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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.

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

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

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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

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

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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) B) and E)
G) B) and C)

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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

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

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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 point P,as the charge moves through the origin,is equal to When the charge is at what is the magnitude of the magnetic field at point P? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.57 μT B) 0.74 μT C) 0.92 μT D) 1.1 μT E) 1.3 μT 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 point P,as the charge moves through the origin,is equal to When the charge is at what is the magnitude of the magnetic field at point P? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.57 μT B) 0.74 μT C) 0.92 μT D) 1.1 μT E) 1.3 μT The magnetic field produced at 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 point P,as the charge moves through the origin,is equal to When the charge is at what is the magnitude of the magnetic field at point P? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.57 μT B) 0.74 μT C) 0.92 μT D) 1.1 μT E) 1.3 μT When the charge is 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 point P,as the charge moves through the origin,is equal to When the charge is at what is the magnitude of the magnetic field at point P? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.57 μT B) 0.74 μT C) 0.92 μT D) 1.1 μT E) 1.3 μT what is the magnitude of the magnetic field at point P? (μ0 = 4π × 10-7 T ∙ m/A)


A) 0.57 μT
B) 0.74 μT
C) 0.92 μT
D) 1.1 μT
E) 1.3 μT

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

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A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N


A) (+1.1 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N - 1.8 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N ) N
B) (-1.1 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N + 1.8 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N ) N
C) (-1.1 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N - 1.8 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N ) N
D) (+1.8 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N - 1.1 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N ) N
E) (-1.8 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N + 1.1 A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment? A) (+1.1 - 1.8 ) N B) (-1.1 + 1.8 ) N C) (-1.1 - 1.8 ) N D) (+1.8 - 1.1 ) N E) (-1.8 + 1.1 ) N ) N

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

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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

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

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A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long.If this solenoid carries a current of A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long.If this solenoid carries a current of what is the magnitude of the magnetic field near the center of the solenoid? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 16 mT B) 4.9 mT C) 15 mT D) 6.0 mT E) 9.0 mT what is the magnitude of the magnetic field near the center of the solenoid? (μ0 = 4π × 10-7 T ∙ m/A)


A) 16 mT
B) 4.9 mT
C) 15 mT
D) 6.0 mT
E) 9.0 mT

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

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The figure shows two long wires carrying equal currents I1 and I2 flowing in opposite directions.Which of the arrows labeled A through D correctly represents the direction of the magnetic field due to the wires at a point located at an equal distance d from each wire? The figure shows two long wires carrying equal currents I<sub>1</sub> and I<sub>2</sub> flowing in opposite directions.Which of the arrows labeled A through D correctly represents the direction of the magnetic field due to the wires at a point located at an equal distance d from each wire? A) A B) B C) C D) D E) The magnetic field is zero at that point.


A) A
B) B
C) C
D) D
E) The magnetic field is zero at that point.

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

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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.

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

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The figure shows the cross-section of a hollow cylinder of inner radius a = 5.0 cm and outer radius b = 7.0 cm.A uniform current density of 1.0 A/ cm2 flows through the cylinder parallel to its axis.Calculate the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder.(μ0 = 4π × 10-7 T ∙ m/A) The figure shows the cross-section of a hollow cylinder of inner radius a = 5.0 cm and outer radius b = 7.0 cm.A uniform current density of 1.0 A/ cm<sup>2</sup> flows through the cylinder parallel to its axis.Calculate the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder.(μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 0.00 T B) 1.5 × 10<sup>-4</sup> T C) 2.5 × 10<sup>-4</sup> T D) 4.5 × 10<sup>-4</sup> T E) 0.50 × 10<sup>-4</sup> T


A) 0.00 T
B) 1.5 × 10-4 T
C) 2.5 × 10-4 T
D) 4.5 × 10-4 T
E) 0.50 × 10-4 T

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

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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 the left current flows in the +y direction and the right current flows 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 the left current flows in the +y direction and the right current flows 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 the left current flows in the +y direction and the right current flows 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) C) and D)
G) B) and D)

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A 15-turn rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it.Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T,and the other two sides are perpendicular to the magnetic field. (a)What is the magnitude of the magnetic moment of the loop? (b)What torque does the magnetic field exert on the loop?

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(a)0.75 A ...

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A very long,solid,conducting cylinder of radius R carries a current along its length uniformly distributed throughout the cylinder.Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis? A very long,solid,conducting cylinder of radius R carries a current along its length uniformly distributed throughout the cylinder.Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis? A) 1 B) 2 C) 3 D) 4 E) 5


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

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

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The figure shows three long,parallel current-carrying wires.The magnitudes of the currents are equal and their directions are indicated in the figure.Which of the arrows drawn near the wire carrying current 1 correctly indicates the direction of the magnetic force acting on that wire? The figure shows three long,parallel current-carrying wires.The magnitudes of the currents are equal and their directions are indicated in the figure.Which of the arrows drawn near the wire carrying current 1 correctly indicates the direction of the magnetic force acting on that wire? A) A B) B C) C D) D E) The magnetic force on current 1 is equal to zero.


A) A
B) B
C) C
D) D
E) The magnetic force on current 1 is equal to zero.

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

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An alpha particle is moving at a speed of 5.0 × 105 m/s in a direction perpendicular to a uniform magnetic field of strength 0.040 T.The charge on an alpha particle is 3.2 × 10-19 C and its mass is 6.6 × 10-27 kg. (a)What is the radius of the path of the alpha particle? (b)How long does it take the alpha particle to make one complete revolution around its path?

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A straight wire that is 0.60 m long is carrying a current of 2.0 A.It is placed in a uniform magnetic field of strength 0.30 T.If the wire experiences a force of 0.18 N,what angle does the wire make with respect to the magnetic field?


A) 25°
B) 30°
C) 35°
D) 60°
E) 90°

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

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As shown in the figure,a wire is bent into the shape of a tightly closed omega (Ω) ,with a circular loop of radius 4.0 cm and two long straight sections.The loop is in the xy-plane,with the center at the origin.The straight sections are parallel to the x-axis.The wire carries a 5.0-A current,as shown.What is the magnitude of the magnetic field at the center of the loop? (μ0 = 4π × 10-7 T ∙ m/A) As shown in the figure,a wire is bent into the shape of a tightly closed omega (Ω) ,with a circular loop of radius 4.0 cm and two long straight sections.The loop is in the xy-plane,with the center at the origin.The straight sections are parallel to the x-axis.The wire carries a 5.0-A current,as shown.What is the magnitude of the magnetic field at the center of the loop? (μ<sub>0</sub> = 4π × 10<sup>-7</sup> T ∙ m/A) A) 25 µT B) 40 µT C) 54 µT D) 80 µT E) 104 µT


A) 25 µT
B) 40 µT
C) 54 µT
D) 80 µT
E) 104 µT

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

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Two very long parallel wires are a distance d apart and carry equal currents in opposite directions.The locations where the net magnetic field due to these currents is equal to zero are


A) midway between the wires.
B) a distance d/2 to the left of the left wire and also a distance d/2 to the right of the right wire.
C) a distance d to the left of the left wire and also a distance d to the right of the right wire.
D) a distance d/ Two very long parallel wires are a distance d apart and carry equal currents in opposite directions.The locations where the net magnetic field due to these currents is equal to zero are A) midway between the wires. B) a distance d/2 to the left of the left wire and also a distance d/2 to the right of the right wire. C) a distance d to the left of the left wire and also a distance d to the right of the right wire. D) a distance d/ to the left of the left wire and also a distance d/ to the right of the right wire. E) The net field is not zero anywhere. to the left of the left wire and also a distance d/ Two very long parallel wires are a distance d apart and carry equal currents in opposite directions.The locations where the net magnetic field due to these currents is equal to zero are A) midway between the wires. B) a distance d/2 to the left of the left wire and also a distance d/2 to the right of the right wire. C) a distance d to the left of the left wire and also a distance d to the right of the right wire. D) a distance d/ to the left of the left wire and also a distance d/ to the right of the right wire. E) The net field is not zero anywhere. to the right of the right wire.
E) The net field is not zero anywhere.

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

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