Magnets and Magnetic Fields Magnets Magnets attract iron-containing objects. Magnets have two...

Magnets and Magnetic Fields

Magnets

• Magnets attract iron-containing objects.

• Magnets have two distinct poles called the north pole and the south pole. These names are derived from a magnet’s behavior on Earth.

• Like poles of magnets repel each other; unlike poles attract each other.

Magnetic Domains• Magnetic Domain

A region composed of a group of atoms whose magnetic fields are aligned in the same direction is called a magnetic domain.

• Some materials can be made into permanent magnets.– Soft magnetic materials (for example iron) are

easily magnetized but tend to lose their magnetism easily.

– Hard magnetic materials (for example nickel) tend to retain their magnetism.

Magnetic Fields

• A magnetic field is a region in which a magnetic force can be detected.

• Magnetic field lines can be drawn with the aid of a compass.

Magnetic Field of a Bar Magnet

Magnetic Fields, continued

• Earth’s magnetic field is similar to that of a bar magnet.

• The magnetic south pole is near the Geographic North Pole. The magnetic north pole is near the Geographic South Pole.

• Magnetic declination is a measure of the difference between true north and north indicated by a compass.

Earth’s Magnetic Field

Magnetic Field of a Current-Carrying Wire

• A long, straight, current-carrying wire has a cylindrical magnetic field.

• Compasses can be used to shown the direction of the magnetic field induced by the wire.

• The right-hand rule can be used to determine the direction of the magnetic field in a current-carrying wire.

Magnetism from Electricity

The Right-Hand Rule

Negative Current Positive CurrentZero Current

Magnetic Field of a Current Loop

• Solenoids produce a strong magnetic field by combining several loops.

• A solenoid is a long, helically wound coil of insulated wire.

Magnetic Force

Charged Particles in a Magnetic Field

• A charge moving through a magnetic field experiences a force proportional to the charge, velocity, and the magnetic field.

magnetic

magnetic field = magnetic force on a charged particle

(magnitude of charge)(speed of charge)

Charged Particles in a Magnetic Field, continued• The direction of the magnetic force on a moving

charge is always perpendicular to both the magnetic field and the velocity of the charge.

• An alternative right-hand rule can be used to find the direction of the magnetic force.

• A charge moving through a magnetic field follows a circular path.

Magnetic Force

Alternative Right-Hand Rule: Force on a Moving Charge

Magnetic Force

Sample Problem

Particle in a Magnetic Field

A proton moving east experiences a force of 8.8 10–19 N upward due to the Earth’s magnetic field.At this location, the field has a magnitude of 5.5 10–5 T to the north. Find the speed of the particle.

Magnetic Force

Sample Problem, continued

Given:

q = 1.60 10–19 C

B = 5.5 10–5 T

Fmagnetic = 8.8 10–19 N

Unknown:

Magnetic Force

Use the definition of magnetic field strength. Rearrange to solve for v.

–19 –5

8.8 19 N

(1.60 19 )(5.5 10 )

1.0 10 m/s

magnetic

Magnetic Force

Magnetic Force on a Current-Carrying Conductor• A current-carrying wire in an external magnetic field

undergoes a magnetic force.

• The force on a current-carrying conductor perpendicular to a magnetic field is given by:

magnitude of magnetic force = (magnitude of magnetic field) (current) (length of conductor within B)

Force on a Current-Carrying Wire in a Magnetic Field

Magnetic Force

Magnetic Force on a Current-Carrying Conductor, continued• Two parallel current-carrying wires exert a force on

one another that are equal in magnitude and opposite in direction.

• If the currents are in the same direction, the two wires attract one another.

• If the currents are in opposite direction, the wires repel one another.

• Loudspeakers use magnetic force to produce sound.

Force Between Parallel Conducting Wires

Magnetic Force

Sample Problem

Force on a Current-Carrying Conductor

A wire 36 m long carries a current of 22 A from east to west. If the magnetic force on the wire due to Earth’s magnetic field is downward (toward Earth) and has a magnitude of 4.0 10–2 N, find the magnitude and direction of the magnetic field at this location.

Magnetic Force

Given:

I = 22 A

Fmagnetic = 4.0 10–2 N

Unknown:

Magnetic Force

Force on a Current-Carrying ConductorUse the equation for the force on a current-carrying conductor perpendicular to a magnetic field.

Rearrange to solve for B.

Magnetic Force

Using the right-hand rule to find the direction of B, face north with your thumb pointing to the west (in the direction of the current) and the palm of your hand down (in the direction of the force). Your fingers point north. Thus, Earth’s magnetic field is from south to north.

Multiple Choice

1. Which of the following statements best describes the domains in unmagnetized iron?

A. There are no domains.

B. There are domains, but the domains are smaller than in magnetized iron.

C. There are domains, but the domains are oriented randomly.

D. There are domains, but the domains are not magnetized.

Multiple Choice, continued

1. Which of the following statements best describes the domains in unmagnetized iron?

A. There are no domains.

B. There are domains, but the domains are smaller than in magnetized iron.

C. There are domains, but the domains are oriented randomly.

D. There are domains, but the domains are not magnetized.

2. Which of the following statements is most correct?F. The north pole of a freely rotating magnet points north because the magnetic pole near the geographic North Pole is like the north pole of a magnet.G. The north pole of a freely rotating magnet points north because the magnetic pole near the geographic North Pole is like the south pole of a magnet.H. The north pole of a freely rotating magnet points south because the magnetic pole near the geographic South Pole is like the north pole of a magnet.J. The north pole of a freely rotating magnet points south because the magnetic pole near the geographic South Pole is like the south pole of a magnet.

3. If you are standing at Earth’s magnetic north pole and holding a bar magnet that is free to rotate in three dimensions, which direction will the south pole of the magnet point?

A. straight up

B. straight down

C. parallel to the ground, toward the north

D. parallel to the ground, toward the south

3. If you are standing at Earth’s magnetic north pole and holding a bar magnet that is free to rotate in three dimensions, which direction will the south pole of the magnet point?

A. straight up

B. straight down

C. parallel to the ground, toward the north

D. parallel to the ground, toward the south

4. How can you increase the strength of a magnetic field inside a solenoid?

F. increase the number of coils per unit length

G. increase the current

H. place an iron rod inside the solenoid

J. all of the above

4. How can you increase the strength of a magnetic field inside a solenoid?

F. increase the number of coils per unit length

G. increase the current

H. place an iron rod inside the solenoid

J. all of the above

5. How will the electron move once it passes into the magnetic field?A. It will curve to the right and then continue moving in a straight line to the right.B. It will curve to the left and then continue moving in a straight line to the left.C. It will move in a clockwise circle.D. It will move in a counterclockwise circle.

6. What will be the magnitude of the force on the electron once it passes into the magnetic field?

F. qvB

G. –qvB

H. qB/v

6. What will be the magnitude of the force on the electron once it passes into the magnetic field?

F. qvB

G. –qvB

H. qB/v

7. An alpha particle (q = 3.2 10–19 C) moves at a speed of 2.5 106 m/s perpendicular to a magnetic field of strength 2.0 10–4 T. What is the magnitude of the magnetic force on the particle?

A. 1.6 10–16 N

B. –1.6 10–16 N

C. 4.0 10–9 N

D. zero

7. An alpha particle (q = 3.2 10–19 C) moves at a speed of 2.5 106 m/s perpendicular to a magnetic field of strength 2.0 10–4 T. What is the magnitude of the magnetic force on the particle?

A. 1.6 10–16 N

B. –1.6 10–16 N

C. 4.0 10–9 N

D. zero

Use the passage below to answer questions 8–9.A wire 25 cm long carries a 12 A current from east to west. Earth’s magnetic field at the wire’s location has a magnitude of 4.8 10–5 T and is directed from south to north.

8. What is the magnitude of the magnetic force on the wire?F. 2.3 10–5 NG. 1.4 10–4 NH. 2.3 10–3 NJ. 1.4 10–2 N

9. What is the direction of the magnetic force on the wire?A. northB. southC. up, away from EarthD. down, toward Earth

• Wire 1 carries current I1 and creates magnetic field B1.

10. What is the direction of the magnetic field B1 at the location of wire 2?

F. to the left

G. to the right

H. into the page

J. out of the page

10. What is the direction of the magnetic field B1 at the location of wire 2?

F. to the left

G. to the right

H. into the page

J. out of the page

11. What is the direction of the force on wire 2 as a result of B1?

A. to the left

B. to the right

C. into the page

D. out of the page

11. What is the direction of the force on wire 2 as a result of B1?

A. to the left

B. to the right

C. into the page

D. out of the page

I 2 2 2B

12. What is the magnitude of the magnetic force on wire 2?

Short Response

13. Sketch the magnetic field lines around a bar magnet.

Short Response, continued

13. Sketch the magnetic field lines around a bar magnet.

Answer:

14. Describe how to use the right-hand rule to determine the direction of a magnetic field around a current-carrying wire.

Answer: Imagine wrapping the fingers of your right hand around the wire and pointing your thumb in the direction of the current. The magnetic field lines form concentric circles that are centered on the wire and curve in the same direction as your fingers.

15. Draw a diagram showing the path of a positively charged particle moving in the plane of a piece of paper if a uniform magnetic field is coming out of the page.

Answer:

Magnetic Field of a Current Loop

Electricity from Magnetism

Electromagnetic Induction

• Electromagnetic induction is the process of creating a current in a circuit by a changing magnetic field.

• A change in the magnetic flux through a conductor induces an electric current in the conductor.

• The separation of charges by the magnetic force induces an emf.

Electromagnetic Induction in a Circuit Loop

Electromagnetic Induction, continued

• The angle between a magnetic field and a circuit affects induction.

• A change in the number of magnetic field lines induces a current.

Characteristics of Induced Current• Lenz’s Law

The magnetic field of the induced current is in a direction to produce a field that opposes the change causing it.

• Note: the induced current does not oppose the applied field, but rather the change in the applied field.

Characteristics of Induced Current, continued• The magnitude of the induced emf can be predicted

by Faraday’s law of magnetic induction.

• Faraday’s Law of Magnetic Induction

average induced emf = –the number of loops in the circuit

the time rate of change in the magnetic flux

– Memf Nt

• The magnetic flux is given by M = ABcos

Sample Problem

Induced emf and Current

A coil with 25 turns of wire is wrapped around a hollow tube with an area of 1.8 m2. Each turn has the same area as the tube. A uniform magnetic field is applied at a right angle to the plane of the coil. If the field increases uniformly from 0.00 T to 0.55 T in 0.85 s, find the magnitude of the induced emf in the coil. If the resistance in the coil is 2.5 Ω, find the magnitude of the induced current in the coil.

1. Define

Given:

∆t = 0.85 s A = 1.8 m2 = 0.0º

N = 25 turns R = 2.5 Ω

Bi = 0.00 T = 0.00 V•s/m2

Bf = 0.55 T = 0.55 V•s/m2

Unknown:

emf = ?

Induced emf and Current1. Define, continued

Diagram: Show the coil before and after the change in the magnetic field.

2. Plan

Choose an equation or situation. Use Faraday’s law of magnetic induction to find the induced emf in the coil.

cos– –M

ABemf N N

t tSubstitute the induced emf into the definition of resistance to determine the induced current in the coil.

2. Plan, continued

Rearrange the equation to isolate the unknown. In this example, only the magnetic field strength changes with time. The other components (the coil area and the angle between the magnetic field and the coil) remain constant.

– cos

Bemf NA

Induced emf and Current3. Calculate

Substitute the values into the equation and solve.

V•s0.55 – 0.00

m–(25)(1.8 m )(cos0.0º ) –29 V

(0.85 s)

–29 V–12 A

2.5 Ω

–29 V

–12 A

Induced emf and Current4. Evaluate

The induced emf, and therefore the induced current, is directed through the coil so that the magnetic field produced by the induced current opposes the change in the applied magnetic field. For the diagram shown on the previous page, the induced magnetic field is directed to the right and the current that produces it is directed from left to right through the resistor.

Generators, Motors, and Mutual Inductance

Generators and Alternating Current• A generator is a machine that converts mechanical

energy into electrical energy.

• Generators use induction to convert mechanical energy into electrical energy.

• A generator produces a continuously changing emf.

Induction of an emf in an AC Generator

Generators and Alternating Current, continued

• Alternating current is an electric current that changes direction at regular intervals.

• Alternating current can be converted to direct current by using a device called a commutator to change the direction of the current.

Motors

• Motors are machines that convert electrical energy to mechanical energy.

• Motors use an arrangement similar to that of generators.

• Back emf is the emf induced in a motor’s coil that tends to reduce the current in the coil of a motor.

Mutual Inductance

• The ability of one circuit to induce an emf in a nearby circuit in the presence of a changing current is called mutual inductance.

• In terms of changing primary current, Faraday’s law is given by the following equation, where M is the mutual inductance:

– –M I

emf N Mt t

AC Circuits and Transformers

Objectives

• Distinguish between rms values and maximum values of current and potential difference.

• Solve problems involving rms and maximum values of current and emf for ac circuits.

• Apply the transformer equation to solve problems involving step-up and step-down transformers.

Effective Current

• The root-mean-square (rms) current of a circuit is the value of alternating current that gives the same heating effect that the corresponding value of direct current does.

• rms Current

maxmax0.707

Effective Current, continued

• The rms current and rms emf in an ac circuit are important measures of the characteristics of an ac circuit.

• Resistance influences current in an ac circuit.

Sample Problem

rms Current and emf

A generator with a maximum output emf of 205 V is connected to a 115 Ω resistor. Calculate the rms potential difference. Find the rms current through the resistor. Find the maximum ac current in the circuit.

1. DefineGiven:

∆Vrms = 205 VR = 115 ΩUnknown:

∆Vrms = ? Irms = ? Imax = ?

rms Current and emf2. Plan

Choose an equation or situation. Use the equation for the rms potential difference to find ∆Vrms.

∆Vrms = 0.707 ∆Vmax

Rearrange the definition for resistance to calculate Irms.

rmsrms

Use the equation for rms current to find Irms.

Irms = 0.707 Imax

rms Current and emf2. Plan, continued

Rearrange the equation to isolate the unknown. Rearrange the equation relating rms current to maximum current so that maximum current is calculated.

max 0.707rmsI

rms Current and emf3. Calculate

Substitute the values into the equation and solve.

(0.707)(205 V) 145 V

145 V1.26 A

115 Ω1.26 A

1.78 A0.707

4. Evaluate The rms values for emf and current are a little more than two-thirds the maximum values, as expected.

Transformers

• A transformer is a device that increases or decreases the emf of alternating current.

• The relationship between the input and output emf is given by the transformer equation.

induced emf in secondary =

number of turns in secondaryapplied emf in primary

number of turns in primary

Transformers, continued

• The transformer equation assumes that no power is lost between the primary and secondary coils. However, real transformers are not perfectly efficient.

• Real transformers typically have efficiencies ranging from 90% to 99%.

• The ignition coil in a gasoline engine is a transformer.

A Step-Up Transformer in an Auto Ignition System

Electromagnetic Waves

Propagation of Electromagnetic Waves• Electromagnetic waves travel at the speed of light

and are associated with oscillating, perpendicular electric and magnetic fields.

• Electromagnetic waves are transverse waves; that is, the direction of travel is perpendicular to the the direction of oscillating electric and magnetic fields.

• Electric and magnetic forces are aspects of a single force called the electromagnetic force.

Propagation of Electromagnetic Waves, continued• All electromagnetic waves are produced by

accelerating charges.

• Electromagnetic waves transfer energy. The energy of electromagnetic waves is stored in the waves’ oscillating electric and magnetic fields.

• Electromagnetic radiation is the transfer of energy associated with an electric and magnetic field. Electromagnetic radiation varies periodically and travels at the speed of light.

The Sun at Different Wavelengths of Radiation

Propagation of Electromagnetic Waves, continued• High-energy electromagnetic waves behave like

particles.

• An electromagnetic wave’s frequency makes the wave behave more like a particle. This notion is called the wave-particle duality.

• A photon is a unit or quantum of light. Photons can be thought of as particles of electromagnetic radiation that have zero mass and carry one quantum of energy.

The Electromagnetic Spectrum

• The electromagnetic spectrum ranges from very long radio waves to very short-wavelength gamma waves.

• The electromagnetic spectrum has a wide variety of applications and characteristics that cover a broad range of wavelengths and frequencies.

The Electromagnetic Spectrum, continued• Radio Waves

– longest wavelengths– communications, tv

• Microwaves– 30 cm to 1 mm– radar, cell phones

• Infrared– 1 mm to 700 nm– heat, photography

• Visible light– 700 nm (red) to 400 nm

(violet)

• Ultraviolet– 400 nm to 60 nm– disinfection,

spectroscopy• X rays

– 60 nm to 10–4 nm– medicine, astronomy,

security screening• Gamma Rays

– less than 0.1 nm– cancer treatment,

astronomy

The Electromagnetic Spectrum

Multiple Choice

1. Which of the following equations correctly describes Faraday’s law of induction?

( tan ) –

( cos )

( cos ) –

( cos )

ABemf N

emf Nt

ABemf N

emf Mt

1. Which of the following equations correctly describes Faraday’s law of induction?

( tan ) –

( cos )

ABemf N

emf Nt

ABemf M

ABemf N

2. For the coil shown at right, what must be done to induce a clockwise current?

F. Either move the north pole of a magnet down into the coil, or move the south pole of the magnet up and out of the coil.

G. Either move the south pole of a magnet down into the coil, or move the north pole of the magnet up and out of the coil.

H. Move either pole of the magnet down into the coil.

J. Move either pole of the magnet up and out of the coil.

2. For the coil shown at right, what must be done to induce a clockwise current?

F. Either move the north pole of a magnet down into the coil, or move the south pole of the magnet up and out of the coil.

G. Either move the south pole of a magnet down into the coil, or move the north pole of the magnet up and out of the coil.

H. Move either pole of the magnet down into the coil.

J. Move either pole of the magnet up and out of the coil.

3. Which of the following would not increase the emf produced by a generator?

A. rotating the generator coil faster

B. increasing the strength of the generator magnets

C. increasing the number of turns of wire in the coil

D. reducing the cross-sectional area of the coil

3. Which of the following would not increase the emf produced by a generator?

A. rotating the generator coil faster

B. increasing the strength of the generator magnets

C. increasing the number of turns of wire in the coil

D. reducing the cross-sectional area of the coil

4. By what factor do you multiply the maximum emf to calculate the rms emf for an alternating current?

5. Which of the following correctly describes the composition of an electromagnetic wave?A. a transverse electric wave and a magnetic transverse wave that are parallel and are moving in the same directionB. a transverse electric wave and a magnetic transverse wave that are perpendicular and are moving in the same directionC. a transverse electric wave and a magnetic transverse wave that are parallel and are moving at right angles to each otherD. a transverse electric wave and a magnetic transverse wave that are perpendicular and are moving at right angles to each other

6. A coil is moved out of a magnetic field in order to induce an emf. The wire of the coil is then rewound so that the area of the coil is increased by 1.5 times. Extra wire is used in the coil so that the number of turns is doubled. If the time in which the coil is removed from the field is reduced by half and the magnetic field strength remains unchanged, how many times greater is the new induced emf than the original induced emf ?F. 1.5 timesG. 2 timesH. 3 timesJ. 6 times

7. From left to right, what are the types of the two transformers?A. Both are step-down transformers.B. Both are step-up transformers.C. One is a step-down transformer; and one is a step-up transformer.D. One is a step-up transformer; and one is a step-down transformer.

Use the passage below to answer questions 7–8.A pair of transformers is connected in series, as shown in the figure below.

7. From left to right, what are the types of the two transformers?A. Both are step-down transformers.B. Both are step-up transformers.C. One is a step-down transformer; and one is a step-up transformer.D. One is a step-up transformer; and one is a step-down transformer.

8. What is the output potential difference from the secondary coil of the transformer on the right?

F. 400 V

G. 12 000 V

H. 160 000 V

J. 360 000 V

8. What is the output potential difference from the secondary coil of the transformer on the right?

F. 400 V

G. 12 000 V

H. 160 000 V

J. 360 000 V

9. What are the particles that can be used to describe electromagnetic radiation called?

A. electrons

B. magnetons

C. photons

D. protons

9. What are the particles that can be used to describe electromagnetic radiation called?

A. electrons

B. magnetons

C. photons

D. protons

10. The maximum values for the current and potential difference in an ac circuit are 3.5 A and 340 V, respectively. How much power is dissipated in this circuit?

F. 300 W

G. 600 W

H. 1200 W

J. 2400 W

10. The maximum values for the current and potential difference in an ac circuit are 3.5 A and 340 V, respectively. How much power is dissipated in this circuit?

F. 300 W

G. 600 W

H. 1200 W

J. 2400 W

Short Response

11. The alternating current through an electric toaster has a maximum value of 12.0 A. What is the rms value of this current?

Answer:

8.48 A

12. What is the purpose of a commutator in an ac generator?

Answer:

It converts ac to a changing current in one direction only.

13. How does the energy of one photon of an electromagnetic wave relate to the wave’s frequency?

Answer:

The energy is directly proportional to the wave’s frequency (E = hf ).

14. A transformer has 150 turns of wire on the primary coil and 75 000 turns on the secondary coil. If the input potential difference across the primary is 120 V, what is the output potential difference across the secondary?

Answer:

6.0 104 V

Extended Response

15. Why is alternating current used for power transmission instead of direct current? Be sure to include power dissipation and electrical safety considerations in your answer.

Extended Response, continued

15. Answer:For electric power to be transferred over long distances without a large amount of power dissipation, the electric power must have a high potential difference and low current. However, to be safely used in homes, the potential difference must be lower than that used for long-distance power transmission. Because of induction, the potential difference and current of electricity can be transformed to higher or lower values, but the current must change continuously (alternate) for this to happen.

Extended Response, continuedBase your answers to questions 16–18 on the information below.

A device at a carnival’s haunted house involves a metal ring that flies upward from a table when a patron passes near the table’s edge. The device consists of a photoelectric switch that activates the circuit when anyone walks in front of the switch and of a coil of wire into which a current is suddenly introduced when the switch is triggered.

16. Why must the current enter the coil just as someone comes up to the table?

Answer: The change in current in the coil will produce a changing magnetic field, which will induce a current in the ring. The induced current produces a magnetic field that interacts with the magnetic field from the coil, causing the ring to rise from the table.

Base your answers to questions 16–18 on the information below.

17. Using Lenz’s law, explain why the ring flies upward when there is an increasing current in the coil?

Answer: According to Lenz’s law, the magnetic field induced in the ring must oppose the magnetic field that induces the current in the ring. The opposing fields cause the ring, which can move freely, to rise upward from the coil under the table’s surface.

18. Suppose the change in the magnetic field is 0.10 T/s. If the radius of the ring is 2.4 cm and the ring is assumed to consist of one turn of wire, what is the emf induced in the ring?

Answer: 1.8 10–4 V

Ways of Inducing a Current in a Circuit

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