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A sheet of copper is pulled at constant velocity v from a region that contains a uniform magnetic field.At the instant shown in the figure,the sheet is partially in and partially out of the field.The induced emf in the sheet leads to the eddy current shown.Which one of the following statements concerning the direction of the magnetic field is true? A sheet of copper is pulled at constant velocity v from a region that contains a uniform magnetic field.At the instant shown in the figure,the sheet is partially in and partially out of the field.The induced emf in the sheet leads to the eddy current shown.Which one of the following statements concerning the direction of the magnetic field is true? A) The magnetic field points to the right. B) The magnetic field points to the left. C) The magnetic field points into the paper. D) The magnetic field points out of the paper. E) The direction of the magnetic field cannot be determined from the information given.


A) The magnetic field points to the right.
B) The magnetic field points to the left.
C) The magnetic field points into the paper.
D) The magnetic field points out of the paper.
E) The direction of the magnetic field cannot be determined from the information given.

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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 S has been closed for a long time.Which one of the following statements is true when coil 1 and its core are moved toward point B? A) There is no induced current in r. B) There is a magnetic field in coil 1 that points toward B. C) There is an induced current in R that flows from left to right. D) There is an induced current in R that flows from right to left. E) There is an induced magnetic field in coil 2 that points toward B. -Assume S has been closed for a long time.Which one of the following statements is true when coil 1 and its core are moved toward point B?


A) There is no induced current in r.
B) There is a magnetic field in coil 1 that points toward B.
C) There is an induced current in R that flows from left to right.
D) There is an induced current in R that flows from right to left.
E) There is an induced magnetic field in coil 2 that points toward B.

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A 0.45-m metal rod moves 0.11 m in a direction that is perpendicular to a 0.80-T magnetic field in an elapsed time of 0.036 s.Assuming that the acceleration of the rod is zero m/s²,determine the emf that exists between the ends of the rod.


A) 1.1 V
B) 0.27 V
C) 0.076 V
D) 9.1 × 10-⁵ V
E) This cannot be determined without knowing the orientation of the rod relative to the magnetic field.

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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 0.100-m long solenoid has a radius of 0.050 m and 1.50 × 10⁴ turns.The current in the solenoid changes at a rate of 6.0 A/s.A conducting loop of radius 0.0200 m is placed at the center of the solenoid with its axis the same as that of the solenoid as shown. A 0.100-m long solenoid has a radius of 0.050 m and 1.50 × 10⁴ turns.The current in the solenoid changes at a rate of 6.0 A/s.A conducting loop of radius 0.0200 m is placed at the center of the solenoid with its axis the same as that of the solenoid as shown. -Determine the self-induced emf in the solenoid due to the changing current. A) 60 V B) 98 V C) 130 V D) 180 V E) 250 V -Determine the self-induced emf in the solenoid due to the changing current.


A) 60 V
B) 98 V
C) 130 V
D) 180 V
E) 250 V

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A solenoid with 1000 turns has a cross-sectional area of 7.0 cm² and length of 25 cm.How much energy is stored in the magnetic field of the solenoid when it carries a current of 10.0 A?


A) 0.10 J
B) 2.8 J
C) 0.18 J
D) 28 J
E) 0.36 J

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A 0.100-m long solenoid has a radius of 0.050 m and 1.50 × 10⁴ turns.The current in the solenoid changes at a rate of 6.0 A/s.A conducting loop of radius 0.0200 m is placed at the center of the solenoid with its axis the same as that of the solenoid as shown. A 0.100-m long solenoid has a radius of 0.050 m and 1.50 × 10⁴ turns.The current in the solenoid changes at a rate of 6.0 A/s.A conducting loop of radius 0.0200 m is placed at the center of the solenoid with its axis the same as that of the solenoid as shown. -Determine the mutual inductance of this combination. A) 1.8 × 10<sup>-</sup>⁴ H B) 2.4 × 10<sup>-</sup>⁴ H C) 3.6 × 10<sup>-</sup>⁴ H D) 4.4 × 10<sup>-</sup>⁴ H E) 5.9 × 10<sup>-</sup>⁴ H -Determine the mutual inductance of this combination.


A) 1.8 × 10-⁴ H
B) 2.4 × 10-⁴ H
C) 3.6 × 10-⁴ H
D) 4.4 × 10-⁴ H
E) 5.9 × 10-⁴ H

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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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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 that S has been closed for a long time.Which one of the following changes will not result in an induced current in coil 2 that flows from left to right through R. A) Coil 1 and its core are moved toward A. B) Coil 2 and its core are moved toward B. C) Coil 2 and its core are moved toward C. D) The switch S is opened. E) The iron core is removed from coil 1. -Assume that S has been closed for a long time.Which one of the following changes will not result in an induced current in coil 2 that flows from left to right through R.


A) Coil 1 and its core are moved toward A.
B) Coil 2 and its core are moved toward B.
C) Coil 2 and its core are moved toward C.
D) The switch S is opened.
E) The iron core is removed from coil 1.

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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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Which of the following units are equivalent to those of motional emf?


A) T × m/s
B) V × m²/s
C) J/s
D) A × Which of the following units are equivalent to those of motional emf? A) T × m/s B) V × m²/s C) J/s D) A × E) T × m
E) T × m

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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 that S has been closed for a long time.Which one of the following changes will result in an induced magnetic field in coil 2 that points toward C? A) The switch S is opened. B) The iron core is removed from coil 1. C) Coil 1 and its core are moved toward A. D) Coil 1 and its core are moved toward B. E) Coil 2 and its core are moved toward C. -Assume that S has been closed for a long time.Which one of the following changes will result in an induced magnetic field in coil 2 that points toward C?


A) The switch S is opened.
B) The iron core is removed from coil 1.
C) Coil 1 and its core are moved toward A.
D) Coil 1 and its core are moved toward B.
E) Coil 2 and its core are moved toward C.

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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 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 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>³ V B) 9.8 × 10<sup>-</sup>² V C) 2.7 × 10<sup>-</sup>² V D) 5.4 × 10<sup>-</sup>² V E) 6.4 × 10<sup>-</sup>² Vand 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 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>³ V B) 9.8 × 10<sup>-</sup>² V C) 2.7 × 10<sup>-</sup>² V D) 5.4 × 10<sup>-</sup>² V E) 6.4 × 10<sup>-</sup>² 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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A circular copper loop is placed perpendicular to a uniform magnetic field of 0.75 T.Due to external forces,the area of the loop decreases at a rate of 7.26 × 10-³ m²/s.Determine the induced emf in the loop.


A) 3.1 × 10-⁴ V
B) 6.3 × 10-⁴ V
C) 1.2 × 10-³ V
D) 5.4 × 10-³ V
E) 3.1 V

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A circular coil of wire has 25 turns and has a radius of 0.075 m.The coil is located in a variable magnetic field whose behavior is shown on the graph.At all times,the magnetic field is directed at an angle of 75° relative to the normal to the plane of a loop.What is the average emf induced in the coil in the time interval from t = 5.00 s to 7.50 s? A circular coil of wire has 25 turns and has a radius of 0.075 m.The coil is located in a variable magnetic field whose behavior is shown on the graph.At all times,the magnetic field is directed at an angle of 75° relative to the normal to the plane of a loop.What is the average emf induced in the coil in the time interval from t = 5.00 s to 7.50 s? A) -18 mV B) -49 mV C) -92 mV D) -140 mV E) -180 mV


A) -18 mV
B) -49 mV
C) -92 mV
D) -140 mV
E) -180 mV

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A 1.2-kg rod that has a length of 1.0 m and a resistance of 5.0 A 1.2-kg rod that has a length of 1.0 m and a resistance of 5.0 slides with constant speed down a pair of frictionless vertical conducting rails that are joined at the bottom.Other than the rod,the rest of the circuit is resistanceless.A uniform magnetic field of magnitude 3.0 T is perpendicular to the plane formed by the rod and the rails as shown.Determine the speed of the rod. A) 0.38 m/s B) 0.90 m/s C) 2.6 m/s D) 6.5 m/s E) 8.7 m/s slides with constant speed down a pair of frictionless vertical conducting rails that are joined at the bottom.Other than the rod,the rest of the circuit is resistanceless.A uniform magnetic field of magnitude 3.0 T is perpendicular to the plane formed by the rod and the rails as shown.Determine the speed of the rod. A 1.2-kg rod that has a length of 1.0 m and a resistance of 5.0 slides with constant speed down a pair of frictionless vertical conducting rails that are joined at the bottom.Other than the rod,the rest of the circuit is resistanceless.A uniform magnetic field of magnitude 3.0 T is perpendicular to the plane formed by the rod and the rails as shown.Determine the speed of the rod. A) 0.38 m/s B) 0.90 m/s C) 2.6 m/s D) 6.5 m/s E) 8.7 m/s


A) 0.38 m/s
B) 0.90 m/s
C) 2.6 m/s
D) 6.5 m/s
E) 8.7 m/s

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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 that S has been closed for a long time.Which one of the following statements is true if coil 2 is moved toward C? A) There is an induced magnetic field in coil 2 that points toward B. B) There is an induced magnetic field in coil 2 that points toward C. C) There is an induced current in R that flows from right to left. D) There is an induced north pole at the right end of coil 2. E) There is no induced current in R. -Assume that S has been closed for a long time.Which one of the following statements is true if coil 2 is moved toward C?


A) There is an induced magnetic field in coil 2 that points toward B.
B) There is an induced magnetic field in coil 2 that points toward C.
C) There is an induced current in R that flows from right to left.
D) There is an induced north pole at the right end of coil 2.
E) There is no induced current in R.

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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 conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown.As a result of the bar moving through a constant magnetic field,a current I is induced in the indicated direction.Which one of the following directions is that of the magnetic field? A conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown.As a result of the bar moving through a constant magnetic field,a current I is induced in the indicated direction.Which one of the following directions is that of the magnetic field? A) toward the right B) toward the left C) parallel to the long axis of the bar D) into the page E) out of the page


A) toward the right
B) toward the left
C) parallel to the long axis of the bar
D) into the page
E) out of the page

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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 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 .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>⁴ N B) 2.1 × 10<sup>-</sup>⁴ N C) 3.7 × 10<sup>-</sup>⁴ N D) 6.8 × 10<sup>-</sup>⁴ N E) 9.0 × 10<sup>-</sup>⁴ N.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 .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>⁴ N B) 2.1 × 10<sup>-</sup>⁴ N C) 3.7 × 10<sup>-</sup>⁴ N D) 6.8 × 10<sup>-</sup>⁴ N E) 9.0 × 10<sup>-</sup>⁴ 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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