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A rectangular loop of wire carrying a 4.0-A current is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire when the plane of the loop makes a 30° angle with the field is measured to be 1.1 N ∙ m. What is the area of this loop?


A) 0.20 m2
B) 0.40 m2
C) 0.26 m2
D) 0.80 m2
E) 0.53 m2

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

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A vertical wire carries a current vertically upward in a region where the magnetic field vector points toward the north. What is the direction of the magnetic force on this current due to the field?


A) downward
B) toward the north
C) toward the south
D) toward the east
E) toward the west

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

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A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T . The normal to the loop is parallel to a unit vector = -0.60 - 0.80 . Calculate the magnitude of the torque on the loop due to the magnetic field. A) 4.7 × 10<sup>-4</sup> N ∙ m B) 2.8 × 10<sup>-4</sup> N ∙ m C) 0.60 × 10<sup>-4</sup> N ∙ m D) 1.2 × 10<sup>-4</sup> N ∙ m E) zero = 0.30 T A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T . The normal to the loop is parallel to a unit vector = -0.60 - 0.80 . Calculate the magnitude of the torque on the loop due to the magnetic field. A) 4.7 × 10<sup>-4</sup> N ∙ m B) 2.8 × 10<sup>-4</sup> N ∙ m C) 0.60 × 10<sup>-4</sup> N ∙ m D) 1.2 × 10<sup>-4</sup> N ∙ m E) zero . The normal to the loop is parallel to a unit vector A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T . The normal to the loop is parallel to a unit vector = -0.60 - 0.80 . Calculate the magnitude of the torque on the loop due to the magnetic field. A) 4.7 × 10<sup>-4</sup> N ∙ m B) 2.8 × 10<sup>-4</sup> N ∙ m C) 0.60 × 10<sup>-4</sup> N ∙ m D) 1.2 × 10<sup>-4</sup> N ∙ m E) zero = -0.60 A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T . The normal to the loop is parallel to a unit vector = -0.60 - 0.80 . Calculate the magnitude of the torque on the loop due to the magnetic field. A) 4.7 × 10<sup>-4</sup> N ∙ m B) 2.8 × 10<sup>-4</sup> N ∙ m C) 0.60 × 10<sup>-4</sup> N ∙ m D) 1.2 × 10<sup>-4</sup> N ∙ m E) zero - 0.80 A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T . The normal to the loop is parallel to a unit vector = -0.60 - 0.80 . Calculate the magnitude of the torque on the loop due to the magnetic field. A) 4.7 × 10<sup>-4</sup> N ∙ m B) 2.8 × 10<sup>-4</sup> N ∙ m C) 0.60 × 10<sup>-4</sup> N ∙ m D) 1.2 × 10<sup>-4</sup> N ∙ m E) zero . Calculate the magnitude of the torque on the loop due to the magnetic field.


A) 4.7 × 10-4 N ∙ m
B) 2.8 × 10-4 N ∙ m
C) 0.60 × 10-4 N ∙ m
D) 1.2 × 10-4 N ∙ m
E) zero

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

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Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure. The +z direction points perpendicular to the xy-plane in a right-handed coordinate system. If both currents flow in the +y direction, which one of the graphs shown in the figure below best represents the z component of the net magnetic field, in the xy-plane, as a function of x? (Caution: These graphs are not magnetic field lines.) Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure. The +z direction points perpendicular to the xy-plane in a right-handed coordinate system. If both currents flow in the +y direction, which one of the graphs shown in the figure below best represents the z component of the net magnetic field, in the xy-plane, as a function of x? (Caution: These graphs are not magnetic field lines.) A) 1 B) 2 C) 3 D) 4 E) 5 Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure. The +z direction points perpendicular to the xy-plane in a right-handed coordinate system. If both currents flow in the +y direction, which one of the graphs shown in the figure below best represents the z component of the net magnetic field, in the xy-plane, as a function of x? (Caution: These graphs are not magnetic field lines.) A) 1 B) 2 C) 3 D) 4 E) 5


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

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

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A tube with a 3.0-mm radius has ions flowing through it along its length. To determine the rate at which the charge is being moved through the tube, the magnetic field just outside the tube is measured and found to be A tube with a 3.0-mm radius has ions flowing through it along its length. To determine the rate at which the charge is being moved through the tube, the magnetic field just outside the tube is measured and found to be If the only contributor to the magnetic field is the moving ions, and if the walls of the container are very thin and do not screen magnetism, what is the magnitude of the current flowing through the tube? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 66 A B) 132 A C) 829 A D) 415 A If the only contributor to the magnetic field is the moving ions, and if the walls of the container are very thin and do not screen magnetism, what is the magnitude of the current flowing through the tube? (μ0 = 4π × 10-7 T ∙ m/A)


A) 66 A
B) 132 A
C) 829 A
D) 415 A

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

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A horizontal wire carries a current straight toward you. From your point of view, the magnetic field at a point directly below the wire points


A) directly away from you.
B) to the left.
C) to the right.
D) directly toward you.
E) vertically upward.

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

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Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ0 = 4π × 10-7 T ∙ m/A)


A) 1.5 µT
B) 3.3 µT
C) 6.7 µT
D) 33 µT
E) 67 µT

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

Correct Answer

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Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively, Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively, A) 1 is neutral, 2 is negative, and 3 is positive. B) 1 is neutral, 2 is positive, and 3 is negative. C) 1 is positive, 2 is neutral, and 3 is negative. D) 1 is positive, 2 is negative, and 3 is neutral. E) 1 is negative, 2 is neutral, and 3 is positive.


A) 1 is neutral, 2 is negative, and 3 is positive.
B) 1 is neutral, 2 is positive, and 3 is negative.
C) 1 is positive, 2 is neutral, and 3 is negative.
D) 1 is positive, 2 is negative, and 3 is neutral.
E) 1 is negative, 2 is neutral, and 3 is positive.

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

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A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward. The wires are parallel to each other and are 42 cm apart. Calculate the force on a 6.4 m length of one of the wires. (μ0 = 4π × 10-7 T ∙ m/A)


A) 8.0 × 10-7 N
B) 5.1 × 10-4 N
C) 8.0 × 10-5 N
D) 5.1 × 10-6 N
E) 2.2 × 10-4 N

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

Correct Answer

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The figure shows a velocity selector that can be used to measure the speed of a charged particle. A beam of particles is directed along the axis of the instrument. A parallel plate capacitor sets up an electric field E, which is oriented perpendicular to a uniform magnetic field B. If the plates are separated by 2.0 mm and the value of the magnetic field is 0.60 T, what voltage between the plates will allow particles of speed 5.0 × 105 m/s to pass straight through without deflection? The figure shows a velocity selector that can be used to measure the speed of a charged particle. A beam of particles is directed along the axis of the instrument. A parallel plate capacitor sets up an electric field E, which is oriented perpendicular to a uniform magnetic field B. If the plates are separated by 2.0 mm and the value of the magnetic field is 0.60 T, what voltage between the plates will allow particles of speed 5.0 × 10<sup>5</sup> m/s to pass straight through without deflection? A) 600 V B) 1900 V C) 3800 V D) 190 V E) 94 V


A) 600 V
B) 1900 V
C) 3800 V
D) 190 V
E) 94 V

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

Correct Answer

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A wire carrying a current is shaped in the form of a circular loop of radius A wire carrying a current is shaped in the form of a circular loop of radius If the magnetic field strength that this current produces at the center of the loop is what is the magnitude of the current that flows through the wire? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 5.3 A B) 16 A C) 9.1 A D) 23 A If the magnetic field strength that this current produces at the center of the loop is A wire carrying a current is shaped in the form of a circular loop of radius If the magnetic field strength that this current produces at the center of the loop is what is the magnitude of the current that flows through the wire? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 5.3 A B) 16 A C) 9.1 A D) 23 A what is the magnitude of the current that flows through the wire? (μ0 = 4π × 10-7 T ∙ m/A)


A) 5.3 A
B) 16 A
C) 9.1 A
D) 23 A

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

Correct Answer

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A point charge Q moves on the x-axis in the positive direction with a speed of A point charge Q moves on the x-axis in the positive direction with a speed of A point P is on the y-axis at The magnetic field produced at the point P, as the charge moves through the origin, is equal to What is the charge Q? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) -53 μC B) +53 μC C) -39 μC D) +39 μC E) +26 μC A point P is on the y-axis at A point charge Q moves on the x-axis in the positive direction with a speed of A point P is on the y-axis at The magnetic field produced at the point P, as the charge moves through the origin, is equal to What is the charge Q? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) -53 μC B) +53 μC C) -39 μC D) +39 μC E) +26 μC The magnetic field produced at the point P, as the charge moves through the origin, is equal to A point charge Q moves on the x-axis in the positive direction with a speed of A point P is on the y-axis at The magnetic field produced at the point P, as the charge moves through the origin, is equal to What is the charge Q? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) -53 μC B) +53 μC C) -39 μC D) +39 μC E) +26 μC What is the charge Q? (μ0 = 4π × 10-7 T ∙ m/A)


A) -53 μC
B) +53 μC
C) -39 μC
D) +39 μC
E) +26 μC

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

Correct Answer

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A very long thin wire produces a magnetic field of A very long thin wire produces a magnetic field of at a distance of from the central axis of the wire. What is the magnitude of the current in the wire? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 7.5 mA B) 1.7 mA C) 3300 mA D) 24,000 mA at a distance of A very long thin wire produces a magnetic field of at a distance of from the central axis of the wire. What is the magnitude of the current in the wire? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 7.5 mA B) 1.7 mA C) 3300 mA D) 24,000 mA from the central axis of the wire. What is the magnitude of the current in the wire? (μ0 = 4π × 10-7 T ∙ m/A)


A) 7.5 mA
B) 1.7 mA
C) 3300 mA
D) 24,000 mA

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

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A charged particle of mass 0.0020 kg is subjected to a A charged particle of mass 0.0020 kg is subjected to a magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius at a speed of what is the magnitude of the charge on the particle? A) 0.0083 C B) 120 C C) 0.00040 C D) 2500 C magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius A charged particle of mass 0.0020 kg is subjected to a magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius at a speed of what is the magnitude of the charge on the particle? A) 0.0083 C B) 120 C C) 0.00040 C D) 2500 C at a speed of A charged particle of mass 0.0020 kg is subjected to a magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius at a speed of what is the magnitude of the charge on the particle? A) 0.0083 C B) 120 C C) 0.00040 C D) 2500 C what is the magnitude of the charge on the particle?


A) 0.0083 C
B) 120 C
C) 0.00040 C
D) 2500 C

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

Correct Answer

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A beam of electrons is accelerated through a potential difference of 10 kV before entering a region having uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the direction in which the electron is moving. If the magnetic field in this region has a value of 0.010 T, what magnitude of the electric field is required if the particles are to be undeflected as they pass through the region?


A) 2.3 × 103 V/m
B) 7.9 × 103 V/m
C) 5.9 × 105 V/m
D) 6.0 × 105 V/m
E) 7.2 × 106 V/m

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

Correct Answer

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Two long parallel wires placed side-by-side on a horizontal table carry identical size currents in opposite directions. The wire on your right carries current toward you, and the wire on your left carries current away from you. From your point of view, the magnetic field at the point exactly midway between the two wires


A) points upward.
B) points downward.
C) points toward you.
D) points away from you.
E) is zero.

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

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A ring with a clockwise current (as seen from above the ring) is situated with its center directly above another ring, which has a counter-clockwise current, as shown in the figure. In what direction is the net magnetic force exerted on the top ring? A ring with a clockwise current (as seen from above the ring) is situated with its center directly above another ring, which has a counter-clockwise current, as shown in the figure. In what direction is the net magnetic force exerted on the top ring? A) upward B) downward C) to the right D) to the left E) The net force is zero.


A) upward
B) downward
C) to the right
D) to the left
E) The net force is zero.

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

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A type of transmission line for electromagnetic waves consists of two parallel conducting plates (assumed infinite in width) separated by a distance a. Each plate carries the same uniform surface current density of 16.0 A/m, but the currents run in opposite directions. What is the magnitude of the magnetic field between the plates at a point 1.00 mm from one of the plates if a = 0.800 cm? (μ0 = 4π × 10-7 T ∙ m/A)


A) 3.20 × 10-3 T
B) 1.00 × 10-5 T
C) 4.63 × 10-5 T
D) 2.01 × 10-5 T
E) 7.07 × 10-4 T

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

Correct Answer

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A charged particle is moving with speed v perpendicular to a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field. If the frequency of revolution of the first particle is f, the frequency of revolution of the second particle is


A) f.
B) 2f.
C) 4f.
D) f/2.
E) f/4.

F) All of the above
G) None of the above

Correct Answer

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An electron moves with a speed of 8.0 × 106 m/s along the +x-axis. It enters a region where there is a magnetic field of 2.5 T, directed at an angle of 60° to the +x-axis and lying in the xy-plane. (1 eV = 1.60 × 10-19 C, mel = 9.11 × 10-31 kg) Calculate the magnitude of (a) the magnetic force on the electron. (b) the acceleration of the electron.

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(a) 2.8 × ...

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