Chapter 28: Magnetic Induction Section 28-1: Magnetic Flux

Chapter 28: Magnetic Induction

Section 28-1: Magnetic Flux

A square loop of sides a lies in the yz plane with one corner at the origin. A varying magnetic field B = ky passes through the loop and points in the +x direction. The magnetic flux through the loop is

A. ka2

B. ka2/2

C. ka3/2

D. ka3/3

E. None of these is correct.x

y

z

a

a

B

A square loop of sides a lies in the yz plane with one corner at the origin. A varying magnetic field B = ky passes through the loop and points in the +x direction. The magnetic flux through the loop is

A. ka2

B. ka2/2

C. ka3/2

D. ka3/3

E. None of these is correct.x

y

z

a

a

B

You can change the magnetic flux through a given surface by

A. changing the magnetic field.

B. changing the surface area over which the magnetic field is distributed.

C. changing the angle between the magnetic field and surface in question.

D. any combination of a through c.

E. none of these strategies.

You can change the magnetic flux through a given surface by

A. changing the magnetic field.

B. changing the surface area over which the magnetic field is distributed.

C. changing the angle between the magnetic field and surface in question.

D. any combination of a through c.

E. none of these strategies.

Suppose you double the magnetic field in a given region and quadruple the area through which this magnetic field exists. The effect on the flux through this area would be to

A. leave it unchanged.

B. double it.

C. quadruple it.

D. increase it by a factor of six.

E. increase it by a factor of eight.

Suppose you double the magnetic field in a given region and quadruple the area through which this magnetic field exists. The effect on the flux through this area would be to

A. leave it unchanged.

B. double it.

C. quadruple it.

D. increase it by a factor of six.

E. increase it by a factor of eight.

The magnetic flux through a loop is made to vary according to the relation

where the units are SI. The emf induced in the loop when t = 2 s is

A. 38 V

B. 39 V

C. 40 V

D. 31 V

E. 19 V

176 2m tt

The magnetic flux through a loop is made to vary according to the relation

where the units are SI. The emf induced in the loop when t = 2 s is

A. 38 V

B. 39 V

C. 40 V

D. 31 V

E. 19 V

176 2m tt

The magnetic flux through a certain coil is given by

where the units are SI. The coil has 100 turns. The magnitude of the induced emf when t = 1/200 s is

A. 100 V

B. 200 V

C. zero

D. 2/pi V

E. 1/50pi V

)100cos()50/1(m t

The magnetic flux through a certain coil is given by

where the units are SI. The coil has 100 turns. The magnitude of the induced emf when t = 1/200 s is

A. 100 V

B. 200 V

C. zero

D. 2/pi V

E. 1/50pi V

)100cos()50/1(m t

For which of the diagram(s) will current flow through the light bulb? (In 3 and 4 assume the magnets move in the plane of the loop.)

A. 1

B. 2

C. 3

D. 4

E. 1 and 2

NS

NS N S N S

1 2 3 4

For which of the diagram(s) will current flow through the light bulb? (In 3 and 4 assume the magnets move in the plane of the loop.)

A. 1

B. 2

C. 3

D. 4

E. 1 and 2

NS

NS N S N S

1 2 3 4

A circular loop of radius R has 50 turns. It lies in the xy plane. A time dependent magnetic field B(t) = A sin (ωt) where A is a constant, passes through the loop in the +z direction. The emf induced in the loop is

A. 50πAR2 sin (ωt)

B. 50πAR2 cos (ωt)

C. 50πωAR2 sin (ωt)

D. 50πωAR2 cos (ωt)

E. None of these is correct.

A circular loop of radius R has 50 turns. It lies in the xy plane. A time dependent magnetic field B(t) = A sin (ωt) where A is a constant, passes through the loop in the +z direction. The emf induced in the loop is

A. 50πAR2 sin (ωt)

B. 50πAR2 cos (ωt)

C. 50πωAR2 sin (ωt)

D. 50πωAR2 cos (ωt)



Section 28-2: Induced EMF and Faraday’s Law

The plane of a circular, 200-turn coil of radius 5.25 cm is perpendicular to a uniform magnetic field produced by a large electromagnet. This field is changed at a steady rate from 0.650 T to 0.150 T in 0.0100 s. What is the magnitude of the emf induced in the coil?

A. 110 V

B. 170 V

C. 1.7 V

D. 26 V

E. 87 V

The plane of a circular, 200-turn coil of radius 5.25 cm is perpendicular to a uniform magnetic field produced by a large electromagnet. This field is changed at a steady rate from 0.650 T to 0.150 T in 0.0100 s. What is the magnitude of the emf induced in the coil?

A. 110 V

B. 170 V

C. 1.7 V

D. 26 V

E. 87 V

According to Faraday's law, a necessary and sufficient condition for an electromotive force to be induced in a closed circuit loop is the presence in the loop of

A. a magnetic field.

B. magnetic materials.

C. an electric current.

D. a time-varying magnetic flux.

E. a time-varying magnetic field.

According to Faraday's law, a necessary and sufficient condition for an electromotive force to be induced in a closed circuit loop is the presence in the loop of

A. a magnetic field.

B. magnetic materials.

C. an electric current.

D. a time-varying magnetic flux.

E. a time-varying magnetic field.

The instantaneous induced emf in a coil of wire located in a magnetic field

A. depends on the time rate of change of flux through the coil.

B. depends on the instantaneous value of flux through the coil.

C. is independent of the area of the coil.

D. is independent of the number of turns of the coil.

E. is determined by the resistance in series with the coil.

The instantaneous induced emf in a coil of wire located in a magnetic field

A. depends on the time rate of change of flux through the coil.

B. depends on the instantaneous value of flux through the coil.

C. is independent of the area of the coil.

D. is independent of the number of turns of the coil.

E. is determined by the resistance in series with the coil.


Section 28-3: Lenz’s Law and Concept Check 28-1

Using the alternative statement of Lenz’s law, find the direction of the induced current in the loop shown if the magnet is moving to the left (away from the loop).

A. Clockwise.

B. Counterclockwise.

C. No current is induced.

Using the alternative statement of Lenz’s law, find the direction of the induced current in the loop shown if the magnet is moving to the left (away from the loop).

A. Clockwise.

B. Counterclockwise.

C. No current is induced.

A copper ring lies in the yz plane as shown. The magnet's long axis lies along the x axis. Induced current flows through the ring as indicated. The magnet

A. must be moving away from the ring.

B. must be moving toward the ring.

C. must remain stationary to keep the current flowing.

A copper ring lies in the yz plane as shown. The magnet's long axis lies along the x axis. Induced current flows through the ring as indicated. The magnet

A. must be moving away from the ring.

B. must be moving toward the ring.

C. must remain stationary to keep the current flowing.

A conducting loop around a bar magnet begins to move away from the magnet. Which of the following statements is true?

A. The magnet and the loop repel one another.

B. The magnet and the loop attract one another.

C. The magnet and loop neither attract nor repel one another.

A conducting loop around a bar magnet begins to move away from the magnet. Which of the following statements is true?

A. The magnet and the loop repel one another.

B. The magnet and the loop attract one another.

C. The magnet and loop neither attract nor repel one another.

A loop rests in the xy plane. The z axis is normal to the plane and positive upward. The direction of the changing flux is indicated by the arrow along the z axis. Which diagram correctly shows the direction of the resultant induced current in the loop?

A loop rests in the xy plane. The z axis is normal to the plane and positive upward. The direction of the changing flux is indicated by the arrow along the z axis. Which diagram correctly shows the direction of the resultant induced current in the loop?

For which of the following diagrams will current flow in the clockwise direction?

A. 1 and 2

B. 3 and 4

C. 1 and 3

D. 2 and 4

E. 2 and 3

NS N

S

1 2 3 4

NS N

S

For which of the following diagrams will current flow in the clockwise direction?

A. 1 and 2

B. 3 and 4

C. 1 and 3

D. 2 and 4

E. 2 and 3

NS N

S

1 2 3 4

NS N

S

A bar magnet is dropped through a loop of copper wire as shown. Recall that magnetic field lines point away from a north pole and toward a south pole. If the positive direction of the induced current I in the loop is as shown by the arrows on the loop, the variation of I with time as the bar magnet falls through the loop is illustrated qualitatively by which of the graphs?

The time when the midpoint of the magnet passes through the loop is indicated by C.

A bar magnet is dropped through a loop of copper wire as shown. Recall that magnetic field lines point away from a north pole and toward a south pole. If the positive direction of the induced current I in the loop is as shown by the arrows on the loop, the variation of I with time as the bar magnet falls through the loop is illustrated qualitatively by which of the graphs?

The time when the midpoint of the magnet passes through the loop is indicated by C.

Which law does the following statement express? "In all cases of electromagnetic induction, the induced voltages have a direction such that the currents they produce oppose the effect that produces them."

A. Maxwell's law

B. Fleming's rule

C. Lenz's law

D. Gauss's law

E. Ampère's law

Which law does the following statement express? "In all cases of electromagnetic induction, the induced voltages have a direction such that the currents they produce oppose the effect that produces them."

A. Maxwell's law

B. Fleming's rule

C. Lenz's law

D. Gauss's law

E. Ampère's law


Section 28-4: Motional EMF and Concept Check 28-2

When a generator delivers electric energy to a circuit, where does the energy come from?

A. The energy comes from an external source of electrical power, such as a battery or electrical outlet.

B. The energy comes from the heat being absorbed by the coil as it turns.

C. The energy comes from an external agent, which is doing mechanical work on the coil.

D. The energy comes from chemical reactions within the coil.

E. The energy comes from nuclear reactions within the coil.

When a generator delivers electric energy to a circuit, where does the energy come from?

A. The energy comes from an external source of electrical power, such as a battery or electrical outlet.

B. The energy comes from the heat being absorbed by the coil as it turns.

C. The energy comes from an external agent, which is doing mechanical work on the coil.

D. The energy comes from chemical reactions within the coil.

E. The energy comes from nuclear reactions within the coil.

A wire rod rolls with a speed of 20 m/s on two metallic rails, 1.0 m apart, that form a closed loop. If the magnetic field is 1.5 T into the page, the power dissipated in the resistor R and the current direction are, respectively,

A. 33 mW, clockwise.

B. 33 mW, counterclockwise.

C. 76 mW, counterclockwise.

D. 76 mW, clockwise.

E. 50 mW, clockwise.

A wire rod rolls with a speed of 20 m/s on two metallic rails, 1.0 m apart, that form a closed loop. If the magnetic field is 1.5 T into the page, the power dissipated in the resistor R and the current direction are, respectively,

A. 33 mW, clockwise.


C. 76 mW, counterclockwise.

D. 76 mW, clockwise.

E. 50 mW, clockwise.

A wire rod rolls with a speed of 30 m/s on two metallic rails, 2.0 m apart, that form a closed loop. The power dissipated in the resistor R and the current direction are, respectively, A. 33 mW, clockwise.


C. 2.0 W, counterclockwise.

D. 10 W, clockwise.

E. 10 W, counterclockwise.

A wire rod rolls with a speed of 30 m/s on two metallic rails, 2.0 m apart, that form a closed loop. The power dissipated in the resistor R and the current direction are, respectively, A. 33 mW, clockwise.


C. 2.0 W, counterclockwise.

D. 10 W, clockwise.

E. 10 W, counterclockwise.

A wire rod rolls with a speed of 8.0 m/s on two metallic rails, 30 cm apart, that form a closed loop. A uniform magnetic field of magnitude 1.20 T is into the page. The magnitude and direction of the current induced in the resistor R are

A. 0.82 A, clockwise.

B. 0.82 A, counterclockwise.

C. 1.2 A, clockwise.

D. 1.2 A, counterclockwise.

E. 2.9 A, counterclockwise.

A wire rod rolls with a speed of 8.0 m/s on two metallic rails, 30 cm apart, that form a closed loop. A uniform magnetic field of magnitude 1.20 T is into the page. The magnitude and direction of the current induced in the resistor R are

A. 0.82 A, clockwise.

B. 0.82 A, counterclockwise.

C. 1.2 A, clockwise.

D. 1.2 A, counterclockwise.

E. 2.9 A, counterclockwise.

A rectangular coil moving at a constant speed v enters a region of uniform magnetic field from the left. While the coil is entering the field, which arrow shows the direction of the magnetic force?

A rectangular coil moving at a constant speed v enters a region of uniform magnetic field from the left. While the coil is entering the field, which arrow shows the direction of the magnetic force?

A rectangular coil moving at a constant speed v enters a region of uniform magnetic field from the left. While the coil is exiting the field on the right, which arrow shows the direction of the magnetic force?

A rectangular coil moving at a constant speed v enters a region of uniform magnetic field from the left. While the coil is exiting the field on the right, which arrow shows the direction of the magnetic force?

A rectangular coil of length l = 20 cm and width w = 15 cm is moving at a constant speed v = 5 m/s. It enters a region of uniform magnetic field B = 0.2 T from the left. While the coil is completely immersed in the field, the voltage across points a and b is

A. 0.20 V

B. 0.15 V

C. 0.20 V

D. 0.15 V

E. zero

A rectangular coil of length l = 20 cm and width w = 15 cm is moving at a constant speed v = 5 m/s. It enters a region of uniform magnetic field B = 0.2 T from the left. While the coil is completely immersed in the field, the voltage across points a and b is

A. 0.20 V

B. 0.15 V

C. 0.20 V

D. 0.15 V

E. zero

The motion of a conducting rod through a magnetic field creates a motional emf E. If the rod accelerates to twice the speed, what will the motional emf be?

A. E

B. 2E

C. E / 2

D. 4 E

E. E 2

The motion of a conducting rod through a magnetic field creates a motional emf E. If the rod accelerates to twice the speed, what will the motional emf be?

A. E

B. 2E

C. E / 2

D. 4 E

E. E 2

A 0.8-m-long pole rotates about a perpendicular axis at one end. As the pole rotates, it passes through the earth's magnetic field, which has a perpendicular component of 3 × 10–5 T to the plane of rotation. If the pole rotates with a frequency of 5 revolutions per second, calculate the induced emf across the ends of the pole.

A. 3.0 × 10–4 V

B. 1.2 × 10–5 V

C. 1.0 × 10–4 V

D. 3.8 × 10–4 V

E. 2.4 × 10–4 V

A 0.8-m-long pole rotates about a perpendicular axis at one end. As the pole rotates, it passes through the earth's magnetic field, which has a perpendicular component of 3 × 10–5 T to the plane of rotation. If the pole rotates with a frequency of 5 revolutions per second, calculate the induced emf across the ends of the pole.

A. 3.0 × 10–4 V

B. 1.2 × 10–5 V

C. 1.0 × 10–4 V

D. 3.8 × 10–4 V

E. 2.4 × 10–4 V


Section 28-5: Eddy Currents

Two identical bar magnets are dropped from equal heights. Magnet A is dropped over bare earth and magnet B over a metal plate. Which magnet strikes first?

A. magnet A

B. magnet B

C. both strike at the same time

Two identical bar magnets are dropped from equal heights. Magnet A is dropped over bare earth and magnet B over a metal plate. Which magnet strikes first?

A. magnet A

B. magnet B

C. both strike at the same time

Eddy currents

A. are a consequence of changing magnetic flux.

B. generate heat and result in power loss.

C. can be used for damping and braking purposes.

D. are described by both Faraday's and Lenz's laws.

E. All of these are correct.

Eddy currents

A. are a consequence of changing magnetic flux.

B. generate heat and result in power loss.

C. can be used for damping and braking purposes.

D. are described by both Faraday's and Lenz's laws.

E. All of these are correct.

A classic demonstration illustrating eddy currents is performed by dropping a permanent magnet inside a conducting cylinder. The magnet does not go into free fall. Instead it reaches terminal velocity and can take a few seconds to drop a length of about a meter. Suppose the mass of the magnet is 70 g and it has a terminal velocity of 10 cm/s. The length of the pipe is 80 cm. What is the magnitude of the magnetic force on the magnet when it is falling at the terminal velocity?

A. 0.35 N

B. 0.79 N

C. 0.97 N

D. 0.69 N


magnet

conductingcylinder

v

A classic demonstration illustrating eddy currents is performed by dropping a permanent magnet inside a conducting cylinder. The magnet does not go into free fall. Instead it reaches terminal velocity and can take a few seconds to drop a length of about a meter. Suppose the mass of the magnet is 70 g and it has a terminal velocity of 10 cm/s. The length of the pipe is 80 cm. What is the magnitude of the magnetic force on the magnet when it is falling at the terminal velocity?

A. 0.35 N

B. 0.79 N

C. 0.97 N

D. 0.69 N


magnet

conductingcylinder

v

A classic demonstration illustrating eddy currents is performed by dropping a permanent magnet inside a conducting cylinder. The magnet does not go into free fall. Instead it reaches terminal velocity and can take a few seconds to drop a length of about a meter. Suppose the mass of the magnet is 70 g and width of 1.0 cm. It falls with a terminal velocity of 10 cm/s and the length of the pipe is 80 cm. The magnitude of the Joule heating from the eddy currents is approximately

A. 0.55 J

B. 8.8 10-5 J

C. 1.1 J

D. 1.8 10-4 J


magnet

conductingcylinder

v

A classic demonstration illustrating eddy currents is performed by dropping a permanent magnet inside a conducting cylinder. The magnet does not go into free fall. Instead it reaches terminal velocity and can take a few seconds to drop a length of about a meter. Suppose the mass of the magnet is 70 g and width of 1.0 cm. It falls with a terminal velocity of 10 cm/s and the length of the pipe is 80 cm. The magnitude of the Joule heating from the eddy currents is approximately

A. 0.55 J

B. 8.8 10-5 J

C. 1.1 J

D. 1.8 10-4 J


magnet

conductingcylinder

v


Section 28-6: Inductance

For the current in a stationary circuit to induce a current in an independent stationary circuit, it is necessary for the first circuit to have

A. a steady current.

B. a large current.

C. no current.

D. a changing current.


For the current in a stationary circuit to induce a current in an independent stationary circuit, it is necessary for the first circuit to have

A. a steady current.

B. a large current.

C. no current.

D. a changing current.


The self-inductance of a wire coil is a proportionality constant that relates

A. electric field to current.

B. electric flux to current.

C. magnetic flux to current.

D. magnetic field to current.

E. voltage to current.

The self-inductance of a wire coil is a proportionality constant that relates

A. electric field to current.

B. electric flux to current.

C. magnetic flux to current.

D. magnetic field to current.

E. voltage to current.

After you measure the self-inductance of a coil, you unwind it and then rewind half the length of wire into a coil with the same diameter but half the number of turns. How does this change the self-inductance?

A. It is the same.

B. It is doubled.

C. It is quadrupled.

D. It is halved.

E. It is quartered.

After you measure the self-inductance of a coil, you unwind it and then rewind half the length of wire into a coil with the same diameter but half the number of turns. How does this change the self-inductance?

A. It is the same.

B. It is doubled.

C. It is quadrupled.

D. It is halved.

E. It is quartered.

A coil with self-inductance L carries a current I given by

I = I0 sin 2πft

Which graph best describes the self-induced emf as a function of time?

A coil with self-inductance L carries a current I given by

I = I0 sin 2πft

Which graph best describes the self-induced emf as a function of time?

For the two solenoids above, if l = 50 cm, N1 = N2 = 200 turns and r1 = 5 cm and r2 = 10 cm, the mutual inductance of the two solenoids is

A. 1.58 mH

B. 0.790 mH

C. 3.20 mH

D. 6.31 mH


For the two solenoids above, if l = 50 cm, N1 = N2 = 200 turns and r1 = 5 cm and r2 = 10 cm, the mutual inductance of the two solenoids is

A. 1.58 mH

B. 0.790 mH

C. 3.20 mH

D. 6.31 mH



Section 28-7: Magnetic Energy

A device used chiefly for storing energy in a magnetic field is

A. an inductor.

B. a resistor.

C. a capacitor.

D. a galvanometer.

E. a dielectric.

A device used chiefly for storing energy in a magnetic field is

A. an inductor.

B. a resistor.

C. a capacitor.

D. a galvanometer.

E. a dielectric.


Section 28-8: RL Circuits

An open switch in an RL circuit is closed at time t = 0, as shown. Which curve best illustrates the variation of potential difference across the resistor as a function of time?

An open switch in an RL circuit is closed at time t = 0, as shown. Which curve best illustrates the variation of potential difference across the resistor as a function of time?

An open switch in an RL circuit is closed at time t = 0, as shown. Which curve best illustrates the variation of potential difference across the inductor as a function of time?

An open switch in an RL circuit is closed at time t = 0, as shown. Which curve best illustrates the variation of potential difference across the inductor as a function of time?

An open switch in an RL circuit is closed at time t = 0, as shown. Which curve best illustrates the variation of current with time?

An open switch in an RL circuit is closed at time t = 0, as shown. Which curve best illustrates the variation of current with time?

The growth of current in the inductive circuit in the inset diagram is represented by the curve in the graph. The broken line is tangent to the curve at the origin. The time constant of the circuit is approximately

A. 3.0 ms

B. 2/R ms

C. 0.40 ms

D. 4.0 ms

E. 2.0 ms

The growth of current in the inductive circuit in the inset diagram is represented by the curve in the graph. The broken line is tangent to the curve at the origin. The time constant of the circuit is approximately

A. 3.0 ms

B. 2/R ms

C. 0.40 ms

D. 4.0 ms

E. 2.0 ms

The time constant for the RL circuit is of the order of a few seconds. Describe what happens to the light bulb when the switch S is closed.

A. The light bulb comes on immediately and then goes off in a few seconds.

B. The light bulb comes gradually in a few seconds and stays on.

C. The light bulb does not come on at all.

D. The light bulb comes on in a few seconds and then goes off instantaneously.

E. The light bulb comes on in a few seconds and then goes off in a few seconds.

bulb

L

S

V

The time constant for the RL circuit is of the order of a few seconds. Describe what happens to the light bulb when the switch S is closed.

A. The light bulb comes on immediately and then goes off in a few seconds.

B. The light bulb comes gradually in a few seconds and stays on.

C. The light bulb does not come on at all.

D. The light bulb comes on in a few seconds and then goes off instantaneously.

E. The light bulb comes on in a few seconds and then goes off in a few seconds.

bulb

L

S

V


Section 28-9: Magnetic Properties of Superconductors

Which of the following statements about superconductors is true?A. Both type I and type II superconductors have

zero resistance below the critical temperature Tc.

B. In type I superconductors, the magnetic is expelled from the superconductors below the critical temperature Tc.

C. In type II superconductors, the magnetic is expelled from the superconductors below the critical temperature Tc and below a certain field Bc1.

D. Superconductors are prefect diamagnetics.

E. All the above statements are true.

Which of the following statements about superconductors is true?A. Both type I and type II superconductors have

zero resistance below the critical temperature Tc.

B. In type I superconductors, the magnetic is expelled from the superconductors below the critical temperature Tc.

C. In type II superconductors, the magnetic is expelled from the superconductors below the critical temperature Tc and below a certain field Bc1.

D. Superconductors are prefect diamagnetics.

E. All the above statements are true.

Documents

Chapter 28: Magnetic Induction Section 28-1: Magnetic Flux