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A loop with a resistance of 4.0 Ω\varOmega is pushed to the left at a constant speed of 2.0 m/s by a 24 N force. At the instant shown in the figure, the loop is partially in and partially out of a uniform magnetic field. An induced current flows from left to right through the resistor. The length and width of the loop are 2.0 m and 1.0 m, respectively. A loop with a resistance of 4.0 \varOmega is pushed to the left at a constant speed of 2.0 m/s by a 24 N force. At the instant shown in the figure, the loop is partially in and partially out of a uniform magnetic field. An induced current flows from left to right through the resistor. The length and width of the loop are 2.0 m and 1.0 m, respectively. -Determine the magnitude of the induced emf in the loop. A) 2.0 V B) 4.0 V C) 8.0 V D) 14 V E) 16 V -Determine the magnitude of the induced emf in the loop.


A) 2.0 V
B) 4.0 V
C) 8.0 V
D) 14 V
E) 16 V

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A single conducting loop with an area of 2.0 m2 rotates in a uniform magnetic field so that the induced emf has a sinusoidal time dependence as shown. A single conducting loop with an area of 2.0 m<sup>2</sup> rotates in a uniform magnetic field so that the induced emf has a sinusoidal time dependence as shown. -What is the period of the induced current? A) 1.25 s B) 2.50 s C) 3.75 s D) 5.00 s E) 6.25 s -What is the period of the induced current?


A) 1.25 s
B) 2.50 s
C) 3.75 s
D) 5.00 s
E) 6.25 s

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A coil of wire with a resistance of 0.45 Ω\varOmega has a self-inductance of 0.083 H. If a 6.0-V battery is connected across the ends of the coil and the current in the circuit reaches an equilibrium value, what is the stored energy in the inductor?


A) 7.4 J
B) 4.6 J
C) 1.6 J
D) 5.1 J
E) 3.4 J

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A uniform magnetic field passes through two areas, A1 and A2. The angles between the magnetic field and the normals of areas A1 and A2 are 30.0° and 60.0°, respectively. If the magnetic flux through the two areas is the same, what is the ratio A1/A2?


A) 0.354
B) 0.866
C) 1.00
D) 1.23
E) 1.73

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The current in a solenoid is decreased to one-half of its original value. Which one of the following statements is true concerning the self-inductance of the solenoid?


A) The self-inductance does not change.
B) The self-inductance increases by a factor of two.
C) The self-inductance decreases by a factor of two.
D) The self-inductance increases by a factor of four.
E) The self-inductance decreases by a factor of four.

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A

A single conducting loop with an area of 2.0 m2 rotates in a uniform magnetic field so that the induced emf has a sinusoidal time dependence as shown. A single conducting loop with an area of 2.0 m<sup>2</sup> rotates in a uniform magnetic field so that the induced emf has a sinusoidal time dependence as shown. -With what angular frequency does the loop rotate? A) 0.16 rad/s B) 0.30 rad/s C) 0.52 rad/s D) 0.80 rad/s E) 1.26 rad/s -With what angular frequency does the loop rotate?


A) 0.16 rad/s
B) 0.30 rad/s
C) 0.52 rad/s
D) 0.80 rad/s
E) 1.26 rad/s

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A circular coil has 275 turns and a radius of 0.045 m. The coil is used as an ac generator by rotating it in a 0.500 T magnetic field, as shown in the figure. At what angular speed should the coil be rotated so that the maximum emf is 175 V? A circular coil has 275 turns and a radius of 0.045 m. The coil is used as an ac generator by rotating it in a 0.500 T magnetic field, as shown in the figure. At what angular speed should the coil be rotated so that the maximum emf is 175 V? A) 28 rad/s B) 50 rad/s C) 130 rad/s D) 200 rad/s E) 490 rad/s


A) 28 rad/s
B) 50 rad/s
C) 130 rad/s
D) 200 rad/s
E) 490 rad/s

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A loop is pulled with a force F to the right to maintain a constant speed of 8.0 m/s. The loop has a length of 0.15 m, a width of 0.080 m, and a resistance of 200.0 Ω\varOmega . At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. The magnitude of the field is 1.2 T. A loop is pulled with a force F to the right to maintain a constant speed of 8.0 m/s. The loop has a length of 0.15 m, a width of 0.080 m, and a resistance of 200.0 \varOmega . At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. The magnitude of the field is 1.2 T. -What is the magnitude of the emf induced in the loop? A) zero volts B) 0.77 V C) 1.4 V D) 4.9 V E) 9.6 V -What is the magnitude of the emf induced in the loop?


A) zero volts
B) 0.77 V
C) 1.4 V
D) 4.9 V
E) 9.6 V

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A 250-turn solenoid carries a current of 9.0 A. The radius of the solenoid is 0.075 m; and its length is 0.14 m. Determine the magnetic flux through the circular cross-sectional area at the center of the solenoid.


A) 1.8 × 10-5 Wb
B) 9.9 × 10-5 Wb
C) 3.6 × 10-4 Wb
D) 7.0 × 10-4 Wb
E) 2.2 × 10-3 Wb

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C

A conducting loop has an area of 0.065 m2 and is positioned such that a uniform magnetic field is perpendicular to the plane of the loop. When the magnitude of the magnetic field decreases to 0.30 T in 0.087 s, the average induced emf in the loop is 1.2 V. What is the initial value of the magnetic field?


A) 0.42 T
B) 0.75 T
C) 0.87 T
D) 1.2 T
E) 1.9 T

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A circuit is pulled with a 21-N force toward the right to maintain a constant speed v. At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. As the circuit moves, a 4.0-A current flows through a 6.0- Ω\varOmega resistor. A circuit is pulled with a 21-N force toward the right to maintain a constant speed v. At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. As the circuit moves, a 4.0-A current flows through a 6.0- \varOmega resistor. -Which one of the following statements concerning this situation is true? A) The temperature of the circuit remains constant. B) The induced current flows clockwise around the circuit. C) Since the circuit moves with constant speed, the force F does zero work. D) If the circuit were replaced with a wooden loop, there would be no induced emf. E) As the circuit moves through the field, the field does work to produce the current. -Which one of the following statements concerning this situation is true?


A) The temperature of the circuit remains constant.
B) The induced current flows clockwise around the circuit.
C) Since the circuit moves with constant speed, the force F does zero work.
D) If the circuit were replaced with a wooden loop, there would be no induced emf.
E) As the circuit moves through the field, the field does work to produce the current.

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The current in the secondary coil of a step-up transformer is 1.25 A when the current in the primary coil is 0.30 A. Determine the turns ratio, Ns/Np, of the transformer.


A) 5.6
B) 4.2
C) 0.24
D) 0.18
E) 0.12

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C

A loop is pulled with a force F to the right to maintain a constant speed of 8.0 m/s. The loop has a length of 0.15 m, a width of 0.080 m, and a resistance of 200.0 Ω\varOmega . At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. The magnitude of the field is 1.2 T. A loop is pulled with a force F to the right to maintain a constant speed of 8.0 m/s. The loop has a length of 0.15 m, a width of 0.080 m, and a resistance of 200.0 \varOmega . At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. The magnitude of the field is 1.2 T. -Determine the magnitude of the force required to pull the loop. A) 1.3 × 10<sup>-</sup><sup>4</sup> N B) 2.1 × 10<sup>-</sup><sup>4</sup> N C) 3.7 × 10<sup>-</sup><sup>4</sup> N D) 6.8 × 10<sup>-</sup><sup>4</sup> N E) 9.0 × 10<sup>-</sup><sup>4</sup> N -Determine the magnitude of the force required to pull the loop.


A) 1.3 × 10-4 N
B) 2.1 × 10-4 N
C) 3.7 × 10-4 N
D) 6.8 × 10-4 N
E) 9.0 × 10-4 N

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A conducting loop of wire is placed in a magnetic field that is normal to the plane of the loop. Which one of the following actions will not result in an induced current in the loop?


A) Rotate the loop about an axis that is parallel to the field and passes through the center of the loop.
B) Increase the strength of the magnetic field.
C) Decrease the area of the loop.
D) Decrease the strength of the magnetic field.
E) Rotate the loop about an axis that is perpendicular to the field and passes through the center of the loop.

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A transformer has 450 turns in its primary coil and 30 turns in its secondary coil. Which one of the following statements concerning this transformer is true?


A) This is a step-up transformer.
B) The turns ratio is 15 for this transformer.
C) The ratio of the voltages Vs / Vp is 15 for this transformer.
D) The ratio of the currents Is / Ip is 0.067 for this transformer.
E) The power delivered to the secondary must be the same as that delivered to the primary.

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Two coils, 1 and 2, with iron cores are positioned as shown in the figure. Coil 1 is part of a circuit with a battery and a switch. Two coils, 1 and 2, with iron cores are positioned as shown in the figure. Coil 1 is part of a circuit with a battery and a switch. -Assume the switch S has been closed for a long time. Which one of the following statements is true? A) An induced current will flow from right to left in R. B) An induced current will flow from left to right in r. C) A magnetic field that points toward B appears inside coil 1. D) An induced magnetic field that points toward B appears inside coil 2. E) A current will pass through r, but there will be no current through R. -Assume the switch S has been closed for a long time. Which one of the following statements is true?


A) An induced current will flow from right to left in R.
B) An induced current will flow from left to right in r.
C) A magnetic field that points toward B appears inside coil 1.
D) An induced magnetic field that points toward B appears inside coil 2.
E) A current will pass through r, but there will be no current through R.

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A long, straight wire is in the same plane as a rectangular, conducting loop. The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop? A long, straight wire is in the same plane as a rectangular, conducting loop. The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop? A) There will be no induced emf and no induced current. B) There will be an induced emf, but no induced current. C) There will be an induced current that is clockwise around the loop. D) There will be an induced current that is counterclockwise around the loop. E) There will be an induced electric field that is clockwise around the loop.


A) There will be no induced emf and no induced current.
B) There will be an induced emf, but no induced current.
C) There will be an induced current that is clockwise around the loop.
D) There will be an induced current that is counterclockwise around the loop.
E) There will be an induced electric field that is clockwise around the loop.

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A metal ring is dropped from rest below a bar magnet that is fixed in position as suggested in the figure. An observer views the ring from below. Which one of the following statements concerning this situation is true? A metal ring is dropped from rest below a bar magnet that is fixed in position as suggested in the figure. An observer views the ring from below. Which one of the following statements concerning this situation is true? A) As the ring falls, an induced current will flow counterclockwise as viewed by the observer. B) As the ring falls, an induced current will flow clockwise as viewed by the observer. C) As the ring falls, there will be an induced magnetic field around the ring that appears counterclockwise as viewed by the observer. D) As the ring falls, there will be an induced magnetic field around the ring that appears clockwise as viewed by the observer. E) Since the magnet is stationary, there will be no induced current in the ring.


A) As the ring falls, an induced current will flow counterclockwise as viewed by the observer.
B) As the ring falls, an induced current will flow clockwise as viewed by the observer.
C) As the ring falls, there will be an induced magnetic field around the ring that appears counterclockwise as viewed by the observer.
D) As the ring falls, there will be an induced magnetic field around the ring that appears clockwise as viewed by the observer.
E) Since the magnet is stationary, there will be no induced current in the ring.

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A loop with a resistance of 4.0 Ω\varOmega is pushed to the left at a constant speed of 2.0 m/s by a 24 N force. At the instant shown in the figure, the loop is partially in and partially out of a uniform magnetic field. An induced current flows from left to right through the resistor. The length and width of the loop are 2.0 m and 1.0 m, respectively. A loop with a resistance of 4.0 \varOmega is pushed to the left at a constant speed of 2.0 m/s by a 24 N force. At the instant shown in the figure, the loop is partially in and partially out of a uniform magnetic field. An induced current flows from left to right through the resistor. The length and width of the loop are 2.0 m and 1.0 m, respectively. -At what rate is energy dissipated by the resistor? A) 130 W B) 96 W C) 32 W D) 49 W E) 8.0 W -At what rate is energy dissipated by the resistor?


A) 130 W
B) 96 W
C) 32 W
D) 49 W
E) 8.0 W

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The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting, circular loop with a resistance of 1.5 Ω\varOmega and a radius of 0.024 m. The magnetic field is directed out of the paper as shown. Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop. The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting, circular loop with a resistance of 1.5 \varOmega and a radius of 0.024 m. The magnetic field is directed out of the paper as shown. Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop. -If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, what is the magnitude of the average induced emf in the loop? A) 8.6 × 10<sup>-</sup><sup>3</sup> V B) 9.8 × 10<sup>-</sup><sup>2</sup> V C) 2.7 × 10<sup>-</sup><sup>2</sup> V D) 5.4 × 10<sup>-</sup><sup>2</sup> V E) 6.4 × 10<sup>-</sup><sup>2</sup> V -If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, what is the magnitude of the average induced emf in the loop?


A) 8.6 × 10-3 V
B) 9.8 × 10-2 V
C) 2.7 × 10-2 V
D) 5.4 × 10-2 V
E) 6.4 × 10-2 V

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