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As shown in the figure,a wire and a 10-Ω resistor are used to form a circuit in the shape of a square with dimensions 20 cm by 20 cm.A uniform but non-steady magnetic field is directed into the plane of the circuit.The magnitude of the magnetic field is steadily decreased from 2.70 T to 0.90 T in a time interval of 96 ms.What is the induced current in the circuit,and what is its direction through the resistor? As shown in the figure,a wire and a 10-Ω resistor are used to form a circuit in the shape of a square with dimensions 20 cm by 20 cm.A uniform but non-steady magnetic field is directed into the plane of the circuit.The magnitude of the magnetic field is steadily decreased from 2.70 T to 0.90 T in a time interval of 96 ms.What is the induced current in the circuit,and what is its direction through the resistor? A) 75 mA,from b to a B) 45 mA,from b to a C) 75 mA,from a to b D) 45 mA,from a to b E) 110 mA,from a to b


A) 75 mA,from b to a
B) 45 mA,from b to a
C) 75 mA,from a to b
D) 45 mA,from a to b
E) 110 mA,from a to b

F) B) and C)
G) B) and D)

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As shown in the figure,one end of a metal bar is in contact with a circular rail and the other end is pivoted at P.A steady uniform,magnetic field B into the page is present.As the bar rotates about point P in a clockwise direction,the direction of the induced current through the resistor R is As shown in the figure,one end of a metal bar is in contact with a circular rail and the other end is pivoted at P.A steady uniform,magnetic field B into the page is present.As the bar rotates about point P in a clockwise direction,the direction of the induced current through the resistor R is A) from a to b. B) from b to a. C) No current is induced.


A) from a to b.
B) from b to a.
C) No current is induced.

D) All of the above
E) A) and C)

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A circular coil of copper wire is lying flat on a horizontal table.A bar magnet is held above the center of the coil with its south pole downward.The magnet and the coil are now both raised upward with the same velocities.As viewed from above,what is the direction of the current induced in the coil as the magnet approaches the coil?


A) counterclockwise
B) clockwise
C) No current is induced in the coil.
D) An emf but no current is induced in the coil.

E) A) and D)
F) B) and C)

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A resistor and an inductor are connected in series to a battery.The battery is suddenly removed from the circuit and replaced by a wire to complete the circuit.The time constant for of the new circuit represents the time required for the current to decrease to


A) 25% of the original value.
B) 37% of the original value.
C) 63% of the original value.
D) 75% of the original value.
E) zero.

F) None of the above
G) B) and D)

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A conducting rod whose length is ℓ = 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω as shown in the figure.The wire and the rod are in the plane of the page.A constant uniform magnetic field of strength 0.40 T is applied perpendicular to and out of the paper.An external applied force moves the rod to the left with a constant speed of 12 m/s.What are the magnitude and direction of the induced current in the circuit? A conducting rod whose length is ℓ = 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω as shown in the figure.The wire and the rod are in the plane of the page.A constant uniform magnetic field of strength 0.40 T is applied perpendicular to and out of the paper.An external applied force moves the rod to the left with a constant speed of 12 m/s.What are the magnitude and direction of the induced current in the circuit? A) 150 mA clockwise B) 150 mA counterclockwise C) 34 mA counterclockwise D) 34 mA clockwise E) 100 mA clockwise


A) 150 mA clockwise
B) 150 mA counterclockwise
C) 34 mA counterclockwise
D) 34 mA clockwise
E) 100 mA clockwise

F) A) and E)
G) None of the above

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A flat coil having 160 turns,each with an area of 0.20 m2,is placed with the plane of its area perpendicular to a magnetic field of 0.40 T.The magnetic field changes uniformly from 0.40 T in the +x direction to 0.40 T in the -x direction in 2.0 s.If the resistance of the coil is 16 Ω,at what rate is power generated in the coil during this change?


A) 5.0 W
B) 10 W
C) 15 W
D) 20 W

E) B) and C)
F) A) and D)

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As shown in the figure,two solenoids are side by side.The switch S is initially open.When S is suddenly closed,the direction of the induced current through the resistor R is As shown in the figure,two solenoids are side by side.The switch S is initially open.When S is suddenly closed,the direction of the induced current through the resistor R is A) from a to b. B) from b to a. C) No current is induced.


A) from a to b.
B) from b to a.
C) No current is induced.

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

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An ideal solenoid has a self-inductance L.If you now double its radius and its length,but do not change the number of coils,what will its self-inductance be?


A) 4L
B) 2L
C) L
D) L/2
E) L/4

F) None of the above
G) A) and B)

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The wire in the figure carries a current I that is decreasing with time at a constant rate.The wire and the three loops are all in the same plane.What is true about the currents induced in each of the three loops shown? The wire in the figure carries a current I that is decreasing with time at a constant rate.The wire and the three loops are all in the same plane.What is true about the currents induced in each of the three loops shown? A) No current is induced in any loop. B) The currents are counterclockwise in all three loops. C) The currents are clockwise in all three loops. D) Loop A has clockwise current,loop B has no induced current,and loop C has counterclockwise current. E) Loop A has counterclockwise current,loop B has no induced current,and loop C has clockwise current.


A) No current is induced in any loop.
B) The currents are counterclockwise in all three loops.
C) The currents are clockwise in all three loops.
D) Loop A has clockwise current,loop B has no induced current,and loop C has counterclockwise current.
E) Loop A has counterclockwise current,loop B has no induced current,and loop C has clockwise current.

F) B) and D)
G) All of the above

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A bar magnet is oriented above a copper ring,as shown in the figure.If the magnet is pulled upward,what is the direction of the current induced in the ring,as viewed from above? A bar magnet is oriented above a copper ring,as shown in the figure.If the magnet is pulled upward,what is the direction of the current induced in the ring,as viewed from above? A) There is no current in the ring. B) counterclockwise C) clockwise


A) There is no current in the ring.
B) counterclockwise
C) clockwise

D) A) and B)
E) All of the above

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A circular conducting loop with a radius of A circular conducting loop with a radius of And a small gap filled with a Resistor is oriented in the If a uniform magnetic field of Making an angle of With the Increases to In What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A And a small gap filled with a A circular conducting loop with a radius of And a small gap filled with a Resistor is oriented in the If a uniform magnetic field of Making an angle of With the Increases to In What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A Resistor is oriented in the A circular conducting loop with a radius of And a small gap filled with a Resistor is oriented in the If a uniform magnetic field of Making an angle of With the Increases to In What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A If a uniform magnetic field of A circular conducting loop with a radius of And a small gap filled with a Resistor is oriented in the If a uniform magnetic field of Making an angle of With the Increases to In What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A Making an angle of A circular conducting loop with a radius of And a small gap filled with a Resistor is oriented in the If a uniform magnetic field of Making an angle of With the Increases to In What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A With the A circular conducting loop with a radius of And a small gap filled with a Resistor is oriented in the If a uniform magnetic field of Making an angle of With the Increases to In What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A Increases to A circular conducting loop with a radius of And a small gap filled with a Resistor is oriented in the If a uniform magnetic field of Making an angle of With the Increases to In What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A In A circular conducting loop with a radius of And a small gap filled with a Resistor is oriented in the If a uniform magnetic field of Making an angle of With the Increases to In What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A What is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance?


A) 0.01530393 A
B) 0.08835729 A
C) 0.15303932 A
D) 0 A

E) B) and C)
F) A) and D)

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A circular coil of 20 turns and radius 5.0 cm is placed with its plane oriented at 90° to a uniform magnetic field of A circular coil of 20 turns and radius 5.0 cm is placed with its plane oriented at 90° to a uniform magnetic field of The field is now increased at a steady rate,reaching a value of After 4.0 seconds.What emf is induced in the coil? A) 0.016 V B) 0.021 V C) 0.026 V D) 0.031 V E) 0.036 V The field is now increased at a steady rate,reaching a value of A circular coil of 20 turns and radius 5.0 cm is placed with its plane oriented at 90° to a uniform magnetic field of The field is now increased at a steady rate,reaching a value of After 4.0 seconds.What emf is induced in the coil? A) 0.016 V B) 0.021 V C) 0.026 V D) 0.031 V E) 0.036 V After 4.0 seconds.What emf is induced in the coil?


A) 0.016 V
B) 0.021 V
C) 0.026 V
D) 0.031 V
E) 0.036 V

F) All of the above
G) B) and D)

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As shown in the figure,a straight wire carries a current I into the page.The wire passes through the center of a toroidal coil.If the current I is quickly reduced to zero,the direction of the induced current through the resistor R is As shown in the figure,a straight wire carries a current I into the page.The wire passes through the center of a toroidal coil.If the current I is quickly reduced to zero,the direction of the induced current through the resistor R is A) from a to b. B) from b to a. C) No current is induced.


A) from a to b.
B) from b to a.
C) No current is induced.

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

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The secondary coil of an ideal neon sign transformer provides 7500 V at 10.0 mA.The primary coil operates on 120 V.What current does the primary draw?


A) 0.625 A
B) 0.625 mA
C) 0.160 A
D) 1.66 A

E) B) and D)
F) A) and B)

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A conducting rod whose length is ℓ = 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 Ω as shown in the figure.The rails and the rod are in the plane of the page.A constant uniform magnetic field of strength 2.20 T is applied perpendicular to and out of the paper.An external applied force moves the rod to the right with a constant speed of 6.00 m/s.At what rate is energy dissipated in the lightbulb? A conducting rod whose length is ℓ = 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 Ω as shown in the figure.The rails and the rod are in the plane of the page.A constant uniform magnetic field of strength 2.20 T is applied perpendicular to and out of the paper.An external applied force moves the rod to the right with a constant speed of 6.00 m/s.At what rate is energy dissipated in the lightbulb? A) 60.0 W B) 121 W C) 21.2 W D) 112 W E) 11.5 W


A) 60.0 W
B) 121 W
C) 21.2 W
D) 112 W
E) 11.5 W

F) All of the above
G) A) and E)

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A conducting rod whose length is ℓ = 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 Ω as shown in the figure.The rails and the rod are in the plane of the page.A constant uniform magnetic field of strength 2.20 T is applied perpendicular to and out of the paper.What is the magnitude of the external applied force needed to move the rod to the right with a constant speed of 6.00 m/s? A conducting rod whose length is ℓ = 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 Ω as shown in the figure.The rails and the rod are in the plane of the page.A constant uniform magnetic field of strength 2.20 T is applied perpendicular to and out of the paper.What is the magnitude of the external applied force needed to move the rod to the right with a constant speed of 6.00 m/s? A) 8.60 N B) 9.30 N C) 10.6 N D) 12.6 N E) 18.6 N


A) 8.60 N
B) 9.30 N
C) 10.6 N
D) 12.6 N
E) 18.6 N

F) A) and E)
G) D) and E)

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A flat coil is wrapped with 200 turns of very thin wire on a square frame with sides 18 cm long.A uniform magnetic field is applied perpendicular to the plane of the coil.If the field changes uniformly from 0.50 T to 0.00 T in 8.0 s,find the emf induced in the coil.


A) 2.1 mV
B) 4.1 mV
C) 0.21 V
D) 0.41 V

E) B) and D)
F) C) and D)

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A bar magnet is pushed through a coil of wire of cross-sectional area 0.020 m2 as shown in the figure.The coil has seven turns,and the rate of change of the strength of the magnetic field in it due to the motion of the bar magnet is 0.040 T/s.What is the magnitude of the induced emf in that coil of wire? A bar magnet is pushed through a coil of wire of cross-sectional area 0.020 m<sup>2</sup> as shown in the figure.The coil has seven turns,and the rate of change of the strength of the magnetic field in it due to the motion of the bar magnet is 0.040 T/s.What is the magnitude of the induced emf in that coil of wire? A) 5.6 × 10<sup>-3</sup> V B) 5.6 × 10<sup>-2</sup> V C) 5.6 × 10<sup>-1</sup> V D) 5.6 × 10<sup>-4</sup> V E) 5.6 × 10<sup>-5</sup> V


A) 5.6 × 10-3 V
B) 5.6 × 10-2 V
C) 5.6 × 10-1 V
D) 5.6 × 10-4 V
E) 5.6 × 10-5 V

F) C) and E)
G) A) and E)

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A flux of 4.0 × 10-5 T ∙ m2 is maintained through a coil of area 7.5 cm2 for 0.50 s.What emf is induced in this coil during this time by this flux?


A) 8.0 × 10-5 V
B) 4.0 × 10-5 V
C) 3.0 × 10-5 V
D) 2.0 × 10-5 V
E) No emf is induced in this coil.

F) A) and B)
G) A) and E)

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A conductor is formed into a flat loop that encloses an area of A conductor is formed into a flat loop that encloses an area of The plane of the loop is oriented at a 30.0° angle with the xy-plane.A uniform time-varying magnetic field is oriented parallel to the z-axis.If the emf induced in the loop is What is the rate at which the magnetic field strength is changing? A) 29 T/s B) 22 T/s C) 50 T/s D) 13 T/s The plane of the loop is oriented at a 30.0° angle with the xy-plane.A uniform time-varying magnetic field is oriented parallel to the z-axis.If the emf induced in the loop is A conductor is formed into a flat loop that encloses an area of The plane of the loop is oriented at a 30.0° angle with the xy-plane.A uniform time-varying magnetic field is oriented parallel to the z-axis.If the emf induced in the loop is What is the rate at which the magnetic field strength is changing? A) 29 T/s B) 22 T/s C) 50 T/s D) 13 T/s What is the rate at which the magnetic field strength is changing?


A) 29 T/s
B) 22 T/s
C) 50 T/s
D) 13 T/s

E) A) and D)
F) A) and B)

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