Chapter (31)

Chapter 31

Faraday’s Law

Multiple Choice

1. 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

2. 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

3. 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

189

190 CHAPTER 31

4. 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

5. 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

6. 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?

I

D

d

L a. 34 mA b. 30 mA c. 27 mA d. 38 mA e. 0.50 mA

7. 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

Faraday’s Law 191

8. 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

9. 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

10. 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

11. 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

192 CHAPTER 31

12. 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

13. 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.

I

x

a

b a. 5.3 μV b. 2.4 μV c. 4.8 μV d. 2.6 μV e. 1.3 μV

14. 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

Faraday’s Law 193

15. 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?

B

A C a. –7.2 V b. +7.2 V c. –4.8 V d. +4.8 V e. –12 V

16. 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

17. 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

194 CHAPTER 31

18. 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

b

g

x x x x x

x x x x x

x x x x x

x x x x x a. 1.6 m/s b. 20 m/s c. 2.2 m/s d. 26 m/s e. 5.3 m/s

19. 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

20. 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

Faraday’s Law 195

21. 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

22. 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?

v2.0 Ω L

a. 8.6 W b. 7.8 W c. 7.1 W d. 9.3 W e. 1.8 W

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?

v12 Ω L

a. 0.32 A b. 0.34 A c. 0.37 A d. 0.39 A e. 0.43 A

24. 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

196 CHAPTER 31

25. 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

26. 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 moving in the plane shown so that the distance x changes at a constant rate of 20 cm/s, what is the magnitude of the emf induced in the loop at the instant x = 5.0 cm? Let I = 50 A, a = 50 cm, b = 6.0 cm.

I

x

b

a

a. 11 μV b. 22 μV c. 27 μV d. 16 μV e. 34 μV

27. 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

28. 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

Faraday’s Law 197

29. 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?

b

a

80 A

v

a. –0.24 mV b. +0.24 mV c. –0.19 mV d. +0.19 mV e. –0.76 mV

30. 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

v

50 A

L

A B

a. +15 mV b. –15 mV c. +20 mV d. –20 mV e. +10 mV

31. 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?

vR L

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

198 CHAPTER 31

32. 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?

L/2 L/2

A

P

B

a. +24 mV b. –24 mV c. +16 mV d. –16 mV e. +32 mV

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?

L/2 L/2

A

P

a. –12 mV b. +8.0 mV c. –8.0 mV d. +12 mV e. –16 mV

34. A long solenoid (radius = 3.0 cm, 2500 turns per meter) carries a current given by I = 0.30 sin(200πt) A, where t is measured in s. When t = 5.0 ms, what is the magnitude of the induced electric field at a point which is 2.0 cm from the axis of the solenoid?

a. 7.3 × 10–3 V/m b. 6.4 × 10–3 V/m c. 6.9 × 10–3 V/m d. 5.9 × 10–3 V/m e. 8.9 × 10–3 V/m

35. A long solenoid (radius = 3.0 cm, 2500 turns per meter) carries a current given by I = 0.30 sin(200 t) A, where t is measured in s. When t = 2.5 ms, what is the magnitude of the induced electric field at a point which is 4.0 cm from the axis of the solenoid?

a. 9.3 × 10–3 V/m b. 8.0 × 10–3 V/m c. 6.7 × 10–3 V/m d. 5.3 × 10–3 V/m e. 1.9 × 10–3 V/m

Faraday’s Law 199

36. A long solenoid has a radius of 4.0 cm and has 800 turns/m. If the current in the solenoid is increasing at the rate of 3.0 A/s, what is the magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid?

a. 3.3 × 10–5 V/m b. 3.6 × 10–5 V/m c. 3.9 × 10–5 V/m d. 4.2 × 10–5 V/m e. 6.0 × 10–5 V/m

37. An electric field of 4.0 μV/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm, 800 turns/m). At what rate is the current in the solenoid changing at this instant?

a. 0.50 A/s b. 0.40 A/s c. 0.60 A/s d. 0.70 A/s e. 0.27 A/s

38. A long solenoid has a radius of 2.0 cm and has 700 turns/m. If the current in the solenoid is decreasing at the rate of 8.0 A/s, what is the magnitude of the induced electric field at a point 2.5 cm from the axis of the solenoid?

a. 56 μV/m b. 8.8 μV/m c. 88 μV/m d. 69 μV/m e. 44 μV/m

39. 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

40. 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

200 CHAPTER 31

41. 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.

42. 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.

43. 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.

44. 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.

Faraday’s Law 201

45. 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?

S

N

S

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.

46. 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.

47. Alternating currents in power lines usually cannot produce significant electrical currents in human brains because power lines

a. carry high current at high voltage. b. carry low current at high voltage. c. carry low current at low voltage. d. carry high current at low voltage. e. have high I2R (resistive) losses.

48. Human brain activity produces weak variable electric currents. The way these are detected without surgery is by

a. measuring the force on a wire carrying a large electric current that is placed near the brain.

b. measuring the force on a solenoid carrying a large electric current that is placed near the brain.

c. measuring the magnetic fields they produce by means of small loops of wire of very low resistance placed near the brain.

d. measuring the potential difference between the leaves of an electroscope that is placed near the brain.

e. attaching the leads of an ohmmeter to a person’s ears.

202 CHAPTER 31

49. The correct form of Ampere’s law for circuits with gaps in them is

a. ∫ =⋅ 0sB d .

b. ∫ =⋅ enclosedIdsB .

c. ∫ =⋅ enclosedId 0μsB .

d. dt

dId E

enclosedΦ

+=⋅∫ 000 εμμsB .

e. ( ) dtd

dtd

Id BEenclosed

Φ−

Φ+=⋅∫ 2

0

0000 μ

εεμμsB .

50. A plane parallel plate capacitor has plates of 10 cm2 area that are 1.0 mm apart. At an instant when charge is being accumulated on the plates at a rate of 12 nC/s, the displacement current between the plates is

a. . AA

A1085.8 9−×

10061 16−×.b. . 1021 8−×.

c. . d. 1.00 A. e. 1.36 A.

51. 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 B C D E a. A. b. B. c. C. d. D. e. A and E.

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 lowest potential is(are)

A B C D E a. A. b. B. c. C. d. D. e. A and E.

Faraday’s Law 203

53. 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 B C D E a. 0.

b. dt

dR

BΦ1.

c. dt

dR

BΦ2.

d. dt

dR

BΦ2.

e. dt

dR

BΦ22.

54. 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,

Bulb 1 Bulb 2Switch B

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.

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,

Bulb 1 Bulb 2

Switch B

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.

204 CHAPTER 31

56. 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,

Bulb 1 Bulb 2

Switch B

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.

57. 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 v directed to the right. Judd says that the emf induced in the loop is zero. Roger claims that it has magnitude B v . Which one, if either, is correct, and why?

• • • • • • • • • •• • • • •• • • • •• • • • •• • • • • • • • • •

• • • • • • • • • • • • • • •

v

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 v ≠ 0 . d. Roger, because the magnetic flux through the loop is not constant if v ≠ 0 . e. Roger, because the magnetic flux through the loop is ΦB = 0 .

Faraday’s Law 205

58. 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 v 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?

• • • • • • • • • •• • • • • • • • • •• • • • • • • • • •• • • • • • • • • •• • • • • • • • • •

v

a. The electric field E is directed upwards in both the right and left sides of the loop.

b. The electric field E is directed upwards in the right side and downwards in the left side of the loop.

c. The electric field E is directed upwards in the left side and downwards in the right side of the loop.

d. The electric field E 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.

59. Starting outside the region with the magnetic field, a single square coil of wire moves across the region with a uniform magnetic field B perpendicular to the page. The loop moves at constant velocity v . 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?

• • • • • • • • • •• • • • • •• • • • • •• • • • • •• • • • • • • • • •

• • • •• • • •• • • •

emf

t

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.

206 CHAPTER 31

60. 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 B perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity v . As seen from above, a counterclockwise emf is regarded as positive.. In which direction did the loop move over the plane of the page?

• • • • • • • • • •• • • • • • • • • •• • • • • • • • • •• • • • • • • • • •• • • • • • • • • •

emf

t

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.

61. 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 B perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity v . As seen from above, a counterclockwise emf is regarded as positive.. In which direction did the loop move over the plane of the page?

× × × × × × × × × ×× × × × × × ×× × × × × × ×

× × × × × × × × ×

× × × × × × ×× × × × × × × × × ×

emf

t

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.

Faraday’s Law 207

62. 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.

Open-Ended Problems

63. A rectangular coil of 100 turns measures 40 cm by 20 cm. This coil is placed next to an electromagnet which is switched on, increasing the magnetic field through the coil from zero to 0.8 T in 50 ms. If the resistance of the coil is 2 ohms, what are the induced voltage and current in the coil?

64. 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?

65. A car with a radio antenna 1 m long travels at 80 km/h in a locality where the Earth’s magnetic field is 5 × 10–5 T. What is the maximum possible emf induced in the antenna as a result of moving through the Earth’s magnetic field?

66. 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 0.80 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?]

200 m

0.800 m

208 CHAPTER 31

Faraday’s Law 209

Chapter 31

Faraday’s Law

1. b

2. c

3. b

4. a

5. c

6. c

7. c

8. b

9. d

10. a

11. d

12. a

13. c

14. b

15. a

16. c

17. a

18. a

19. d

20. c

21. b

22. c

23. a

24. c

25. b

26. a

27. d

28. c

29. a

30. a

31. b

32. a

33. c

34. d

35. e

36. a

37. b

38. a

39. d

40. b

41. d

42. d

43. c

44. c

45. d

46. c

47. b

48. c

49. d

50. b

51. e

52. c

53. a

54. d

55. c

56. e

57. a

58. d

59. e

60. e

61. e

62. c

210 CHAPTER 31

63. 128 V, 64 A

64. 5.2 × 10–5 T

65. 1.11 mV

66. 115 000 V