equivalent drawing for a NOT

gate. When the switch is closed (ON)the lamp is (OFF) and vice versa

input output

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operations, such as inversion (NOT), simultaneity or coincidence (AND) and optionality (OR) asfollows :1) Inverter (NOT Gate) has one input and one output, and has the following truth table:

input output1 00 1

2) AND Gate: has two inputs or more and one output and has the following truth table: input output

00 001 010 011 1

input Ainput B

output

Fig (15-20a)AND gate symbol

Fig (15-20c)An equivalent drawing for an AND gate. The lamp

does not glow until both switches are closed

lamp

Fig (15-20b)States of an AND gate

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Fig (15-21c)An equivalent drawing for an OR gate.

One switch need be closed for the lamp to glow

Fig (15-21b)States of OR gate

Fig (15-21a)OR gate symbol

Thus, there is no output (1) unless both inputs are (1) each, i.e., two conditions or moreare met to satisfy an output (1). It can be represented by two switches in series. They bothhave to be closed at the same time for current to flow and the lamp to glow.3) OR Gate has two inputs or more and one output (Fig 15–21). One condition (1) may

suffice to have an output (1) . input Output0 0 001 110 111 1

input Ainput B

output

Lamp

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This can be represented by two switches inparallel, one of them only need be closed to passcurrent.

All operations performed by the computer arebased on these gates and others.

These gates can be implemented by transistors.In this case, the transistor may not be lookedupon as an amplifier but as a switch .

Thus, we can use the transistor as an inverter(NOT gate).

A transistor with more than one emitter maybe used as an AND gate, so that the transistorwill not pass current unless each emitter has positive voltage (1).

Also, we may envision the transistor as an OR gate in the form of a pair of paralleltransistors. If (1) exists at either one of the inputs, one of the transistors conducts and (1)appears at the output .

Transistors are also used in memory circuits, where data ( 0 or 1 ) is retained temporarilyin the RAM and permanently in the hard disk or CD. In a CD, a laser beam engraves a bit ina plastic disk for 1 and no bit for 0. This is the Write process. In a CD drive, a laser beam isused for the Read process (Fig 15 – 22a). A DVD is a modified version of a CD with higherstorage capacity. There are also digital cameras, which convert images to electrical signalspixel by pixel, and store them on a magnetic tape, or download them onto a PC (Fig 15 –23). These cameras use a new technique for handling and transferring electrical charges,namely, charge coupled devices (CCD). This makes the cameras light weighted (portable)and inexpensive. This is the basis for the camcorder, Fax machines and mobile camera.

Fig (15-22a)A CD - drive

Plasticdisk

Collimatingcoil

prism

laser

pits

lens

sensitivelight

detector

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Fig (15-21c)An equivalent drawing for an OR gate.

One switch need be closed for the lamp to glow

Fig (15-21b)States of OR gate

Fig (15-21a)OR gate symbol

Thus, there is no output (1) unless both inputs are (1) each, i.e., two conditions or moreare met to satisfy an output (1). It can be represented by two switches in series. They bothhave to be closed at the same time for current to flow and the lamp to glow.3) OR Gate has two inputs or more and one output (Fig 15–21). One condition (1) may

suffice to have an output (1) . input Output0 0 001 110 111 1

input Ainput B

output

Lamp

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This can be represented by two switches inparallel, one of them only need be closed to passcurrent.

All operations performed by the computer arebased on these gates and others.

These gates can be implemented by transistors.In this case, the transistor may not be lookedupon as an amplifier but as a switch .

Thus, we can use the transistor as an inverter(NOT gate).

A transistor with more than one emitter maybe used as an AND gate, so that the transistorwill not pass current unless each emitter has positive voltage (1).

Also, we may envision the transistor as an OR gate in the form of a pair of paralleltransistors. If (1) exists at either one of the inputs, one of the transistors conducts and (1)appears at the output .

Transistors are also used in memory circuits, where data ( 0 or 1 ) is retained temporarilyin the RAM and permanently in the hard disk or CD. In a CD, a laser beam engraves a bit ina plastic disk for 1 and no bit for 0. This is the Write process. In a CD drive, a laser beam isused for the Read process (Fig 15 – 22a). A DVD is a modified version of a CD with higherstorage capacity. There are also digital cameras, which convert images to electrical signalspixel by pixel, and store them on a magnetic tape, or download them onto a PC (Fig 15 –23). These cameras use a new technique for handling and transferring electrical charges,namely, charge coupled devices (CCD). This makes the cameras light weighted (portable)and inexpensive. This is the basis for the camcorder, Fax machines and mobile camera.

Fig (15-22a)A CD - drive

Plasticdisk

Collimatingcoil

prism

laser

pits

lens

sensitivelight

detector

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Images may be transferred via the internet using a newfeature called Bluetooth.

Learn at Leisure

LEDWhen current passes through a pn junction, electrons and

holes transporting from one side to the other, are annihiltedin a recombination process. This process is accompanied bythe emission of light in the form of photons. A solid statelamp can, thus, be made out of a pn junction. This is calledlight emitting diode (LED) (Fig 15 – 23 a). It is used in

Fig (15-22b)Digital camera

Fig (15-22c)A CCD element

Fig (15-22d)Storing date on a magnetic tape in the digital

cameraFig (15-22e)

Downloading onto a computer

Fig (15-23a)LED

axis light

transparentdome

terminal

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Fig (15-24b)Different versions of transistors and diodes

electronic bulletins, watches and measuring equipment. Iflight from a forward biased heavily doped pn junction isconcentrated by laser action, we may have a junction (solid

state) laser (Fig 15 – 23 b), which is used in surgery,

communication through fiber optics and in modern warfare,

such as missile guidance and radar (laser radar is called

LADAR).

Eelctronic Circuits:Any analog or digital electronic system is composed of

electronic components connected together in a closed path called

circuit. The components may be passive as resistors, inductors,

capacitors, or diodes (Fig 15 – 24). Active components include

transistors in all types.

Circuits formed from separate components and soldered Fig (15-24a)Resistors

Fig (15-23b)A junction laser

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Images may be transferred via the internet using a newfeature called Bluetooth.

Learn at Leisure

LEDWhen current passes through a pn junction, electrons and

holes transporting from one side to the other, are annihiltedin a recombination process. This process is accompanied bythe emission of light in the form of photons. A solid statelamp can, thus, be made out of a pn junction. This is calledlight emitting diode (LED) (Fig 15 – 23 a). It is used in

Fig (15-22b)Digital camera

Fig (15-22c)A CCD element

Fig (15-22d)Storing date on a magnetic tape in the digital

cameraFig (15-22e)

Downloading onto a computer

Fig (15-23a)LED

axis light

transparentdome

terminal

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Fig (15-24b)Different versions of transistors and diodes

electronic bulletins, watches and measuring equipment. Iflight from a forward biased heavily doped pn junction isconcentrated by laser action, we may have a junction (solid

state) laser (Fig 15 – 23 b), which is used in surgery,

communication through fiber optics and in modern warfare,

such as missile guidance and radar (laser radar is called

LADAR).

Eelctronic Circuits:Any analog or digital electronic system is composed of

electronic components connected together in a closed path called

circuit. The components may be passive as resistors, inductors,

capacitors, or diodes (Fig 15 – 24). Active components include

transistors in all types.

Circuits formed from separate components and soldered Fig (15-24a)Resistors

Fig (15-23b)A junction laser

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Fig (15-24c)Tansistors as pairs and quadruples

together are called discrete circuits (Fig 15 – 24). A new era of

integrated circuits(ICs) started in the 1960’s at the peak of space

research. The goal then was to develop electronic circuits with a

new technology ,which would put light weight, compactness,

effectiveness and reliability at prime interest. The answer was

ICs or microchips (Fig 15– 25). The basic idea is to cram all the

needed components onto a silicon wafer, where different regions

are assigned to needed functions without treating them as

separate components. If we want to make a diode, for example,

then starting with an n-type wafer, we allow p atoms to diffuse

in defined regions in the wafer. This is called selective (planar)

diffusion (Fig 15–26). The way this is done is a complicated

chemical process in which a mask is made and light (recently

laser) is used. The process is similar to film developing in

photography, and is called photolithography, which means

carving on stone. If we now want to make an npn transistor, we

open up a window in the p-region, and let n atoms diffuse

selectively there. Interestingly, all these operations are

Fig (15-25a)IC’s in different forms

Fig (15-25b)IC uncovered

Fig (15-25c)Microprocessor in comparison

with a match head

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repeatedly made on a thin wafer of silicon thousands of

times simultaneously. Thus, the wafer is cut up to

thousands of slices, each called a chip, all carrying

exactly the same layout and same specifications. This

technique yields low cost electronic circuits due to the

mass production involved. The burden is really the initial

investment of setting up the foundries, with all the

sophisticated equipment including robots, testing systems,

and in the design, artwork i.e., the brainwork involved in

the programming, particularly when such circuits are

custom made. The commonplace ICs are, however,

inexpensive, since millions are made at a time for the

same design and artwork. This is what has made ICs

popular in both analog and digital electronic systems. In

fact, instead of designing highly complicated and costly

ICs existing or available (off the shelf) ICs are sought

first. Thus, design has shifted toward system engineering,

namely putting the right things together at the lowest

possible cost and highest possible efficiency.

A collection of components including ICs are often

mounted on a board called a printed circuit board (PCB).

An example is the motherboard of a PC (Fig 15 – 27). It

includes the processor, RAM, Arithmetic Logic Unit

(ALU), control circuits etc.

Fig (15-25d)Pentium IC

Fig (15-26)Selective diffusion

Fig (15-27)Motherboard

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Fig (15-24c)Tansistors as pairs and quadruples

together are called discrete circuits (Fig 15 – 24). A new era of

integrated circuits(ICs) started in the 1960’s at the peak of space

research. The goal then was to develop electronic circuits with a

new technology ,which would put light weight, compactness,

effectiveness and reliability at prime interest. The answer was

ICs or microchips (Fig 15– 25). The basic idea is to cram all the

needed components onto a silicon wafer, where different regions

are assigned to needed functions without treating them as

separate components. If we want to make a diode, for example,

then starting with an n-type wafer, we allow p atoms to diffuse

in defined regions in the wafer. This is called selective (planar)

diffusion (Fig 15–26). The way this is done is a complicated

chemical process in which a mask is made and light (recently

laser) is used. The process is similar to film developing in

photography, and is called photolithography, which means

carving on stone. If we now want to make an npn transistor, we

open up a window in the p-region, and let n atoms diffuse

selectively there. Interestingly, all these operations are

Fig (15-25a)IC’s in different forms

Fig (15-25b)IC uncovered

Fig (15-25c)Microprocessor in comparison

with a match head

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repeatedly made on a thin wafer of silicon thousands of

times simultaneously. Thus, the wafer is cut up to

thousands of slices, each called a chip, all carrying

exactly the same layout and same specifications. This

technique yields low cost electronic circuits due to the

mass production involved. The burden is really the initial

investment of setting up the foundries, with all the

sophisticated equipment including robots, testing systems,

and in the design, artwork i.e., the brainwork involved in

the programming, particularly when such circuits are

custom made. The commonplace ICs are, however,

inexpensive, since millions are made at a time for the

same design and artwork. This is what has made ICs

popular in both analog and digital electronic systems. In

fact, instead of designing highly complicated and costly

ICs existing or available (off the shelf) ICs are sought

first. Thus, design has shifted toward system engineering,

namely putting the right things together at the lowest

possible cost and highest possible efficiency.

A collection of components including ICs are often

mounted on a board called a printed circuit board (PCB).

An example is the motherboard of a PC (Fig 15 – 27). It

includes the processor, RAM, Arithmetic Logic Unit

(ALU), control circuits etc.

Fig (15-25d)Pentium IC

Fig (15-26)Selective diffusion

Fig (15-27)Motherboard

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ICs have permeated even medical equipment including instrumentation, diagnosis, and

prognosis. One day pacemakers and insulin control circuits using microcapsules involving

microprocessors may be injected into the body to do their work from within.

Miniaturization, where to ?When the first computer was built in the 1950’s, its capabilities were very limited by

today’s standards. It was bulky, about the size of an apartment. It was built from vacuumtube (valves). Then, transistors were used. ICs have led to the development of PCs whichmade computers available to the public. Since the 1970’s PCs are continually beingenhanced. Their capacity and capability to do complicated calculations are on the increase,while calculation time is getting shorter, and size and weight are getting smaller. Also, costis on the decline. These improvements sound contradictory, but they are happening and at ahigh rate, thanks to the understanding and best application of the basic concepts of modernphysics, materials science, chemistry, laser and to the rapid advancement of the technology.There is a common law called Moore’s law, which states that capacity and speed doubleevery 18 months. If a chip (the size of a pin head) contains 100 transistors, this called smallscale integration (SSI). If it contains 1000 transistors, it is called medium scale integration(MSI). If it contains 10000 transistors, it is called large scale integration (LSI). If it contains100000 transistors, it is called very large scale integration (VLSI). If it exceeds that, it iscalled ultra large scale integration (ULSI). Can you imagine 1 million transistors in a pinhead area?

What then if you know that the figure in 2005 has reached 300 millions with prospect ofeven more?

If the miniaturization keeps going at that rate what next ? we shall soon be limited by thediffraction of light as the physical dimension will soon approach λ of the used light. It seems

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that we are headed to reach the size of the atom itself, i.e., 0 and 1 may be stored in the form ofan electron being in either one of two states in the atom, ground state or an excited state.

Alternatively, the two states may be one direction of electron spin, and the other state in theopposite direction. This is called quantum computer. This is the trend of the near future, which isabout to materialize. It is in harmony with future direction trends of science in search for minutedetails of time and space.

This has led to the advent of new technologies such as Nano and Femto technologies.

Learn at Leisure

Selective Diffusion How can we make phosphorus atoms for example diffuse in a very small area and not

through the rest of the chip ? This happens in several steps. First, we cover the silicon waferwith a layer of oxide (Si O2), then we use a mask prepared in a way similar to photographicdevelopment. We cover the oxide layer with a photoresist, which is a light sensitivematerial. We then put a mask with opaque and transparent regions on top of the photoresist.We then expose the surface to ultraviolet (uv) rays. When the photoresist is exposed to uv,it polymerizes (solidifies) in the region where it is exposed, and remains liquid in theunexposed areas. We then lift the mask and use HCl acid, which interacts with SiO2 (aprocess called etching) in the areas where the photoresist is in liquid form (where SiO2 isuncovered with polymerized photoresist). The acid, thus, opens up a hole in the oxide.Then, phosphorus atoms are allowed to diffuse through the opening in the oxide, while theoxide isolates the remaining areas from diffusion. Thus, miniaturization depends on theaccuracy of the mask. Therefore, laser is used in mask making. For more miniaturization,electron beam and molecular beam are used for shorter λ, and hence smaller dimensions (why?)where they directly carve on the chip. But this cannot be used on a large scale, but is used forspecial ICs only.

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ICs have permeated even medical equipment including instrumentation, diagnosis, and

prognosis. One day pacemakers and insulin control circuits using microcapsules involving

microprocessors may be injected into the body to do their work from within.

Miniaturization, where to ?When the first computer was built in the 1950’s, its capabilities were very limited by

today’s standards. It was bulky, about the size of an apartment. It was built from vacuumtube (valves). Then, transistors were used. ICs have led to the development of PCs whichmade computers available to the public. Since the 1970’s PCs are continually beingenhanced. Their capacity and capability to do complicated calculations are on the increase,while calculation time is getting shorter, and size and weight are getting smaller. Also, costis on the decline. These improvements sound contradictory, but they are happening and at ahigh rate, thanks to the understanding and best application of the basic concepts of modernphysics, materials science, chemistry, laser and to the rapid advancement of the technology.There is a common law called Moore’s law, which states that capacity and speed doubleevery 18 months. If a chip (the size of a pin head) contains 100 transistors, this called smallscale integration (SSI). If it contains 1000 transistors, it is called medium scale integration(MSI). If it contains 10000 transistors, it is called large scale integration (LSI). If it contains100000 transistors, it is called very large scale integration (VLSI). If it exceeds that, it iscalled ultra large scale integration (ULSI). Can you imagine 1 million transistors in a pinhead area?

What then if you know that the figure in 2005 has reached 300 millions with prospect ofeven more?

If the miniaturization keeps going at that rate what next ? we shall soon be limited by thediffraction of light as the physical dimension will soon approach λ of the used light. It seems

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that we are headed to reach the size of the atom itself, i.e., 0 and 1 may be stored in the form ofan electron being in either one of two states in the atom, ground state or an excited state.

Alternatively, the two states may be one direction of electron spin, and the other state in theopposite direction. This is called quantum computer. This is the trend of the near future, which isabout to materialize. It is in harmony with future direction trends of science in search for minutedetails of time and space.

This has led to the advent of new technologies such as Nano and Femto technologies.

Learn at Leisure

Selective Diffusion How can we make phosphorus atoms for example diffuse in a very small area and not

through the rest of the chip ? This happens in several steps. First, we cover the silicon waferwith a layer of oxide (Si O2), then we use a mask prepared in a way similar to photographicdevelopment. We cover the oxide layer with a photoresist, which is a light sensitivematerial. We then put a mask with opaque and transparent regions on top of the photoresist.We then expose the surface to ultraviolet (uv) rays. When the photoresist is exposed to uv,it polymerizes (solidifies) in the region where it is exposed, and remains liquid in theunexposed areas. We then lift the mask and use HCl acid, which interacts with SiO2 (aprocess called etching) in the areas where the photoresist is in liquid form (where SiO2 isuncovered with polymerized photoresist). The acid, thus, opens up a hole in the oxide.Then, phosphorus atoms are allowed to diffuse through the opening in the oxide, while theoxide isolates the remaining areas from diffusion. Thus, miniaturization depends on theaccuracy of the mask. Therefore, laser is used in mask making. For more miniaturization,electron beam and molecular beam are used for shorter λ, and hence smaller dimensions (why?)where they directly carve on the chip. But this cannot be used on a large scale, but is used forspecial ICs only.

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In a Nutshell

• A metallic crystal consists of positive ions and a cloud of free electrons roaming around

the crystal in random motion. There is a force of attraction between the ions and the

electron cloud. But the resultant of all forces of attraction on a single free electron is zero

. If an electron tries to escape from the metal, a net force of attraction due to the atom

layer at the surface pulls it in.

• A pure silicon (semiconductor) crystal consists of atoms covalently bonded. At low

temperatures, there are no free electrons. If temperature increases, some bonds are

broken, electrons become free, leaving behind holes. Both electrons and holes move

randomly.

• The number of broken bonds increases with temperature. It may increase also by an

external stimulus, such as light, provided that the photon energy is sufficient to break the

bond.

• The number of free electrons and holes increases by adding impurities (doping). Thus, the

material becomes n-type or p-type.

• The conductivity of a semiconductor depends on the conduction of free electrons and

holes. Thus, a semiconductor has two current carriers: electrons and holes, while in a

metal there is only one current carrier (the electron). Electron concentration in a metal is

constant and does not depend on temperature.

• Semiconductors are environment-sensitive. They can be used as sensors to light, heat,

pressure humidity, chemical pollution, radiation etc.

• A diode (pn junction) consists of a p–type region and an n-type region. If the p-side is

connected to the positive terminal of the battery and the n-side to the negative terminal

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(forward connection or forward bias) current flows. If the battery is reversed no current

flows.

This is why a diode is used in rectification.

• A transistor may be pnp or npn, and can be used as an amplifier, since the ratio of the

collector current to the base current βe is large. Therefore, any small change in the base

current leads to an amplified change in the collector current.

• A transistor may also be used as a switch. It is used in logic gates, such as an inverter

(NOT), AND, OR gates.

• Digital electronics is superceding analog electronics for its ability to overcome electrical

noise . Its basic concept is to code information in binary form (0 , 1).

• ICs have the advantages of small size and weight, increased speeds and capacity, and yet

low cost. This is the reason for the proliferation of PCs.

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In a Nutshell

• A metallic crystal consists of positive ions and a cloud of free electrons roaming around

the crystal in random motion. There is a force of attraction between the ions and the

electron cloud. But the resultant of all forces of attraction on a single free electron is zero

. If an electron tries to escape from the metal, a net force of attraction due to the atom

layer at the surface pulls it in.

• A pure silicon (semiconductor) crystal consists of atoms covalently bonded. At low

temperatures, there are no free electrons. If temperature increases, some bonds are

broken, electrons become free, leaving behind holes. Both electrons and holes move

randomly.

• The number of broken bonds increases with temperature. It may increase also by an

external stimulus, such as light, provided that the photon energy is sufficient to break the

bond.

• The number of free electrons and holes increases by adding impurities (doping). Thus, the

material becomes n-type or p-type.

• The conductivity of a semiconductor depends on the conduction of free electrons and

holes. Thus, a semiconductor has two current carriers: electrons and holes, while in a

metal there is only one current carrier (the electron). Electron concentration in a metal is

constant and does not depend on temperature.

• Semiconductors are environment-sensitive. They can be used as sensors to light, heat,

pressure humidity, chemical pollution, radiation etc.

• A diode (pn junction) consists of a p–type region and an n-type region. If the p-side is

connected to the positive terminal of the battery and the n-side to the negative terminal

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(forward connection or forward bias) current flows. If the battery is reversed no current

flows.

This is why a diode is used in rectification.

• A transistor may be pnp or npn, and can be used as an amplifier, since the ratio of the

collector current to the base current βe is large. Therefore, any small change in the base

current leads to an amplified change in the collector current.

• A transistor may also be used as a switch. It is used in logic gates, such as an inverter

(NOT), AND, OR gates.

• Digital electronics is superceding analog electronics for its ability to overcome electrical

noise . Its basic concept is to code information in binary form (0 , 1).

• ICs have the advantages of small size and weight, increased speeds and capacity, and yet

low cost. This is the reason for the proliferation of PCs.

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I) Drills:

1) Calculate the number of silicon atoms in 1 cm3, if the density of silicon is 2.33 g/cm3

and its atomic mass is 28

(0.5x1023cm-3)

2) If electron or hole concentration in pure silicon is 1x1010cm-3, phosphorus is added at a

concentration of 1012cm3, calculate the concentrations of electrons and holes in this case.

Is this silicon n-type or p-type? (n=1012cm-3 p=108cm-3 )

(n - type)

3) Calculate the concentration of aluminum to be added so that silicon returns pure .

(NA- = 1012cm-3)

4) A transistor has αe = 0.99 . Calculate βe. Then calculate the collector current if the base

current is 100 µA (βe=99 , Ic = 99x10-4A)

5) The electrical signal in the base of a transistor is 200 µA . The collector current is to be

10 mA. Calculate αe and βe. (αe = 0.98 , βe = 50)

6) A diode can be represented by a forward resistance 100Ω ,while it is infinity in the

reverse direction. We apply +5 V ,and then reverse it to – 5 V. Calculate the current in

both cases. (50 mA, O)

7) If 1 mm2 contains 1 million transistors, calculate the area assigned to each transistor.

(10-12m2)

II) Essay questions:

1) Discuss the importance of digital electronics and mention 5 applications. 2) Deduce the truth table for an AND gate followed by an inverter. 3) Deduce the truth table for an OR gate followed by an inverter.

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I) Drills:

1) Calculate the number of silicon atoms in 1 cm3, if the density of silicon is 2.33 g/cm3

and its atomic mass is 28

(0.5x1023cm-3)

2) If electron or hole concentration in pure silicon is 1x1010cm-3, phosphorus is added at a

concentration of 1012cm3, calculate the concentrations of electrons and holes in this case.

Is this silicon n-type or p-type? (n=1012cm-3 p=108cm-3 )

(n - type)

3) Calculate the concentration of aluminum to be added so that silicon returns pure .

(NA- = 1012cm-3)

4) A transistor has αe = 0.99 . Calculate βe. Then calculate the collector current if the base

current is 100 µA (βe=99 , Ic = 99x10-4A)

5) The electrical signal in the base of a transistor is 200 µA . The collector current is to be

10 mA. Calculate αe and βe. (αe = 0.98 , βe = 50)

6) A diode can be represented by a forward resistance 100Ω ,while it is infinity in the

reverse direction. We apply +5 V ,and then reverse it to – 5 V. Calculate the current in

both cases. (50 mA, O)

7) If 1 mm2 contains 1 million transistors, calculate the area assigned to each transistor.

(10-12m2)

II) Essay questions:

1) Discuss the importance of digital electronics and mention 5 applications. 2) Deduce the truth table for an AND gate followed by an inverter. 3) Deduce the truth table for an OR gate followed by an inverter.

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General Revision

1) A metallic wire is stretched between two vertical fixed pins .Is the velocity ofpropagation of a transverse wave through this wire affected by a change in thetemperature of the surrounding medium? and why ?

2) Two identical strings, one end of each is fixed to the wall, while the other end isstretched by hand . A transverse pulse is sent through one of the wires, and after ashort time another transverse pulse is sent through the other wire. What can be done tomake the second pulse catch up with the first pulse? Give reasons.

3) Give reasons:It is easy to see your reflected image on the window glass of a lit room at night whenit is dark outside the room. But that is difficult when there is light outside the room.

4) Two rays of light converge on a point on a screen. A parallel glass plate is placed inthe path of this light, and the glass plate is parallel to the screen. Will the point ofconvergence remain on the screen or change position ? Give reasons .

5) Explain and give reasons :When a blue light source is placed at the center of a solid glass cube with a whitescreen facing each side, a circular spot of light appears on each screen in front of eachsurface of the cube . When the blue source is replaced by a red color source, the shapeof the spot changes from circular to square .

6) In the following figure, a fiber optic has an external layer from glass. Its refractiveindex is less than that of the glass of the core . If the light beam passes through it asshown in the figure.

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of distance 11 x 10-4 m apart, and the distance between the double slit and the screenwas 5m. Find the distance between two successive similar fringes .12) A rubber hose is connected to a tap, and the water flows through in a steady flow.Explain why the cross sectional area of the flowing water decreases when the end ofthe rubber hose is directed down, and increases when the end of the rubber hose isdirected up.

13) A balloon filled with air is attached to the bottom of a glass tank. Then the tank isfilled completely with water ,with this balloon completely immersed in water. Supposethat the tank with its contents were transferred from the Earth to the Moon. Discuss andgive reason for all what would happen to the balloon?

14) A hollow copper ball is suspended under the surface of water in a tank. Discussand give reason for all what would happen to the position of the ball in the tank if itwere transferred from the Earth to the Moon?

15) Verify the following statement and correct the mistakes if any:When a person divesin a swimming pool near the bottom , each of the upthrust and pressure exerted overhim increases.

16) An ice cube is placed in a glass beaker, then it is filled completely to the rim withwater . Discuss in the light of Archimedes’ principle what changes may happen whenthe ice melts (fuses) .

17) A glass beaker filled to the rim with water is resting on a scale . A block is placedin water, causing some of it to spill over.The water that is spilled is wiped away ,andthe beaker is still filled to the rim . Compare between the initial and final reading on thescale, if the block is made from:a) woodb) iron

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a)explain why the direction of the beam does not change at each of S and P.b)explain why there is a total reflection at each of Q and R.c)explain why the double layer fiber optic is preferred to that of a single layer.7- A teacher gave his students the following figure (A) which expresses a path of lightbeam from A to B through a triangular prism made of glass which has a critical angle42˚. He asked the students to draw the path of the beam before reaching A and afterleaving B. The figure (B) expresses the attempt of a student. But the teacher made itclear that the angles of X and Y were not correct. Suggest without calculations thechanges required to correct the angles X and Y, and give reasons for your suggestion.

(Fig A) (Fig B)

8) The tension of a stretched string is changed from 70N to 80N without a change in itslength. Calculate the ratio of the fundamental frequencies as a result .

9) A string of length 0.06 m and mass 2.5 x 10-3 kg is stretched by a force of 400N.Find the frequency of the produced tone if it vibrates in three segments.10) A triangular prism has an angle of 60˚ and refractive index of. 2 . Calculate theminimum angle of deviation and the corresponding angle of incidence.

11) A monochromatic light of 66 x 10-8 m wavelength strikes a double slit

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24) Show that Van der Waals’ effect can explain the conversion of gases into liquidstate.25) Give reason : Van der Waals’ effect on gases appears clearly at low temperatures.

26) Gas behavior deviates from that of the ideal gas as its density increases. Disuss thisstatement .

27) What is the scientific concept on which the Dewar’s flask is designed?

28) Give reason :Liquid helium is preferred as a cryogenic material.

29) Compare between the characteristics of the adiabatic change and the isothermalchange .

30) What is meant by the transitional (critical) temperature of a metal?

31) Give reason : We use a superconductive coil in manufactering the levitated train.

32) Give reason : A superconductor is used in making satellite's antenna.

33) Give reason: Meissner effect appears only in superconductive materials.

34) Suppose that the atoms of helium gas have the same average velocity as the atomsof argon gas. Which of them has a higher temperature and why?

35) Calculate the average kinetic energy and root mean square of the velocity of a freeelectron at 300˚K , where Boltzmann's constant = 1.38 x 10-23 J/˚K , the mass ofelectron is 9.1 x 10-31kg.

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where the density of water is 1000 kgm-3, that of wood is 550 kgm-3 and that of iron is7860 kgm-3.18) State the conditions which make the liquid flow in a steady flow and prove that in asteady flow, the velocity of liquid flow at any point is inversely proportional to theacross sectional area of the tube at that point?

19) A major artery of radius 0.5 cm branches out into many capillaries,the radius ofeach is 0.2 cm . The speed of blood in the main artery is 0.4 m/s , and the speed ofblood in each capillary is 0.25 m/s . Find the number of the capillaries ?

20) A cross sectional area of one end of a U- shaped tube is twice the other. When asuitable amount of water is placed in the tube and an amount of oil is poured into thewide end, the surface of water in the tube is lowered by 0.5 cm. Calculate the height ofoil in the tube. Knowing that the density of water equals 1000 kg m-3 and that of oilequals 800 kg m-3.

21) The small and large piston cross sectional areas of a hydraulic press are 4 x 10-4m2

and 20 x 10-4m2, respectively, and a force of 200 N is exerted on the small piston.Calculate the mass required to be placed on the large piston to be in the same level withthe small piston ,g = 10 m/s2.

22) What is the least area for a floating layer of ice of thickness 5 cm above the waterof a river which makes this layer carry a car whose mass is16 x103kg. The density of water is 1000 kg/m3 and that of ice is 920 kg/ m3.

23) A cork ball has a volume of 5 x10-3 m3,placed in water of density 1000 kgm-3.

About 2/5 of its volume was immersed. Calculate the density of the cork and the forceneeded to immerse all the volume of the ball.

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step - up transformer decreases the current.

44) There are three essential factors that must be considered when designingtransformers to decrease the loss of the electric energy. What are these factors andhow?

45) Give reason: The eddy current is not generated in the metallic blocks unlessa magnetic field of variable intensity exists.

46) Compare between an AC generator and a DC generator.

47) Give reason: To increase the power of a motor ,several coils seperated by smallangles are used.

48) The following table shows values of resistance of wire of cross sectional area 0.1 m2 and different lengths.

Plot the relation between the length ( l ) on the X axis and Resistance (R) on the Y axis. From the plot find:

a) resistance of a part of the wire of length 12 m .b) the resistivity of the material of the wire.c) the conductivity of the material of the wire.

49) A wire 30 cm long and 0.3 cm2 cross sectional area is connected in series with aDC source and an ammeter . The potential difference between the ends of the wire is

Length l m

Resistance R

2

5

4

10

6

15

10

25

14

35

16

40

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36) An amount of an ideal gas has a mass of 0.8 x 10-3 kg , a volume of 0.285 x 10-3 m-3,at a temperature of 12o C and under pressure of 105N/m2 . Calculatethe molecular mass of the gas where the universal gas constant equals 8.31 J/˚K.

37) Calculate the mean kinetic energy of an oxygen molecule at a temperature of50oC, where Boltzmann's constant is equal to1.38 x 10-23 J/˚K.

38) If the temperature at the surface of the Sun is 6000oK, find the root mean squarespeed of hydrogen molecules at the surface of the Sun, knowing that the hydrogen is inits atomic state. Its atomic mass =1, Avogadro's number (NA)=6.02 x 1023, andBoltzmann's constant=1.38 x 10-23 J/˚K .

39) Give reason : Efficiency of the battery increases by the decrease of its internalresistance.

40) In electric circuits connected in parallel, thick wires are used at the ends of thebattery,but at the ends of each resistor less thick wires are used. Why?

41) What is meant by: a) the effective value of AC. b) eddy current. c) the sensitivity of a galvanometer. d) the efficiency a transformer.

42) What is the physical concept for the operation of the following devices:galvanometer – transformer – current divider (or shunt)– potential multiplier.

43) Give reason :The step- down transformer increases the current, and the

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b) the efficiency of a transformer=90%.c) eddy currents. d) the effective value of an AC current =2A.

55) A step -down transformer of efficiency 100% is to be used to light a lamp ofpower 24 W at a potential difference 12 V. If the power source applied to thetransformer is 240 V, the number of turns of the secondary coil is 480 turn. 1) calculate the current passing through each of the primary and secondary coils 2) the number of the turns of the primary coil.

56) When an electric current is flowing through a perpendicular wire in a uniformmagnetic field, the wire is affected by a force. Which of the following instruments isbased on this principle:(1) electromagnet.(2) motor.(3) generator.(4) transformer.

57) Calculate the emf of a source if the work done to transfer 5C is 100 J.

58)Three resistors 10 , 20 , 30 are connected to a power supply . If the currentsare 0.15 A , 0.2 A , 0.05 A, respectively. Calculate the equivalent resistor for thiscircuit, and illustrate your answer with a labeled diagram.

59) Two resistors 400 and 300 are connected in series to a 130V power supply.Compare between the readings of a voltmeter of resistance 200 when connectedacross each resistor seperately ( neglecting the internal resistance of the power supply).

60) A wire has length 2 m and cross sectional area 0.1 m2 is connected to a sourcewith emf 10 V. Calculate the resistivity and conductivity of its material if it carries a

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0.8 V, when a current of 2A passes through it. Calculate the conductivity of the wirematerial.

50) A rectangular coil of N turns and surface area A is placed parallel to the lines of aregular magnetic field of flux density B Tesla. If the coil starts rotation from thisposition with a regular angular velocity ω, until it compelets half a revolution. Clarifywith a labeled diagram how the value of the emf changes with the rotational angleduring this time, and what is the maximum value of the induced emf generated in thiscoil.

51) A galvanometer has a resistance 40 Ω and reads up to 20 mA. Calculate theresistance of the shunt required to convert it into an ammeter, reading up to 100 mA. Ifthe coil of the galvanometer is connected to a potential multiplier with resistance 210Ω.Calculate the maximum potential difference to be read.

52) Compare between each ofa) a step -down transformer and a step- up transformer in terms of function, use, andnumber of turns of the secondary coil.b) dynamo and motor in terms of function and use.

53) Why does the transmission of the electric power from a generating station requirewires under high voltage?Choose the correct answer and give account

a) to be able to use the transformers .b) to insure that the current will flow for a long distance.c) to minimize the loss in the electric energy .d) to minimize the resistance of the wires.

54)What is meant by :a) the coefficient of mutual induction between two coils =2H.

384

386387

387386

388389

389388

390391

391390

392393

393392

394395

395394

396403

R = VI

= RAL

4 10 .m5

R

e

e

= =

= × ××

= ×

−

−

−

0 82

0 4

0 4 0 3 1030 10

4

2

. .

. .ρ

ρ Ω

Ω

RI RI I

= 200 10

V V R I

sg g

g

-3

g m g

=−

× ×× − ×

== +

= × × + × ×=

− −

− −

400100 10 20 10

10

20 10 40 210 20 105

3 3

3 3

Ω

( ) ( )V V

l

49)

51)

55) I PV

VV

I

VV

N

sw

s

s

p

p

s

p

p

= = =

=

=

= =

=

=

= × =

2412

2

12240 2

24240

0 1

12240

480

480 24012

9600

A

II

I

A

NN

N

p

s

p

s

p

p

.

397

397402

32) A superconductive material is used in making satellite’s antenna, because it has no electrical

resistance. This makes it easily affected by the weakest of electromagnetic waves.

33) Meissner effect appears only in superconductive materials, because they offer no

electrical resistance to the electrons. They are easily affected by external magnetic fields

and retain the kinetic energy acquired due to this field without any loss in the form of

thermal energy.

Hence, current flows continuously ,leading in turn to a counter magnetic field , so that the

net field inside is zero (diamagnetic) .This is why a superconducting magnet is always re-

pulsive to the external magnetic field .

34) The temperature of argon gas is higher than that of helium gas, because the mass of the

argon atom is more than that of a helium atom , so the kinetic energy of an argon atom is

more than that of a helium atom.

35)

39) As the internal resistance of the battery decreases, the lost work done (wasted energy) is

reduced during operation.

40) Because the current intensity in parallel circuits is greater at the input and output compared

to the current in each branch.

12

32

12

32

6.21 x 10-21 x 229.1 x 10-31

12

mv2 = kT

mv2 = x 1.38 x 10-23 x 300

= 6.21 x 10-21 J

v = ( ) = 1.17 x 105 m/s

396

398381

399404

W Q

100

5

VBR+r

122+0.5

2.412

57) VB = = =20V

64)The wasted potential difference is the potential (voltage) drop on the internal resistance of the cell .

I = = =4.8

Ir = 4.8 X 0.5 =2.4V

Percent drop = X 100 = 20%

398

407

serial quantity symbol unit

J

W , Js-1 (watt)

NsCelsius, Fahrenheit, Kelvin

mole

pascal , Nm-2

pascal , Nm-2

J

J kg-1 ˚K-1

JK-1

J kg-1

J kg-1

per degree rise

per degree rise

kg/s

m3/s

Ns m-2

______

C (Coulomb)

C

V (Volt)

V

PEPw

Iimp

t˚C , t˚F , T˚KnPPa

Qth

Cth

qth

Bth

Lth

αV

βPQm

QV

ηvs

ηQ,q

eVVB

potential energy

power

impulse

temperature

quantity of matter

pressure

atmospheric pressure

quantity of heat

specific heat

heat capacity

latent heat for evaporation

latent heat for fusion

volume expansion coefficient

pressure expansion coefficient

mass rate of flow

volume rate of flow

viscosity coefficient

efficiency

electric charge

electron charge

potential difference

battery voltage

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

401

406

serial

Appendix 1

Symbols and Units of Some Physical Quantities

quantity symbol unit

x,y,z,d

A

Vol

t

T

v

α,θ,φω

m,Mme

ρagPL

FFg

τ

WE

KE

m (meter)

m2

m3

s (second)

s

m s-1

deg , rad

rad s-1

kg

kg

kg m-3

m s-2

m s-2

kg m s-1

N , kg ms-2

N(Newton)

Nm

J(Joule)

J

J

displacement

area

volume

time

periodic time

velocity / speed

angle

angular velocity

mass

electron mass

density

acceleration

acceleration due to gravity

linear momentum

force

weight

torque

work

energy

kinetic energy

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

400

409

Appendix 2Fundamental Physical Constants

value

Gk

NA

RKµce

me

mp

hu

RH

mn

g

reMeMmrm

6.677x10-11 N m2 kg-2

1.38x10-23 JK-1

6.02x1026 Molecule.kmol-1

8.31x103 J.kmol-1 K-1

9x109 Nm2C-2

4 x10-7 Weber m-1A-1

3x108 m.s-1

1.6x10-19 C

9.1x10-31 kg

1.79x1011 C.kg-1

1.673x10-27 kg

6.63x10-34 Js

1.66x10-27 kg

1.096x107 m-1

1.675x10-27 kg

22.4x10-3 m3

9.8066 ms-2

6.374x106 m

5.976x1024 kg

7.35x1022 kg

3.844x108 m

eme

symbol Physical Constant1-Universal gravitation constant2-Boltzmann constant 3-Avogadro’s number4- Universal gas constant5-Coulomb’s law constant6-Permeability of free space7-Speed of light in vacuum8-Elementary charge9- Electron rest mass 10-Specific charge of electron11-Proton rest mass12-Planck’s constant13-Atomic mass unit14-Rydberg constant15-Neutron rest mass16-Molar volume of ideal gas at S.T.P17-Standard gravity at the Earth’s surface18-Equatorial radius of the Earth19- Mass of the Earth20-Mass of the Moon 21- Mean radius of the Moon’s orbitaround the Earth

403

408

serial quantity symbol unit

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

V

Vm-1

Gauss

A (Ampere)

Ω (Ohm)

Ω m

Ω-1 m-1

______

Am-1

Tesla , Wb m-2

Wb (Weber)

H (Henry)

H

Weber A-1 m-1

Nm Tesla-1

ms-1

Hertz (Hz)

Hz

m______

______

emfεφe

IRρe

σαe , βe

HBφm

LMµ

md

cνfλn

ωα

electromotive force (emf)

field intensity

electric flux

electric current

electrical resistor

resistivity

conductivity

transistor gain

magnetic field intensity

magnetic flux density

magnetic flux self inductance

mutual inductance

permeability

magnetic dipole

speed of light

frequency of wave

frequency of electric current

wave length

refractive index

dispersive power

402

411

Standard Prefixes

name

Yocto

Zepto

Atto

Femto

Pico

Nano

Micro

Milli

Centi

Deci

___

Deka

Hecto

Kilo

Mega

Giga

Tera

Peta

Exa

Zetta

Yotta

10-24

10-21

10-18

10-15

10-12

10-9

10-6

10-3

10-2

10-1

100

101

102

103

106

109

1012

1015

1018

1021

1024

Appendix 3

power of 10

405

410

value

22-Mass of the Sun 23- Mean radius of the Earth’s orbit around the Sun

24-Period of the Earth’s orbit around the Sun

25- Diameter of our galaxy26- Mass of our galaxy

27- Radius of the Sun

28- Sun’s radiation intensity at the Earth’s surface

symbol Physical ConstantMsresyr

__

__

__

__

1.989x1030 kg1.496x1011 m

3.156x107 s

7.5x1020 m

2.7x1041 kg

7x108 m

0.134 J cm-2 s-1

404

413

Appendix 5Gallery of Scientists

A pioneer in medicine and the discoverer of the laws of motion

Ibn Malka(1072 -1152 )

A pioneer in astronomy and the inventorof the simple pendulum.

Ibn Unis(952 -1009 )

A pioneer in geography and astronomy.Al Baironi(973 - 1048 )

A pioneer in mathematics, astronomy,medicine and the founder of optics.

Ibn Al-Haytham(965 - 1040)

A pioneer in philosophy, physics ,particularly optics.

Al Kindy(800 - 873)

The inventor of the phonograph and theelectric lamp, and other inventions “1000".

Edison (Thomas)(1847-1931)

The discoverer of the ratio of the radius ofa circle to its circumference, buoyancy and

the reflecting mirror.

Arkhimêdês

(287 -212 BC)

The discoverer of the molcular theory Avogadro (Amedeo)(1776 - 1856)

607

412

Greek AlphabetAppendix 4

606

415

The inventor of the barometerTorricelli (Evangelista)

(1608 - 1647)

The inventor of the telescope and thediscoverer of accelration due to gravity.

Galileo (Galilei)(1564 - 1642)

The discoverer of the electric charge inmuscles.

Galvani (Luigi)(1737 - 1798)

The discoverer of the law of mixinggases.

Dalton (John)(1766 - 1844)

The discoverer of radioactivty.Rutherford (Ernest)

(1871 - 1937)

The discoverer of the induction coil.Ruhmkorff (Heinrich)

(1803 - 1877)

The discoverer of X-rays.Rontgen (Wilhelm)

(1845 - 1923)

The discoverer of Quantum Mechanics.Schrodinger (Erwin)

(1887 - 1961)

A pioneer in hydrostatics.Al-Khazin

609

414

He was awarded Nobel prize in 1921 forhis explanation of the photoelectric effect,

the founder of the theory of relativity

Einstein (Albert)(1879 - 1955)

He performed studies on electricity,telegraph and magnetism.

Ampére (André - Marie)(1775 - 1836)

The founder of the theory ofelectromagnetism in 1820

Oersted (Christian)(1777 - 1851)

The discoverer of Ohm’s lawOhm (George)(1789 - 1854)

The discoverer of Pascal’s rule.Pascal (Blaise)(1623 - 1662)

A pioneer in fine mechanics and waterclocks.

Al Joazri

The founder of X-ray diffraction.Bragg (William)

(1862 - 1942)

He produced a model for the atom.Bohr (Neils)(1885 - 1962)

The discoverer of Boyle’s law.Boyle (Robert)(1627 - 1691)

608

417

The discoverer of Lenz’s rule.Lenz (Heinrich)(1804 - 1865)

The discoverer of the photon and theblackbody radiation.

Planck (Max)(1858 - 1947)

The discoverer of Maxwell’s equations.Maxwell (James)

The discoverer of the laws of motion,gravity and colors.

Newton (Isaac)(1642 - 1727)

The discoverer of the electromagneticwaves

Hertz (Heinrich)(1857 - 1894)

He proposed the secondary sources inthe from of a wave.

The discoverer of interference. Young (Thomas)

(1773 - 1829)

Huygens (Christian) (1629 - 1695)

411

416

The discoverer of the laws ofelectromagnetics.

Faraday (Michael)(1791 - 1867)

The discoverer of Van Der Waals’effect.

Van Der Waals (Johannes)(1837 - 1923)

He interpreted the atomic spectra anddiffraction

Fraunhofer (Joseph Von)(1787 - 1826)

The inventor of the battery.Volta (Alessandro)(1745 - 1827)

He contributed to the atomic bomb.Fermi (Enrico) (1901 - 1954)

The discoverer of liquid helium.Kamelingh (Onnes)(1853 - 1926)

The discoverer of the laws of planetarymotion.

Kepler (Johannes)(1571 - 1630)

He proved that the Earth rotates aroundthe Sun.

Copernicus (Nicolas)(1473 - 1543)

The discoverer of Kirchhoff’s law.Kirchhoff (Gustav)(1824 - 1887)

410

418

Selected Physics Sites on the Internet

Appendix 6

http://www.dke-encyc.com

http://imagine.gsfc.nasa.gov

http://csep10.phys.utk.edu

http://www.howstuffworks.com

http://www.colorado.edu/physics/2000/index.pl

http://scienceworld.wolfram.com/physics

http://www.physlink.com

http://www.intuitor.com/moviephysics

http://www.newport.com/spectralanding

http://www.mathpages.com/home/iphysics.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

http://www.smsec.com

412

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