Deck 32: Faradays Law of Induction

Question 1

A long solenoid (n = 1500 turns/m) has a cross-sectional area of 0.40 m² and a current given by I = (4.0 + 3.0t2) A, where t is in seconds. A flat circular coil (N = 300 turns) with a cross-sectional area of 0.15 m² is inside and coaxial with the solenoid. What is the magnitude of the emf induced in the coil at t = 2.0 s?

A)2.7 V
B)1.0 V
C)6.8 V
D)0.68 V
E)1.4 V

Answer 1

1.0 V

Question 2

A long straight wire is parallel to one edge and is in the plane of a single-turn rectangular loop as shown. If the loop is changing width so that the distance x changes at a constant rate of 4.0 cm/s, what is the magnitude of the emf induced in the loop at an instant when x = 6.0 cm? Let a = 2.0 cm, b = 1.2 m, and I = 30 A.

A)5.3 μV
B)2.4 μV
C)4.8 μV
D)2.6 μV
E)1.3 μV

Answer 2

4.8 μV

Question 3

A 50-turn circular coil (radius = 15 cm) with a total resistance of 4.0 Ω is placed in a uniform magnetic field directed perpendicularly to the plane of the coil. The magnitude of this field varies with time according to B = A sin (αt), where A = 80 μT and α = 50π rad/s. What is the magnitude of the current induced in the coil at t = 20 ms?

A)11 mA
B)18 mA
C)14 mA
D)22 mA
E)zero

Answer 3

11 mA

Question 4

A square loop (length along one side = 20 cm) rotates in a constant magnetic field which has a magnitude of 2.0 T. At an instant when the angle between the field and the normal to the plane of the loop is equal to 20° and increasing at the rate of 10°/s, what is the magnitude of the induced emf in the loop?

A)13 mV
B)0.27 V
C)4.8 mV
D)14 mV
E)2.2 mV

Question 5

A circular loop (area = 0.20 m²) turns in a uniform magnetic field with B = 0.13 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is (π) rads and is decreasing at the rate of 0.50 rad/s, what is the magnitude of the emf induced in the loop?

A)zero
B)13 mV
C)26 mV
D)20 mV
E)18 mV

Question 6

A planar loop consisting of four turns of wire, each of which encloses 200 cm², is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms. What is the resulting induced current in the coil if the resistance of the coil is 5.0 Ω?

A)60 mA
B)12 mA
C)0.24 mA
D)48 mA
E)6.0 mA

Question 7

A 5-turn square loop (10 cm along a side, resistance = 4.0 Ω) is placed in a magnetic field that makes an angle of 30° with the plane of the loop. The magnitude of this field varies with time according to B = 0.50t2, where t is measured in s and B in T. What is the induced current in the coil at t = 4.0 s?

A)25 mA
B)5.0 mA
C)13 mA
D)43 mA
E)50 mA

Question 8

A rectangular loop (area = 0.15 m²) turns in a uniform magnetic field with B = 0.20 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is (π/2) rad and increasing at the rate of 0.60 rad/s, what is the magnitude of the emf induced in the loop?

A)24 mV
B)zero
C)18 mV
D)20 mV
E)6.0 mV

Question 9

A loop of wire (resistance = 2.0 mΩ) is positioned as shown with respect to a long wire which carries a current. If d = 1.0 cm, D = 6.0 cm, and L = 1.5 m, what current is induced in the loop at an instant when the current in the wire is increasing at a rate of 100 A/s?

A)34 mA
B)30 mA
C)27 mA
D)38 mA
E)0.50 mA

Question 10

A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magnitude that varies sinusoidally with a frequency of 90 Hz. If the maximum value of the induced emf in the coil is observed to be 4.2 V, what is the maximum value of the magnitude of the varying magnetic field?

A)59 mT
B)62 mT
C)65 mT
D)68 mT
E)31 mT

Question 11

A 40-turn circular coil (radius = 4.0 cm, total resistance = 0.20 Ω) is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies with time as given by B = 50 sin(10 πt) mT where t is measured in s. What is the magnitude of the induced current in the coil at 0.10 s?

A)50 mA
B)1.6 A
C)0.32 A
D)zero
E)0.80 A

Question 12

A rectangular wire loop (length = 60 cm, width = 40 cm) lies completely within a perpendicular and uniform magnetic field of magnitude of 0.5 T. If the length of the loop starts increasing at a rate of 20 mm/s at time t = 0, while the width is decreasing at the same rate, what is the magnitude of the induced emf at time t = 4.0 s?

A)6.8 mV
B)5.2 mV
C)3.6 mV
D)8.4 mV
E)10 mV

Question 13

A conducting rectangular loop of mass M, resistance R, and dimensions a × b is allowed to fall from rest through a uniform magnetic field which is perpendicular to the plane of the loop. The loop accelerates until it reaches a terminal speed (before the upper end enters the magnetic field). If a = 2.0 m, B = 6.0 T, R = 40 Ω, and M = 0.60 kg, what is the terminal speed?

A)1.6 m/s
B)20 m/s
C)2.2 m/s
D)26 m/s
E)5.3 m/s

Question 14

A coil is wrapped with 300 turns of wire on the perimeter of a square frame (side length = 20 cm). Each turn has the same area as the frame, and the total resistance of the coil is 1.5 Ω. A uniform magnetic field perpendicular to the plane of the coil changes in magnitude at a constant rate from 0.50 T to 0.90 T in 2.0 s. What is the magnitude of the induced emf in the coil while the field is changing?

A)2.4 V
B)1.6 V
C)3.2 V
D)4.0 V
E)8.4 V

Question 15

A coil is wrapped with 300 turns of wire on the perimeter of a circular frame (radius = 8.0 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is turned on perpendicular to the plane of the coil. This field changes at a constant rate from 20 to 80 mT in a time of 20 ms. What is the magnitude of the induced emf in the coil at the instant the magnetic field has a magnitude of 50 mT?

A)24 V
B)18 V
C)15 V
D)10 V
E)30 V

Question 16

A flat coil of wire consisting of 20 turns, each with an area of 50 cm², is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 2.0 T to 6.0 T in 2.0 s. If the coil has a total resistance of 0.40 Ω, what is the magnitude of the induced current?

A)0.70 A
B)0.60 A
C)0.50 A
D)0.80 A
E)0.20 A

Question 17

A square coil (length of side = 24 cm) of wire consisting of two turns is placed in a uniform magnetic field that makes an angle of 60° with the plane of the coil. If the magnitude of this field increases by 6.0 mT every 10 ms, what is the magnitude of the emf induced in the coil?

A)55 mV
B)46 mV
C)50 mV
D)60 mV
E)35 mV

Question 18

A conducting rod (length = 80 cm) rotates at a constant angular rate of 15 revolutions per second about a pivot at one end. A uniform field (B = 60 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the emf induced between the ends of the rod?

A)2.7 V
B)2.1 V
C)2.4 V
D)1.8 V
E)3.3 V

Question 19

A metal blade spins at a constant rate of 5.0 revolutions per second about a pivot through one end of the blade. This rotation occurs in a region where the component of the earth's magnetic field perpendicular to the blade is 30 μT. If the blade is 60 cm in length, what is the magnitude of the potential difference between its ends?

A)0.24 mV
B)0.20 mV
C)0.17 mV
D)0.27 mV
E)0.34 mV

Question 20

The coil shown in the figure has 2 turns, a cross-sectional area of 0.20 m², and a field (parallel to the axis of the coil) with a magnitude given by B = (4.0 + 3.0t2) T, where t is in s. What is the potential difference, VA − VC, at t = 3.0 s?

A)−7.2 V
B)+7.2 V
C)−4.8 V
D)+4.8 V
E)−12 V

Question 21

A small airplane with a wing span of 12 m flies horizontally and due north at a speed of 60 m/s in a region where the magnetic field of the earth is 60 μT directed 60° below the horizontal. What is the magnitude of the induced emf between the ends of the wing?

A)50 mV
B)31 mV
C)37 mV
D)44 mV
E)22 mV

Question 22

A conducting bar moves as shown near a long wire carrying a constant 50-A current. If a = 4.0 mm, L = 50 cm, and v = 12 m/s, what is the potential difference, VA − VB?

A)+15 mV
B)−15 mV
C)+20 mV
D)−20 mV
E)+10 mV

Question 23

A rod (length = 10 cm) moves on two horizontal frictionless conducting rails, as shown. The magnetic field in the region is directed perpendicularly to the plane of the rails and is uniform and constant. If a constant force of 0.60 N moves the bar at a constant velocity of 2.0 m/s, what is the current through the 12-Ω load resistor?

A)0.32 A
B)0.34 A
C)0.37 A
D)0.39 A
E)0.43 A

Question 24

In a region of space where the magnetic field of the Earth has a magnitude of 80 μT and is directed 30° below the horizontal, a 50-cm length of wire oriented horizontally along an east-west direction is moved horizontally to the south with a speed of 20 m/s. What is the magnitude of the induced potential difference between the ends of this wire?

A)0.45 mV
B)0.35 mV
C)0.30 mV
D)0.40 mV
E)0.69 mV

Question 25

A metal blade (length = 80 cm) spins at a constant rate of 10 radians/s about a pivot at one end. A uniform magnetic field of 2.0 mT is directed at an angle of 30° with the plane of the rotation. What is the magnitude of the potential difference between the two ends of the blade?

A)5.5 mV
B)6.4 mV
C)3.2 mV
D)11 mV
E)13 mV

Question 26

A 20-cm length of wire is held along an east-west direction and moved horizontally to the north with a speed of 3.0 m/s in a region where the magnetic field of the earth is 60 μT directed 30° below the horizontal. What is the magnitude of the potential difference between the ends of the wire?

A)36 μV
B)18 μV
C)31 μV
D)24 μV
E)21 μV

Question 27

Coil 1, connected to a 100-Ω resistor, sits inside coil 2. Coil 1 is connected to a source of 60 cycle per second AC current. Which statement about coil 2 is correct?

A)No current will be induced in coil 2.
B)DC current (current flow in only one direction) will be induced in coil 2.
C)AC current (current flow in alternating directions) will be induced in coil 2.
D)DC current will be induced in coil 2, but its direction will depend on the initial direction of flow of current in coil 1.
E)Both AC and DC current will be induced in coil 2.

Question 28

The magnetic flux through a loop perpendicular to a uniform magnetic field will change

A)if the loop is replaced by two loops, each of which has half of the area of the original loop.
B)if the loop moves at constant velocity while remaining perpendicular to and within the uniform magnetic field.
C)if the loop moves at constant velocity in a direction parallel to the axis of the loop while remaining in the uniform magnetic field.
D)if the loop is rotated through 180 degrees about an axis through its center and in the plane of the loop.
E)in none of the above cases.

Question 29

At what frequency should a 200-turn, flat coil of cross sectional area of 300 cm² be rotated in a uniform 30-mT magnetic field to have a maximum value of the induced emf equal to 8.0 V?

A)7.5 Hz
B)7.1 Hz
C)8.0 Hz
D)8.4 Hz
E)16 Hz

Question 30

A conducting bar moves as shown near a long wire carrying a constant 80-A current. If a = 1.0 mm, b = 20 mm, and v = 5.0 m/s, what is the potential difference, Va − Vb?

A)−0.24 mV
B)+0.24 mV
C)−0.19 mV
D)+0.19 mV
E)−0.76 mV

Question 31

In the arrangement shown, a conducting bar of negligible resistance slides along horizontal, parallel, frictionless conducting rails connected as shown to a 2.0-Ω resistor. A uniform 1.5-T magnetic field is perpendicular to the plane of the paper. If L = 60 cm, at what rate is thermal energy being generated in the resistor at the instant the speed of the bar is equal to 4.2 m/s?

A)8.6 W
B)7.8 W
C)7.1 W
D)9.3 W
E)1.8 W

Question 32

A conducting rod (length = 2.0 m) spins at a constant rate of 2.0 revolutions per second about an axis that is perpendicular to the rod and through its center. A uniform magnetic field (magnitude = 8.0 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the potential difference between the center of the rod and either of its ends?

A)16 mV
B)50 mV
C)8.0 mV
D)0.10 mV
E)100 mV

Question 33

A conducting bar of length L rotates with a constant angular speed of +2.0 rad/s about a pivot P at one end, as shown. A uniform magnetic field (magnitude = 0.20 T) is directed into the paper. If L = 0.40 m, what is the potential difference, VA − VP?

A)−12 mV
B)+8.0 mV
C)−8.0 mV
D)+12 mV
E)−16 mV

Question 34

An induced emf is produced in

A)a closed loop of wire when it remains at rest in a nonuniform static magnetic field.
B)a closed loop of wire when it remains at rest in a uniform static magnetic field.
C)a closed loop of wire moving at constant velocity in a nonuniform static magnetic field.
D)all of the above.
E)only (b) and (c) above.

Question 35

An AC generator consists of 6 turns of wire. Each turn has an area of 0.040 m². The loop rotates in a uniform field (B = 0.20 T) at a constant frequency of 50 Hz. What is the maximum induced emf?

A)13 V
B)2.4 V
C)3.0 V
D)15 V
E)4.8 V

Question 36

A bar magnet is dropped from above and falls through the loop of wire shown below. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct?

A)The current in the loop always flows in a clockwise direction.
B)The current in the loop always flows in a counterclockwise direction.
C)The current in the loop flows first in a clockwise, then in a counterclockwise direction.
D)The current in the loop flows first in a counterclockwise, then in a clockwise direction.
E)No current flows in the loop because both ends of the magnet move through the loop.

Question 37

The difference between a DC and an AC generator is that

A)the DC generator has one unbroken slip ring.
B)the AC generator has one unbroken slip ring.
C)the DC generator has one slip ring split in two halves.
D)the AC generator has one slip ring split in two halves.
E)the DC generator has two unbroken slip rings.

Question 38

A bar (L = 80 cm) moves on two frictionless rails, as shown, in a region where the magnetic field is uniform (B = 0.30 T) and into the paper. If v = 50 cm/s and R = 60 mΩ, what is the magnetic force on the moving bar?

A)0.48 N to the right
B)0.48 N to the left
C)0.32 N to the left
D)0.32 N to the right
E)None of the above

Question 39

A conducting bar of length L rotates in a counterclockwise direction with a constant angular speed of +2.0 rad/s about a pivot P at one end, as shown. A uniform magnetic field (magnitude = 0.20 T) is directed into the paper. If L = 0.40 m, what is the potential difference, VA − VB?

A)+24 mV
B)−24 mV
C)+16 mV
D)−16 mV
E)+32 mV

Question 40

A current may be induced in a coil by

A)moving one end of a bar magnet through the coil.
B)moving the coil toward one end of the bar magnet.
C)holding the coil near a second coil while the electric current in the second coil is increasing.
D)all of the above.
E)none of the above.

Question 41

Starting outside the region with the magnetic field, a single square coil of wire enters, moves across, and then leaves the region with a uniform magnetic field perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. In which direction did the loop move over the plane of the page? ​ ​

A)The loop moved from bottom to top.
B)The loop moved from top to bottom.
C)The loop moved from left to right.
D)The loop moved from right to left.
E)All of these directions of motion will produce the graph of emf vs t.

Question 42

Starting outside the region with the magnetic field, a single square coil of wire moves across the region with a uniform magnetic field ​ perpendicular to the page. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. Roger claims that the graph shown below represents the induced emf. Martin says he's wrong. In which direction did the loop move over the plane of the page, or is Martin correct?
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A)Roger is correct: the loop moved from bottom to top.
B)Roger is correct: the loop moved from top to bottom.
C)Roger is correct: the loop moved from left to right.
D)Roger is correct: the loop moved from right to left.
E)Martin is correct: none of these directions of motion will produce the graph of emf vs t.

Question 43

In a demonstration, a 4.00 cm² square coil with 10,000 turns enters a larger square region with a uniform 1.50-T magnetic field at a speed of 100 m/s. The plane of the coil is perpendicular to the field lines. If the breakdown voltage of air is 4000 V/cm on that day, the largest gap you can have between the two wires connected to the ends of the coil and still get a spark is

A)7.5 × 10−3 cm.
B)0.015 cm.
C)7.5 cm.
D)13 cm.
E)15 cm.

Question 44

Starting outside the region with the magnetic field, a single square coil of wire enters, moves across, and then leaves the region with a uniform magnetic field perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. In which direction did the loop move over the plane of the page? ​ ​

A)The loop moved from bottom to top.
B)The loop moved from top to bottom.
C)The loop moved from left to right.
D)The loop moved from right to left.
E)All of these directions of motion will produce the graph of emf vs t.

Question 45

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is open,

A)bulb 1 is glowing; bulb 2 is dark.
B)bulb 2 is glowing; bulb 1 is dark.
C)both bulbs glow equally brightly.
D)both bulbs glow one half as brightly as they do with the switch closed.
E)both bulbs are dark.

Question 46

A car with a radio antenna 1.0 m long travels at 80 km/h in a locality where the Earth's magnetic field is 5.0 × 10−5 T. What is the maximum possible emf induced in the antenna as a result of moving through the Earth's magnetic field?

Question 47

A rectangular coil of 100 turns measures 40.0 cm by 20.0 cm. This coil is placed next to an electromagnet which is switched on, increasing the magnetic field through the coil from zero to 0.800 T in 50.0 ms. If the resistance of the coil is 2.0 ohms, what are the induced voltage and current in the coil?

Question 48

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity ω. While it rotates, the point(s) at lowest potential is(are)

A)A.
B)B.
C)C.
D)D.
E)A and E.

Question 49

A 500-turn circular loop 15.0 cm in diameter is initially aligned so that its axis is parallel to the Earth's magnetic field. In 2.77 ms the coil is flipped so that its axis is perpendicular to the Earth's field. If a voltage of 0.166 V is induced in the coil, what is the value of the Earth's magnetic field?

Question 50

As shown below, a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity directed to the right. Which statement regarding the electric field induced in the wires is correct for the wires at the left and right sides of the loop? ​ ​

A)The electric field is directed upwards in both the right and left sides of the loop.
B)The electric field is directed upwards in the right side and downwards in the left side of the loop.
C)The electric field is directed upwards in the left side and downwards in the right side of the loop.
D)The electric field is directed downwards in both the right and left sides of the loop.
E)There is no electric field present in any side of the loop.

Question 51

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates about an axis through its center at constant angular velocity ω. The ends, A and E, make contact with a split ring that connects to an external circuit. The current in the external circuit of resistance R has magnitude

A)0.
B) .
C) .
D) .
E) .

Question 52

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity ω. While it rotates, the point(s) at highest potential is(are)

A)A.
B)B.
C)C.
D)D.
E)A and E.

Question 53

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is closed,

A)bulb 1 glows more brightly.
B)bulb 2 glows more brightly.
C)both bulbs continue to glow with the same brightness.
D)bulb 1 goes out.
E)bulb 2 goes out.

Question 54

As shown below, a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity directed to the right. Judd says that the emf induced in the loop is zero. Roger claims that it has magnitude B . Which one, if either, is correct, and why? ​
​ ​

A)Judd, because the magnetic flux through the loop is constant.
B)Roger, because the magnetic flux through the loop is constant.
C)Judd, because the magnetic flux through the loop is not constant if .
D)Roger, because the magnetic flux through the loop is not constant if .
E)Roger, because the magnetic flux through the loop is ΦB = 0.

Question 55

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is closed,

A)bulb 1 glows more brightly.
B)bulb 2 glows more brightly.
C)both bulbs glow equally brightly.
D)bulb 1 goes out.
E)bulb 2 goes out.

Question 56

A bolt of lightning strikes the ground 200 m from a 100-turn coil oriented vertically and with the plane of the coil pointing toward the lightning strike. The radius of the coil is 0.800 m and the current in the lightning bolt falls from 6.02 × 106 A to zero in 10.5 μs. What is the voltage induced in the coil over this time period? [A question for future electrical engineers: is there any way to get lightning to strike repeatedly at the same point?]
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