Chapter 4Chapter 4Electromagnetic WavesElectromagnetic Waves

1. Introduction: Maxwell’s 1. Introduction: Maxwell’s equationsequations

Electricity and Electricity and magnetism were magnetism were originally thought to be originally thought to be unrelatedunrelated

in 1865, James Clerk in 1865, James Clerk Maxwell provided a Maxwell provided a mathematical theory mathematical theory that showed a close that showed a close relationship between relationship between all electric and all electric and magnetic phenomenamagnetic phenomena

Maxwell’s predictionsMaxwell’s predictions Electric field lines originate on positive charges and terminate on negative chargesElectric field lines originate on positive charges and terminate on negative charges

ElectricElectric field is produced by field is produced by chargescharges Magnetic field lines always form closed loops – they do not begin or end anywhereMagnetic field lines always form closed loops – they do not begin or end anywhere

MagneticMagnetic filed is produced by currents ( filed is produced by currents (moving chargesmoving charges)) A varying magnetic field induces an emf and hence an electric field (Faraday’s Law)A varying magnetic field induces an emf and hence an electric field (Faraday’s Law)

ElectricElectric field is also produced by field is also produced by changing magnetic fieldchanging magnetic field

Magnetic Magnetic field is also produced byfield is also produced by changing electric field. changing electric field.Question:Question: is there a is there a symmetrysymmetry between electric and magnetic fields, i.e. can between electric and magnetic fields, i.e. can magnetic fieldmagnetic field be produced by be produced by changing electric fieldchanging electric field??????

Maxwell: YES!!!

Maxwell’s PredictionsMaxwell’s Predictions If magnetic field can create electric field and vice versa, there is If magnetic field can create electric field and vice versa, there is

a very interesting phenomenon to be observeda very interesting phenomenon to be observed

– Changing electric field produces magnetic field…Changing electric field produces magnetic field…– … … which in turn produces changing electric one (but: energy which in turn produces changing electric one (but: energy

conservation)conservation)– … … which in turn produces changing magnetic field…which in turn produces changing magnetic field…

Maxwell concluded that visible light and all other Maxwell concluded that visible light and all other electromagnetic waves consist of fluctuating electric and electromagnetic waves consist of fluctuating electric and magnetic fields, with each varying field inducing the othermagnetic fields, with each varying field inducing the other

Maxwell calculated the speed of light to be 3x10Maxwell calculated the speed of light to be 3x1088 m/s m/s

Note: Charges and FieldsNote: Charges and Fields

StationaryStationary charges produce only charges produce only electric fieldselectric fields ChargesCharges in in uniform motionuniform motion (constant velocity) produce (constant velocity) produce electricelectric

and and magnetic fieldsmagnetic fields ChargesCharges that are that are acceleratedaccelerated produce produce electric and magnetic fields electric and magnetic fields

and electromagnetic wavesand electromagnetic waves

These fields are These fields are in phasein phase– At any point, both fields reach their maximum value at the At any point, both fields reach their maximum value at the

same timesame time

Electromagnetic WavesElectromagnetic WavesEM waves can be produced by an antenna, which is just some kind of wire that is connected to an ac source.  The ac source produces oscillating + and - charges which set up electric field (due to the separation of charge) and a magnetic field (due to the current in the wire).

Note that the electric and magnetic fields are perpendicular to each other.  This field begins to move away from the antenna and in a little while the ac source has caused the situation to reverse.

Electromagnetic Waves are Electromagnetic Waves are Transverse WavesTransverse Waves

TheThe E E and and BB fields are fields are perpendicularperpendicular to each other to each other

Both fields are perpendicular to Both fields are perpendicular to the direction of motionthe direction of motion

– Therefore, em waves are Therefore, em waves are transverse wavestransverse waves

1 LC

Review problem: car radioReview problem: car radio

An An RLC RLC circuit is used to tune a radio to an FM station broadcasting at circuit is used to tune a radio to an FM station broadcasting at 88.9 MHz. The resistance in the circuit is 12.0 Ω and the capacitance is 88.9 MHz. The resistance in the circuit is 12.0 Ω and the capacitance is 1.40 pF. What inductance should be present in the circuit? 1.40 pF. What inductance should be present in the circuit?

An RLC circuit is used to tune a radio to an FM station broadcasting at 88.9 MHz. The resistance in the circuit is 12.0 Ω and the capacitance is 1.40 pF. What inductance should be present in the circuit?

Given:

RLC circuitf0=88.9 HzR = 12.0 C = 1.40 pF

Find:

L=?

The resonance frequency of the circuit should be chosen to match that of the radio station

0 2 20

1 1or

42f L

f CLC

This is sufficient to know for a solution, as we know all of the quantities on the right hand side

6

22 3 12

12.29 10

4 88.9 10 1.40 10L H

Hz F

Properties of EM WavesProperties of EM Waves

Electromagnetic waves are transverse wavesElectromagnetic waves are transverse waves Electromagnetic waves travel at the speed of lightElectromagnetic waves travel at the speed of light

– Because em waves travel at a speed that is precisely Because em waves travel at a speed that is precisely the speed of light, the speed of light, light is an electromagnetic wavelight is an electromagnetic wave

812.99792 10

o o

c m s

The sun is about 1.5x10The sun is about 1.5x101111 m from the earth.  How long does it take light to m from the earth.  How long does it take light to get here? get here?

11

8

distance 1.5 10500 sec 8.3 min

time 3 10

mt

m s

QuestionQuestion

Properties of EM Waves, 2Properties of EM Waves, 2

The ratio of the electric field to the magnetic field The ratio of the electric field to the magnetic field is equal to the speed of lightis equal to the speed of light

Electromagnetic waves carry energy as they travel Electromagnetic waves carry energy as they travel through space, and this energy can be transferred through space, and this energy can be transferred to objects placed in their pathto objects placed in their path

B

Ec

Energy Carried by Electromagnetic Waves

Electromagnetic waves carry energy, and as they propagate through space they can transfer energy to objects placed in their path

The rate of flow of energy in an electromagnetic wave is described by a vector S, called the Poynting vector, which is defined by the expression

If E X B = EB then:

Because B = E/c, we can also express this as

These equations for S apply at any instant of time and represent the instantaneous rate at which energy is passing through a unit area

Properties of EM Waves, 3Properties of EM Waves, 3

Energy carried by em waves is shared equally by the Energy carried by em waves is shared equally by the electric and magnetic fieldselectric and magnetic fields

What is of greater interest for a sinusoidal plane electromagnetic wave is the time average of S over one or more cycles, which is called the wave intensity I. When this average is taken, we obtain an expression involving the time average of cos2(kx -ωt), which equals .

o

2max

o

2max

o

maxmax

2

Bc

c2

E

2

BE

areaunitperpowerAverage

Properties of EM Waves, finalProperties of EM Waves, final

Electromagnetic waves transport linear Electromagnetic waves transport linear momentum as well as energymomentum as well as energy– For complete absorption of energy U, For complete absorption of energy U,

p=U/cp=U/c– For complete reflection of energy U, For complete reflection of energy U,

p=(2U)/cp=(2U)/c

Radiation pressures can be determined Radiation pressures can be determined experimentallyexperimentally

Determining Radiation PressureDetermining Radiation Pressure

This is an apparatus This is an apparatus for measuring radiation for measuring radiation pressurepressure

In practice, the system In practice, the system is contained in a is contained in a vacuumvacuum

The pressure is The pressure is determined by the determined by the angle at which angle at which equilibrium occursequilibrium occurs

The Spectrum of EM WavesThe Spectrum of EM Waves

Forms of electromagnetic waves exist that are Forms of electromagnetic waves exist that are distinguished by their frequencies and distinguished by their frequencies and wavelengthswavelengths

c = ƒλc = ƒλ

Wavelengths for visible light range from 400 nm Wavelengths for visible light range from 400 nm to 700 nmto 700 nm

There is no sharp division between one kind of There is no sharp division between one kind of em wave and the nextem wave and the next

The EMThe EMSpectrumSpectrum

Note the overlap Note the overlap between types of between types of waveswaves

Visible light is a Visible light is a small portion of small portion of the spectrumthe spectrum

Types are Types are distinguished by distinguished by frequency or frequency or wavelengthwavelength

Notes on The EM SpectrumNotes on The EM Spectrum

Radio WavesRadio Waves– Used in radio and television communication Used in radio and television communication

systemssystems

MicrowavesMicrowaves– Wavelengths from about 1 mm to 30 cmWavelengths from about 1 mm to 30 cm– Well suited for radar systemsWell suited for radar systems– Microwave ovens are an applicationMicrowave ovens are an application

Notes on the EM Spectrum, 2Notes on the EM Spectrum, 2

Infrared wavesInfrared waves– Incorrectly called “heat waves”Incorrectly called “heat waves”– Produced by hot objects and moleculesProduced by hot objects and molecules– Readily absorbed by most materialsReadily absorbed by most materials

Visible lightVisible light– Part of the spectrum detected by the Part of the spectrum detected by the

human eyehuman eye– Most sensitive at about 560 nm (yellow-Most sensitive at about 560 nm (yellow-

green)green)

Notes on the EM Spectrum, 3Notes on the EM Spectrum, 3

Ultraviolet lightUltraviolet light– Covers about 400 nm to 0.6 nmCovers about 400 nm to 0.6 nm– Sun is an important source of uv lightSun is an important source of uv light– Most uv light from the sun is absorbed in the Most uv light from the sun is absorbed in the

stratosphere by ozonestratosphere by ozone

X-raysX-rays– Most common source is acceleration of high-energy Most common source is acceleration of high-energy

electrons striking a metal targetelectrons striking a metal target– Used as a diagnostic tool in medicineUsed as a diagnostic tool in medicine

Notes on the EM Spectrum, finalNotes on the EM Spectrum, final

Gamma raysGamma rays– Emitted by radioactive nucleiEmitted by radioactive nuclei– Highly penetrating and cause serious damage Highly penetrating and cause serious damage

when absorbed by living tissuewhen absorbed by living tissue

Looking at objects in different portions of the Looking at objects in different portions of the spectrum can produce different informationspectrum can produce different information

Example: talking to a submarineExample: talking to a submarine

The U.S. Navy has long proposed the construction of extremely low-The U.S. Navy has long proposed the construction of extremely low-frequency (ELF) communications systems; such waves could penetrate frequency (ELF) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter-the oceans to reach distant submarines. Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency wavelength antenna for a transmitter generating ELF waves of frequency 75 Hz. How practical is this?75 Hz. How practical is this?

The U.S. Navy has long proposed the construction of extremely low-frequency The U.S. Navy has long proposed the construction of extremely low-frequency (ELF) communications systems; such waves could penetrate the oceans to reach (ELF) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter-wavelength antenna for a distant submarines. Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency 75 Hz. How practical is this?transmitter generating ELF waves of frequency 75 Hz. How practical is this?

Given:

¼ wavelengthantennaf0=75 Hz

Find:

L=?

First determine the wavelength, a forth of which will give us the length of an antenna

863.00 10

4.00 10 400075

v m sm km

f Hz

The required length of antenna is then a quarter of this

40001000

4 4

kmL km