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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
z
A. ka2
B.
a
a
ka2/2
C. ka3/2
D. ka3/3
y
x
E. None of these is correct.
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
z
A. ka2
B.
a
a
ka2/2
C. ka3/2
D. ka3/3
y
x
E. None of these is correct.
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
m  6t  7t  1
2
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
The magnetic flux through a loop is made to
vary according to the relation
m  6t  7t  1
2
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
The magnetic flux through a certain coil is
given by
m  (1/ 50 ) cos(100t )
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
The magnetic flux through a certain coil is
given by
m  (1/ 50 ) cos(100t )
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
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
N
S
1
E. 1 and 2
S
N
S
N
N
2
3
4
S
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
N
S
1
E. 1 and 2
S
N
S
N
N
2
3
4
S
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)
E. None of these is correct.
Chapter 28: Magnetic Induction
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.
Chapter 28: Magnetic Induction
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
N
S
S
N
1
2
N
S
S
N
3
4
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
N
S
S
N
1
2
N
S
S
N
3
4
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
Chapter 28: Magnetic Induction
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.
B. 33 mW, counterclockwise.
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.
B. 33 mW, counterclockwise.
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.
B. 33 mW, counterclockwise.
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
Chapter 28: Magnetic Induction
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?
magnet
A. 0.35 N
B. 0.79 N
v
conducting
cylinder
C. 0.97 N
D. 0.69 N
E. None of these is 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?
magnet
A. 0.35 N
B. 0.79 N
v
conducting
cylinder
C. 0.97 N
D. 0.69 N
E. None of these is 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 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
magnet
A. 0.55 J
B. 8.8  10-5 J
v
conducting
cylinder
C. 1.1 J
D. 1.8  10-4 J
E. None of these is 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 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
magnet
A. 0.55 J
B. 8.8  10-5 J
v
conducting
cylinder
C. 1.1 J
D. 1.8  10-4 J
E. None of these is correct.
Chapter 28: Magnetic Induction
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.
E. None of these is correct.
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.
E. None of these is correct.
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
E. None of these is correct.
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
E. None of these is correct.
Chapter 28: Magnetic Induction
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.
Chapter 28: Magnetic Induction
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
bulb
S
The time constant for the RL
circuit is of the order of a few
seconds. Describe what happens V 

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.
L
bulb
S
The time constant for the RL
circuit is of the order of a few
seconds. Describe what happens V 

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.
L
Chapter 28: Magnetic Induction
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.