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Consider a solenoid of length L, N windings, and radius b (L is much longer than b) . A current I is flowing through the wire. If the radius of the solenoid were doubled (becoming 2b) , and all other quantities remained the same, the magnetic field inside the solenoid would


A) remain the same.
B) become twice as strong.
C) become one half as strong.

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Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?


A) 4R
B) 3R
C) Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter? A) 4R B) 3R C) R D) R/ E) R/2 R
D) R/ Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter? A) 4R B) 3R C) R D) R/ E) R/2
E) R/2

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A long straight conductor has a constant current flowing to the right. A wire rectangle is situated above the wire, and also has a constant current flowing through it (as shown in the figure) . Which of the following statements is true? A long straight conductor has a constant current flowing to the right. A wire rectangle is situated above the wire, and also has a constant current flowing through it (as shown in the figure) . Which of the following statements is true? A) The net magnetic force on the wire rectangle is upward, and there is also a net torque on the it. B) The net magnetic force on the wire rectangle is zero, and the net torque on it is zero. C) The net magnetic force on the wire rectangle is downward, and there is also a net torque on the it. D) The net magnetic force on the wire rectangle is zero, but there is a net torque on it. E) The net magnetic force on the wire rectangle is downward, and the net torque on it is zero.


A) The net magnetic force on the wire rectangle is upward, and there is also a net torque on the it.
B) The net magnetic force on the wire rectangle is zero, and the net torque on it is zero.
C) The net magnetic force on the wire rectangle is downward, and there is also a net torque on the it.
D) The net magnetic force on the wire rectangle is zero, but there is a net torque on it.
E) The net magnetic force on the wire rectangle is downward, and the net torque on it is zero.

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Three very long, straight, parallel wires each carry currents of 4.00 A, directed out of the page as shown in the figure. The wires pass through the vertices of a right isosceles triangle of side 2.00 cm. What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle? Three very long, straight, parallel wires each carry currents of 4.00 A, directed out of the page as shown in the figure. The wires pass through the vertices of a right isosceles triangle of side 2.00 cm. What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle? A) 4.42 × 10<sup>-6</sup> T B) 1.77 × 10<sup>-5</sup> T C) 5.66 × 10<sup>-5</sup> T D) 1.26 × 10<sup>-4</sup> T E) 1.77 × 10<sup>-6</sup> T


A) 4.42 × 10-6 T
B) 1.77 × 10-5 T
C) 5.66 × 10-5 T
D) 1.26 × 10-4 T
E) 1.77 × 10-6 T

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A solenoid having N turns and carrying a current of 2.000 A has a length of 34.00 cm. If the magnitude of the magnetic field generated at the center of the solenoid is 9.000 mT, what is the value of N? (μ0 = 4π × 10-7 T ∙ m/A)


A) 860.0
B) 1591
C) 2318
D) 3183
E) 1218

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Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ0 = 4π × 10-7 T ∙ m/A) Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.90 × T B) 3.9 × T C) 1.9 × T D) 6.3 × T E) 9.2 × T


A) 0.90 × Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.90 × T B) 3.9 × T C) 1.9 × T D) 6.3 × T E) 9.2 × T T
B) 3.9 × Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.90 × T B) 3.9 × T C) 1.9 × T D) 6.3 × T E) 9.2 × T T
C) 1.9 × Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.90 × T B) 3.9 × T C) 1.9 × T D) 6.3 × T E) 9.2 × T T
D) 6.3 × Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.90 × T B) 3.9 × T C) 1.9 × T D) 6.3 × T E) 9.2 × T T
E) 9.2 × Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.90 × T B) 3.9 × T C) 1.9 × T D) 6.3 × T E) 9.2 × T T

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An electron, moving toward the west, enters a uniform magnetic field. Because of this field the electron curves upward. The direction of the magnetic field is


A) towards the north.
B) towards the south.
C) towards the west.
D) upward.
E) downward.

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A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the accelerating potential is tripled to 3V, what will be the radius of the circular arc?


A) 9R
B) 3R
C) A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the accelerating potential is tripled to 3V, what will be the radius of the circular arc? A) 9R B) 3R C) R D) R/ E) R/9 R
D) R/ A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the accelerating potential is tripled to 3V, what will be the radius of the circular arc? A) 9R B) 3R C) R D) R/ E) R/9
E) R/9

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A particle with charge -5.00 C initially moves at A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N = (1.00 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N + 7.00 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N ) m/s. If it encounters a magnetic field A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N find the magnetic force vector on the particle.


A) (-350 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N + 50.0 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N ) N
B) (-350 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N - 50.0 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N ) N
C) (350 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N + 50.0 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N ) N
D) (350 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N - 50.0 A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle. A) (-350 + 50.0 ) N B) (-350 - 50.0 ) N C) (350 + 50.0 ) N D) (350 - 50.0 ) N ) N

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A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ0 = 4π × 10-7 T ∙ m/A)


A) 6.6 × A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 6.6 × T B) 2.5 × T C) 1.3 × T D) 3.6 × T E) 9.8 × T T
B) 2.5 × A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 6.6 × T B) 2.5 × T C) 1.3 × T D) 3.6 × T E) 9.8 × T T
C) 1.3 × A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 6.6 × T B) 2.5 × T C) 1.3 × T D) 3.6 × T E) 9.8 × T T
D) 3.6 × A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 6.6 × T B) 2.5 × T C) 1.3 × T D) 3.6 × T E) 9.8 × T T
E) 9.8 × A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 6.6 × T B) 2.5 × T C) 1.3 × T D) 3.6 × T E) 9.8 × T T

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The figure shows three long, parallel, current-carrying wires. The current directions are indicated for currents I1 and I3. The arrow labeled F represents the net magnetic force acting on current I3. The three currents have equal magnitudes. What is the direction of the current I2? The figure shows three long, parallel, current-carrying wires. The current directions are indicated for currents I<sub>1</sub> and I<sub>3</sub>. The arrow labeled F represents the net magnetic force acting on current I<sub>3</sub>. The three currents have equal magnitudes. What is the direction of the current I<sub>2</sub>? A) into the picture (in the direction opposite to that of I<sub>1</sub> and I<sub>3</sub>) B) horizontal to the right C) vertically upward D) vertically downward E) out of the picture (in the same direction as I<sub>1</sub> and I<sub>3</sub>)


A) into the picture (in the direction opposite to that of I1 and I3)
B) horizontal to the right
C) vertically upward
D) vertically downward
E) out of the picture (in the same direction as I1 and I3)

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A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 A. It is placed in a magnetic field of A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 A. It is placed in a magnetic field of with the plane of the coil making an angle of 30° with the magnetic field. What is the magnetic torque on the coil? A) 0.15 N ∙ m B) 0.088 N ∙ m C) 0.29 N ∙ m D) 0.40 N ∙ m E) 0.076 N ∙ m with the plane of the coil making an angle of 30° with the magnetic field. What is the magnetic torque on the coil?


A) 0.15 N ∙ m
B) 0.088 N ∙ m
C) 0.29 N ∙ m
D) 0.40 N ∙ m
E) 0.076 N ∙ m

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A coaxial cable consists of an inner cylindrical conductor of radius R1 = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R2 = 0.080 m and outer radius A coaxial cable consists of an inner cylindrical conductor of radius R<sub>1</sub> = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R<sub>2</sub> = 0.080 m and outer radius The inner conductor carries current in one direction, and the outer conductor carries current in the opposite direction. What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) (a) At r = 0.060 m (in the gap midway between the two conductors) (b) At r = 0.150 m (outside the cable) The inner conductor carries current A coaxial cable consists of an inner cylindrical conductor of radius R<sub>1</sub> = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R<sub>2</sub> = 0.080 m and outer radius The inner conductor carries current in one direction, and the outer conductor carries current in the opposite direction. What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) (a) At r = 0.060 m (in the gap midway between the two conductors) (b) At r = 0.150 m (outside the cable) in one direction, and the outer conductor carries current A coaxial cable consists of an inner cylindrical conductor of radius R<sub>1</sub> = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R<sub>2</sub> = 0.080 m and outer radius The inner conductor carries current in one direction, and the outer conductor carries current in the opposite direction. What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) (a) At r = 0.060 m (in the gap midway between the two conductors) (b) At r = 0.150 m (outside the cable) in the opposite direction. What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ0 = 4π × 10-7 T ∙ m/A) (a) At r = 0.060 m (in the gap midway between the two conductors) (b) At r = 0.150 m (outside the cable)

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A wire along the z-axis carries a current of 6.8 A in the +z direction. Find the magnitude and direction of the force exerted on a 6.1-cm long length of the wire by a uniform magnetic field with magnitude 0.36 T in the -x direction.

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0.15 N, -y...

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A long straight wire on the z-axis carries a current of 6.0 A in the positive direction. A circular loop in the xy-plane, of radius 10 cm, carries a 1.0-A current, as shown in the figure. Point P, at the center of the loop, is 25 cm from the z-axis. An electron is projected from P with a velocity of 1.0 × 106 m/s in the negative x-direction. What is the y component of the force on the electron? (e = 1.60 × 10-19 C, μ0 = 4π × 10-7 T ∙ m/A) A long straight wire on the z-axis carries a current of 6.0 A in the positive direction. A circular loop in the xy-plane, of radius 10 cm, carries a 1.0-A current, as shown in the figure. Point P, at the center of the loop, is 25 cm from the z-axis. An electron is projected from P with a velocity of 1.0 × 10<sup>6</sup> m/s in the negative x-direction. What is the y component of the force on the electron? (e = 1.60 × 10<sup>-19</sup> C, μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) -1.0 × 10<sup>-18</sup> N B) +1.0 × 10<sup>-18</sup> N C) -2.0 × 10<sup>-18</sup> N D) +2.0 × 10<sup>-18</sup> N E) zero


A) -1.0 × 10-18 N
B) +1.0 × 10-18 N
C) -2.0 × 10-18 N
D) +2.0 × 10-18 N
E) zero

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As shown in the figure, an insulated wire is bent into a circular loop of radius 6.0 cm and has two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the z-axis. The wire carries a current of 8.0 A. What is the magnitude of the magnetic field at the origin? (μ0 = 4π × 10-7 T ∙ m/A) As shown in the figure, an insulated wire is bent into a circular loop of radius 6.0 cm and has two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the z-axis. The wire carries a current of 8.0 A. What is the magnitude of the magnetic field at the origin? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 75 µT B) 81 µT C) 88 µT D) 110 µT E) 120 µT


A) 75 µT
B) 81 µT
C) 88 µT
D) 110 µT
E) 120 µT

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An electron enters a magnetic field of An electron enters a magnetic field of with a velocity perpendicular to the direction of the field. At what frequency does the electron traverse a circular path? (m<sub>el</sub> = 9.11 × 10<sup>-31</sup> kg, e = 1.60 × 10<sup>-19</sup> C) A) 2.1 × 10<sup>10</sup> Hz B) 4.8 × 10<sup>-7</sup> Hz C) 2.1 × 10<sup>14</sup> Hz D) 4.8 × 10<sup>-11</sup> Hz with a velocity perpendicular to the direction of the field. At what frequency does the electron traverse a circular path? (mel = 9.11 × 10-31 kg, e = 1.60 × 10-19 C)


A) 2.1 × 1010 Hz
B) 4.8 × 10-7 Hz
C) 2.1 × 1014 Hz
D) 4.8 × 10-11 Hz

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A wire carries a 4.0-A current along the +x-axis through a magnetic field A wire carries a 4.0-A current along the +x-axis through a magnetic field = (5.0 + 7.0 ) T. If the wire experiences a force of 30 N as a result, how long is the wire? A) 1.1 m B) 0.87 m C) 1.5 m D) 0.63 m = (5.0 A wire carries a 4.0-A current along the +x-axis through a magnetic field = (5.0 + 7.0 ) T. If the wire experiences a force of 30 N as a result, how long is the wire? A) 1.1 m B) 0.87 m C) 1.5 m D) 0.63 m + 7.0 A wire carries a 4.0-A current along the +x-axis through a magnetic field = (5.0 + 7.0 ) T. If the wire experiences a force of 30 N as a result, how long is the wire? A) 1.1 m B) 0.87 m C) 1.5 m D) 0.63 m ) T. If the wire experiences a force of 30 N A wire carries a 4.0-A current along the +x-axis through a magnetic field = (5.0 + 7.0 ) T. If the wire experiences a force of 30 N as a result, how long is the wire? A) 1.1 m B) 0.87 m C) 1.5 m D) 0.63 m as a result, how long is the wire?


A) 1.1 m
B) 0.87 m
C) 1.5 m
D) 0.63 m

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A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 5.5 A, as shown in the figure. A uniform external magnetic field of magnitude 2.9 T in the negative x direction is present. Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. Find the magnitude of the external torque needed to keep the loop in static equilibrium. A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 5.5 A, as shown in the figure. A uniform external magnetic field of magnitude 2.9 T in the negative x direction is present. Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. Find the magnitude of the external torque needed to keep the loop in static equilibrium. A) 1.1 N ∙ m B) 0.73 N ∙ m C) 1.3 N ∙ m D) 1.4 N ∙ m E) 1.6 N ∙ m


A) 1.1 N ∙ m
B) 0.73 N ∙ m
C) 1.3 N ∙ m
D) 1.4 N ∙ m
E) 1.6 N ∙ m

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The figure shows four different sets of insulated wires that cross each other at right angles without actually making electrical contact. The magnitude of the current is the same in all the wires, and the directions of current flow are as indicated. For which (if any) configuration will the magnetic field at the center of the square formed by the wires be equal to zero? The figure shows four different sets of insulated wires that cross each other at right angles without actually making electrical contact. The magnitude of the current is the same in all the wires, and the directions of current flow are as indicated. For which (if any) configuration will the magnetic field at the center of the square formed by the wires be equal to zero? A) A B) B C) C D) D E) The field is not equal to zero in any of these cases.


A) A
B) B
C) C
D) D
E) The field is not equal to zero in any of these cases.

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