Deck 20: Electromagnetic Induction

Question 1

A rectangular loop of wire 0.10 m by 0.20 m) carries a current of 5.0 A in a counterclockwise direction. The loop is oriented, as shown, in a uniform magnetic field of 1.5 T. The magnetic flux of B is

A) 0.026 T · m².
B) 1.3 T · m².
C) 0.015 T · m².
D) 0.030 T · m².
E) 1.5 T · m².

Answer 1

0.026 T · m².

Question 2

A 3.0-cm by 5.0-cm rectangular coil has 100 turns. Its axis makes an angle of 55º with a uniform magnetic field of 0.35 T. It requires 0.33 s to turn the coil until its plane is perpendicular to the magnetic field. What is the average) magnitude of the induced EMF?

A) 0.16 V
B) 0.13 V
C) 91 mV
D) 68 mV
E) 29 mV

Answer 2

91 mV

Question 3

A rectangle is bent on two sides at 90º so that one end lies along the xy-plane while the other end lies along the xz-plane. The length a = 10 cm and b = 30 cm. At t = 0, a magnetic field of strength B = 0.1 T lies in the yz-plane and points at an angle Ɵ = 30 and 10 ms later the field points in the opposite direction. The EMF induced in the rectangle is

A) 10.4 V.
B) 6.0 V.
C) 12 V.
D) 8.2 V.
E) None of these is correct.

Answer 3

8.2 V.

Question 4

A circular wire coil of radius 25 cm and 20 turns is sitting in a perpendicular magnetic field of 0.20 T. If the coil is rotated 90^o, what is the magnitude of the change in magnetic flux through the loop?

A) 0 Wb
B) 1.6 Wb
C) 0.080 Wb
D) 0.80 Wb
E) 0.040 Wb

Question 5

For which of the following diagrams) will current flow through the lightbulb?

A) 1
B) 2
C) 3
D) 4
E) 1 and 2

Question 6

A rectangular surface of area 1.0 m² is hinged along the z-axis and makes an angle of 37 with the yz plane. If the local magnetic field is 10 T along the positive x-axis, the magnetic flux through this surface is

A) 6.0 T · m².
B) 8.0 T · m².
C) 10 T · m².
D) 13 T · m².
E) 17 T · m².

Question 7

A rectangle is bent on two sides at 90º so that one end lies along the xy plane while the other end lies along the xz plane. The length a = 10 cm and b = 30 cm. A magnetic field of strength B = 0.1 T lies in the yz plane and points at an angle Ɵ = 30º with the y-axis. The flux through the rectangle is

A) 52.0 mWb.
B) 30.0 mWb.
C) 41.0 mWb.
D) 60.0 mWb.
E) None of these is correct.

Question 8

Which of the following is a vector quantity?

A) current
B) charge
C) magnetic field
D) electric potential
E) magnetic flux

Question 9

A square loop of sides "a" lies in the yz plane with one corner at the origin. A varying magnetic field B = k_y. points in the positive x direction and passes through the loop k is a constant). The magnetic flux through the loop is

A) ka².
B) ka²/2.
C) ka³/2.
D) ka³/3.
E) None of these is correct.

Question 10

A uniform magnetic field of magnitude 0.5 T is parallel to the x-axis. A square coil of side 10 cm has 300 turns and makes an angle of 60 with the z-axis as shown. The total magnetic flux through the coil is approximately

A) 0.14 Wb.
B) 0.75 Wb.
C) 1.5 Wb.
D) 0.27 Wb.
E) 0.56 Wb.

Question 11

A 100-turn coil has a radius of 7.50 cm and a resistance of 50.0 Ω. At what rate must a perpendicular magnetic field change to produce a current of 5.00 A in the coil?

A) 275 T/s
B) 134 T/s
C) 329 T/s
D) 141 T/s
E) 106 T/s

Question 12

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

Question 13

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.

Question 14

0 × 10^-2 Wb. Calculate the current through the solenoid.

A) 53 A
B) 5.4 A
C) 17 A
D) 1.3 A
E) 34 A

Question 15

A uniform magnetic field of 0.5 T is parallel to the y-axis. A square coil of side 10 cm has 300 turns and lies in the xy plane as shown. The magnetic flux through the coil is

A) 0.14 Wb.
B) 0.75 Wb.
C) 1.5 Wb.
D) 0.27 Wb.
E) None of these answers is correct.

Question 16

A 3.0-cm by 5.0-cm rectangular coil has 100 turns. Its axis makes an angle of 55 with a uniform magnetic field of 0.35 T. What is the total magnetic flux through this coil?

A) 3.0 × 10^-4 Wb
B) 4.3 × 10^-4 Wb
C) 3.0 × 10^-2 Wb
D) 4.3 × 10^-2 Wb
E) 5.3 × 10^-2 Wb

Question 17

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 6.
E) increase it by a factor of 8.

Question 18

A uniform magnetic field of 0.5 T is parallel to the x-axis. A square coil of side 10 cm has 300 turns and lies in the xy plane as shown. The magnetic flux through the coil is

A) 0.14 Wb.
B) 0.75 Wb.
C) 1.5 Wb.
D) 0.27 Wb.
E) zero.

Question 19

A uniform magnetic field of 0.5 T is parallel to the z-axis. A square coil of side 10 cm has 300 turns and lies in the xy plane as shown. The magnetic flux through the coil is

A) 0.14 Wb.
B) 0.75 Wb.
C) 1.5 Wb.
D) 0.27 Wb.
E) zero.

Question 20

You place a coil that has 200 turns and a cross-sectional area of 0.050 m² so that its plane is normal to a field of 3.0 T. If the field is uniformly decreased to zero in 5.0 s, what EMF is induced in the coil?

A) 0.15 kV
B) 0.12 kV
C) 6.0 V
D) 50 mV
E) 10 mV

Question 21

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.

Question 22

A straight conductor 10-cm long is perpendicular to a uniform magnetic field of flux density 2.0 mT. When the conductor carries a current of 5.0 A, the force exerted on it by the field is

A) 0.25 kN.
B) 40 mN.
C) 1.0 mN.
D) zero.
E) 5.0 mN.

Question 23

A square coil of wire with side 9.0 cm and 8 turns sits in a uniform magnetic field of 2 T that is perpendicular to the plane of the coil. If an EMF of 0.5 V is induced in the coil when the magnetic field is reversed, find the time taken for the field reversal.

A) 0.26 s
B) 1.0 s
C) 5.8 s
D) 1.6 s
E) 0.52 s

Question 24

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

Question 25

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, the direction of the magnetic force is

A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Question 26

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.

Question 27

You place a single loop of wire 0.50 m by 0.30 m perpendicular to a field of 2.0 T. In 30 ms you turn the loop until it is parallel with the field. The average EMF induced in this loop is

A) 0.30 V.
B) 10 V.
C) 5.0 V.
D) 67 V.
E) 20 V.

Question 28

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 on the left, the direction of the current through the right side of the loop is

A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Question 29

0 s, the average EMF induced in the coil is

A) 0.10 kV.
B) 1.0 kV.
C) 1.0 mV.
D) 0.10 mV.
E) 10 mV.

Question 30

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, the direction of the magnetic force is

A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Question 31

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 is attracted, but the loop is repelled.
D) The magnet is repelled, but the loop is attracted.
E) The magnet and loop neither attract nor repel one another.

Question 32

The plane of a wire loop with an area of 0.20 m² is perpendicular to a magnetic field of 50 mT. In 40 ms you rotate the loop 90º so that its plane is parallel to the magnetic field. The average EMF induced in the loop is

A) 0.25 V.
B) 6.0 V.
C) 3.0 V.
D) 4.0 V.
E) 1.3 V.

Question 33

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

A) ε
B) 2ε
C) ε/2
D) 4ε
E) ε²

Question 34

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 on the z-axis. The diagram that correctly shows the direction of the resultant induced current in the loop is

A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Question 35

A circular loop of radius 25 cm is sitting in a perpendicular magnetic field of 0.2 T. If the magnetic field strength changes to a value of 0.5 T in 2.5 s, calculate the induced EMF in the loop.

A) 7.5 × 10^-3 V
B) 9.6 × 10^-2 V
C) 4.0 × 10^-2 V
D) 2.4 × 10^-2 V
E) None of the above.

Question 36

Which of the following could NOT induce an electric field in a loop of wire?

A) It sits in a very strong constant magnetic field.
B) It sits in a small magnetic field which is getting weaker over time.
C) It is moved closer and closer to the end of a bar magnet.
D) It is squeezed so the area of the loop gets smaller while it is exposed to a constant magnetic field.
E) It is rotated at a constant rate while it is exposed to a constant magnetic field.

Question 37

A 25-cm-long conducting rod moves at a speed of 12 m/s in a plane perpendicular to a uniform magnetic field of magnitude 0.080 T. What is the induced potential difference between the ends of the rod?

A) 24 V
B) 2.4 V
C) 0.24 V
D) 0.60 kV
E) 6.0 V

Question 38

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 be moving either away from or toward the ring.
D) is not necessarily moving.
E) must remain stationary to keep the current flowing.

Question 39

A square coil of wire with side 8.0 cm and 50 turns sits in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is pulled quickly out of the magnetic field in 0.2 s. If the resistance of the coil is 15 ohm and a current of 12 mA is induced in the coil, calculate the value of the magnetic field.

A) 5.6 T
B) 0.11 T
C) 7.5 × 10^-3 T
D) 1.4 T
E) 9.1 T

Question 40

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

Question 41

A circular coil of wire sits in a magnetic field of strength 0.5 mT. The wire has 300 turns, and has a radius of 0.04 m. If it is spinning at a rate of 55 rad/s, what is the angular frequency of the current generated?

A) 0.041 rad/s
B) 0.33 rad/s
C) 55 rad/s
D) It generates a constant, steady current.
E) None of the above.

Question 42

A coil of wire rotates at a constant rate in a uniform magnetic field. Which of the following would NOT increase the induced current in the loop?

A) If the coil spun faster.
B) If the magnetic field was stronger.
C) If the coil had more turns of wire on it.
D) If the coil's area was larger.
E) All of the above would increase the induced current.

Question 43

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.

Question 44

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.

Question 45

A metal disk rotates about its central axis at an angular frequency of 800 radians per second in a uniform magnetic field of 0.8 T. The diameter of the disk is 8 cm. What is the magnitude of the voltage difference between the center and edge of the disk?

A) 0 V
B) 0.80 V
C) 0.51 V
D) 1.0 V
E) 3.1 V

Question 46

2 V, then calculate the number of revolutions per second of the rod.

A) 6.7 × 10¹ revs/s
B) 6.7 × 10³ revs/s
C) 4.7 × 10^-3 revs/s
D) 6.7 × 10² revs/s
E) 2.1 × 10² revs/s

Question 47

A 0.8-m-long pole rotates about a perpendicular axis at one end. As the pole rotates, it passes through 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

Question 48

What is the average induced EMF between the ends of the wings of a plane flying at a speed of 500 km/hr when the vertical component of Earth's magnetic field is 3 × 10^-5 T? The distance between the wingtips is 25 m.

A) 0.20 V
B) 0.050 V
C) 6.0 V
D) 0.10 V
E) None of the above.

Question 49

5 s, calculate the induced current in the loop if it is in series with a 20 ohm resistor.

A) 5.7 × 10^-2 A
B) 1.2 × 10^-2 A
C) 2.8 × 10^-3 A
D) 6.0 × 10^-4 A
E) 1.1 A

Question 50

A circular coil of wire sits in a magnetic field of strength 0.5 mT. The wire has 300 turns, and has a radius of 0.04 m. If it is spinning at a rate of 55 rad/s, what is the maximum induced current in the loop?

A) zero
B) 0.330 A
C) 0.041 A
D) 41.46 A
E) None of the above.