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A single circular loop of radius 1.00 m carries a current of 10.0 mA. It is placed in a uniform magnetic field of magnitude 0.500 T that is directed parallel to the plane of the loop as suggested in the figure. What is the magnitude of the torque exerted on the loop by the magnetic field? A single circular loop of radius 1.00 m carries a current of 10.0 mA. It is placed in a uniform magnetic field of magnitude 0.500 T that is directed parallel to the plane of the loop as suggested in the figure. What is the magnitude of the torque exerted on the loop by the magnetic field?   A) 1.57 × 10<sup>-</sup><sup>2</sup> N . m B) 3.14 × 10<sup>-</sup><sup>2</sup> N . m C) 6.28 × 10<sup>-</sup><sup>2</sup> N . m D) 9.28 × 10<sup>-</sup><sup>2</sup> N . m E) zero N . m


A) 1.57 × 10-2 N . m
B) 3.14 × 10-2 N . m
C) 6.28 × 10-2 N . m
D) 9.28 × 10-2 N . m
E) zero N . m

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

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A coil of wire carries current I as shown in the figure. If the observer could "see" the magnetic field inside this arrangement of loops, how would it appear? A coil of wire carries current I as shown in the figure. If the observer could  see  the magnetic field inside this arrangement of loops, how would it appear?     A) a B) b C) c D) d E) e A coil of wire carries current I as shown in the figure. If the observer could  see  the magnetic field inside this arrangement of loops, how would it appear?     A) a B) b C) c D) d E) e


A) a
B) b
C) c
D) d
E) e

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

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A long, straight wire carries a 10.0-A current in the +y direction as shown in the figure. A long, straight wire carries a 10.0-A current in the +y direction as shown in the figure.   Next to the wire is a square copper loop that carries a 2.00-A current as shown. The length of each side of the square is 1.00 m. -What is the direction of the net magnetic force that acts on the loop? A) +x direction B) -x direction C) +y direction D) -y direction E) 30° with respect to the +x direction Next to the wire is a square copper loop that carries a 2.00-A current as shown. The length of each side of the square is 1.00 m. -What is the direction of the net magnetic force that acts on the loop?


A) +x direction
B) -x direction
C) +y direction
D) -y direction
E) 30° with respect to the +x direction

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

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A long, straight wire carries a 6.0-A current that is directed in the positive x direction. When a uniform magnetic field is applied perpendicular to a 3.0-m segment of the wire, the magnetic force on the segment is 0.36 N, directed in the negative y direction, as shown. What are the magnitude and direction of the magnetic field? A long, straight wire carries a 6.0-A current that is directed in the positive x direction. When a uniform magnetic field is applied perpendicular to a 3.0-m segment of the wire, the magnetic force on the segment is 0.36 N, directed in the negative y direction, as shown. What are the magnitude and direction of the magnetic field?   A) 0.020 T, out of the paper B) 0.020 T, into the paper C) 0.060 T, out of the paper D) 0.060 T, into the paper E) 0.65 T, out of the paper


A) 0.020 T, out of the paper
B) 0.020 T, into the paper
C) 0.060 T, out of the paper
D) 0.060 T, into the paper
E) 0.65 T, out of the paper

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

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Which one of the following statements best explains why a constant magnetic field can do no work on a moving charged particle?


A) The magnetic field is conservative.
B) The magnetic force is a velocity dependent force.
C) The magnetic field is a vector and work is a scalar quantity.
D) The magnetic force is always perpendicular to the velocity of the particle.
E) The electric field associated with the particle cancels the effect of the magnetic field on the particle.

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

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The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin? The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin?   A) zero tesla B) 1 × 10<sup>-</sup><sup>6</sup> T C) 3 × 10<sup>-</sup><sup>6</sup> T D) 4 × 10<sup>-</sup><sup>6</sup> T E) 6 × 10<sup>-</sup><sup>6</sup> T


A) zero tesla
B) 1 × 10-6 T
C) 3 × 10-6 T
D) 4 × 10-6 T
E) 6 × 10-6 T

F) C) and D)
G) A) and D)

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A long straight wire carries a 40.0 A current in the +x direction. At a particular instant, an electron moving at 1.0 × 107 m/s in the +y direction is 0.10 m from the wire. The charge on the electron is -1.6 × 10-19 C. What is the force on the electron at this instant? A long straight wire carries a 40.0 A current in the +x direction. At a particular instant, an electron moving at 1.0 × 10<sup>7</sup> m/s in the +y direction is 0.10 m from the wire. The charge on the electron is -1.6 × 10<sup>-</sup><sup>19</sup> C. What is the force on the electron at this instant?   A) 1.3 × 10<sup>-</sup><sup>16</sup> N in the +x direction B) 1.3 × 10<sup>-</sup><sup>16</sup> N in the -x direction C) 6.5 × 10<sup>-</sup><sup>10</sup> N in the +y direction D) 6.5 × 10<sup>-</sup><sup>10</sup> N in the -y direction E) 6.5 × 10<sup>-</sup><sup>16</sup> N in the -y direction


A) 1.3 × 10-16 N in the +x direction
B) 1.3 × 10-16 N in the -x direction
C) 6.5 × 10-10 N in the +y direction
D) 6.5 × 10-10 N in the -y direction
E) 6.5 × 10-16 N in the -y direction

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

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A wire is bent into the shape of a circle of radius r = 0.10 m and carries a 20.0-A current in the direction shown. A wire is bent into the shape of a circle of radius r = 0.10 m and carries a 20.0-A current in the direction shown.   -What is the magnitude of the magnetic field at the center of the loop? A) 2.0 × 10<sup>-</sup><sup>5</sup> T B) 1.3 × 10<sup>-</sup><sup>5</sup> T C) 2.0 × 10<sup>-</sup><sup>4</sup> T D) 1.3 × 10<sup>-</sup><sup>4</sup> T E) zero tesla -What is the magnitude of the magnetic field at the center of the loop?


A) 2.0 × 10-5 T
B) 1.3 × 10-5 T
C) 2.0 × 10-4 T
D) 1.3 × 10-4 T
E) zero tesla

F) A) and D)
G) B) and D)

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A charged particle is launched with a velocity of 5.2 × 104 m/s at an angle of 35° with respect to a 0.0045-T magnetic field. If the magnetic field exerts a force of 0.0026 N on the particle, determine the magnitude of the charge on the particle.


A) 11 µC
B) 15 µC
C) 19 µC
D) 23 µC
E) 27 µC

F) A) and B)
G) A) and C)

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Two charged particles of equal mass are traveling in circular orbits in a region of uniform, constant magnetic field as shown. The particles are observed to move in circular paths of radii R1 and R2 with speeds v1 and v2, respectively. Two charged particles of equal mass are traveling in circular orbits in a region of uniform, constant magnetic field as shown. The particles are observed to move in circular paths of radii R<sub>1</sub> and R<sub>2</sub> with speeds v<sub>1</sub> and v<sub>2</sub>, respectively.   As the figure shows, the path of particle 2 has a smaller radius than that of particle 1. Which one of the following statements about this system is false? A) |v<sub>1</sub>/Q<sub>1</sub>| < |v<sub>2</sub>/Q<sub>2</sub>| B) Particle 2 carries a positive charge. C) Particle 1 carries a negative charge. D) Neither particle gains energy from the magnetic field. E) The particle velocities have no components parallel to the magnetic field. As the figure shows, the path of particle 2 has a smaller radius than that of particle 1. Which one of the following statements about this system is false?


A) |v1/Q1| < |v2/Q2|
B) Particle 2 carries a positive charge.
C) Particle 1 carries a negative charge.
D) Neither particle gains energy from the magnetic field.
E) The particle velocities have no components parallel to the magnetic field.

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

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Each second, 1.25 × 1019 electrons in a narrow beam pass through a small hole in a wall. The beam is perpendicular to the wall. Using Ampere's law, determine the magnitude of the magnetic field in the wall at a radius of 0.750 m from the center of the beam.


A) 1.18 × 10-9 T
B) 5.34 × 10-7 T
C) 2.62 × 10-3 T
D) 4.14 × 108 T
E) 3.33 × 1012 T

F) A) and D)
G) A) and C)

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A beam consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Note: 1 mass unit = 1.67 × 10-27 kg and e = 1.6 × 10-19 C A beam consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Note: 1 mass unit = 1.67 × 10<sup>-</sup><sup>27</sup> kg and e = 1.6 × 10<sup>-</sup><sup>19</sup> C   -What is the direction of the magnetic field? A) toward the right B) toward the left C) into the page D) out of the page of the page E) toward the bottom -What is the direction of the magnetic field?


A) toward the right
B) toward the left
C) into the page
D) out of the page of the page
E) toward the bottom

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

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Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal. Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.   Which one of the entries in the table below is correct?   A)    B)    C)    D)    E)   Which one of the entries in the table below is correct? Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.   Which one of the entries in the table below is correct?   A)    B)    C)    D)    E)


A) Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.   Which one of the entries in the table below is correct?   A)    B)    C)    D)    E)
B) Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.   Which one of the entries in the table below is correct?   A)    B)    C)    D)    E)
C) Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.   Which one of the entries in the table below is correct?   A)    B)    C)    D)    E)
D) Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.   Which one of the entries in the table below is correct?   A)    B)    C)    D)    E)
E) Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.   Which one of the entries in the table below is correct?   A)    B)    C)    D)    E)

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

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A single circular loop of wire with radius 0.025 m carries a current of 6.0 A. It is placed at the center of a solenoid that has length 0.60 m, radius 0.075 m, and 1200 turns. A single circular loop of wire with radius 0.025 m carries a current of 6.0 A. It is placed at the center of a solenoid that has length 0.60 m, radius 0.075 m, and 1200 turns.   -Determine the value of the current in the solenoid so that the magnetic field at the center of the loop is zero tesla. A) 1.4 × 10<sup>-</sup><sup>1</sup> A B) 2.5 × 10<sup>-</sup><sup>4</sup> A C) 6.0 × 10<sup>-</sup><sup>2</sup> A D) 5.0 × 10<sup>-</sup><sup>3</sup> A E) 9.3 × 10<sup>-</sup><sup>2</sup> A -Determine the value of the current in the solenoid so that the magnetic field at the center of the loop is zero tesla.


A) 1.4 × 10-1 A
B) 2.5 × 10-4 A
C) 6.0 × 10-2 A
D) 5.0 × 10-3 A
E) 9.3 × 10-2 A

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

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Complete the following statement: The magnetic field around a current-carrying, circular loop is most like that of


A) the earth.
B) a short bar magnet.
C) a current-carrying, rectangular loop.
D) a long straight wire that carries a current.
E) two long straight wires that carry currents in opposite directions.

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

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A long, straight wire carries a 10.0-A current in the +y direction as shown in the figure. A long, straight wire carries a 10.0-A current in the +y direction as shown in the figure.   Next to the wire is a square copper loop that carries a 2.00-A current as shown. The length of each side of the square is 1.00 m. -What is the magnitude of the net magnetic force that acts on the loop? A) 8.0 × 10<sup>-</sup><sup>6</sup> N B) 1.1 × 10<sup>-</sup><sup>5</sup> N C) 1.4 × 10<sup>-</sup><sup>5</sup> N D) 1.7 × 10<sup>-</sup><sup>5</sup> N E) 2.3 × 10<sup>-</sup><sup>5</sup> N Next to the wire is a square copper loop that carries a 2.00-A current as shown. The length of each side of the square is 1.00 m. -What is the magnitude of the net magnetic force that acts on the loop?


A) 8.0 × 10-6 N
B) 1.1 × 10-5 N
C) 1.4 × 10-5 N
D) 1.7 × 10-5 N
E) 2.3 × 10-5 N

F) D) and E)
G) C) and E)

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A long, straight, vertical segment of wire traverses a magnetic field of magnitude 2.0 T in the direction shown in the diagram. The length of the wire that lies in the magnetic field is 0.060 m. When the switch is closed, a current of 4.0 A flows through the wire from point P to point Q. A long, straight, vertical segment of wire traverses a magnetic field of magnitude 2.0 T in the direction shown in the diagram.  The length of the wire that lies in the magnetic field is 0.060 m.  When the switch is closed, a current of 4.0 A flows through the wire from point P to point Q.   -Which one of the following statements concerning the effect of the magnetic force on the wire is true? A) The wire will be pushed to the left. B) The wire will be pushed to the right. C) The wire will have no net force acting on it. D) The wire will be pushed downward, into the plane of the paper. E) The wire will be pushed upward, out of the plane of the paper. -Which one of the following statements concerning the effect of the magnetic force on the wire is true?


A) The wire will be pushed to the left.
B) The wire will be pushed to the right.
C) The wire will have no net force acting on it.
D) The wire will be pushed downward, into the plane of the paper.
E) The wire will be pushed upward, out of the plane of the paper.

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

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A long, coaxial cable, shown in cross-section in the drawing, is made using two conductors that share a common central axis, labeled C. The conductors are separated by an electrically insulating material that is also used as the outer cover of the cable. The current in the inner conductor is 2.0 A directed into the page and that in the outer conductor is 2.5 A directed out of the page. The distance from point C to point A is 0.0015 m; and the distance from C to B is 0.0030 m. The radii a and b of the conductors are 6.0 × 10-4 m and 1.9 × 10-3 m, respectively. A long, coaxial cable, shown in cross-section in the drawing, is made using two conductors that share a common central axis, labeled C. The conductors are separated by an electrically insulating material that is also used as the outer cover of the cable. The current in the inner conductor is 2.0 A directed into the page and that in the outer conductor is 2.5 A directed out of the page. The distance from point C to point A is 0.0015 m; and the distance from C to B is 0.0030 m. The radii a and b of the conductors are 6.0 × 10-4 m and 1.9 × 10-3 m, respectively.   -What is the magnitude and direction of the magnetic field at point B? A) 3.3 × 10<sup>-</sup><sup>5</sup> T, clockwise B) 3.3 × 10<sup>-</sup><sup>5</sup> T, counterclockwise C) 6.8 × 10<sup>-</sup><sup>5</sup> T, clockwise D) 6.8 × 10<sup>-</sup><sup>5</sup> T, counterclockwise E) 2.7 × 10<sup>-</sup><sup>4</sup> T, clockwise -What is the magnitude and direction of the magnetic field at point B?


A) 3.3 × 10-5 T, clockwise
B) 3.3 × 10-5 T, counterclockwise
C) 6.8 × 10-5 T, clockwise
D) 6.8 × 10-5 T, counterclockwise
E) 2.7 × 10-4 T, clockwise

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

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A long, straight wire is carrying a current of 5.0 A in the direction shown in the figure. The point P is 0.040 m from the wire. A long, straight wire is carrying a current of 5.0 A in the direction shown in the figure. The point P is 0.040 m from the wire.   -What is the direction of the magnetic field at point P due to the current in the wire? A) to the right of page B) to the left of the page C) toward the bottom of the page D) into the plane of the page E) out of the plane of the page -What is the direction of the magnetic field at point P due to the current in the wire?


A) to the right of page
B) to the left of the page
C) toward the bottom of the page
D) into the plane of the page
E) out of the plane of the page

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

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Two long, straight wires separated by 0.10 m carry currents of 18 A and 6 A in the same direction as shown. Two long, straight wires separated by 0.10 m carry currents of 18 A and 6 A in the same direction as shown.   -What is the direction of the magnetic field at the point P? A) to the left of the page B) to the right of the page C) toward the bottom of the page D) out of the plane of the page E) into the plane of the page -What is the direction of the magnetic field at the point P?


A) to the left of the page
B) to the right of the page
C) toward the bottom of the page
D) out of the plane of the page
E) into the plane of the page

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

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