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If the electric potential in a region is given by V(x) = 6/x2,the x component of the electric field in that region is


A) -12x-3.
B) -6x.
C) 12x-3.
D) 12x.
E) 6x.

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

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A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity) .Which of the following plots correctly shows the potential as a function of distance from the center of the sphere? A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity) .Which of the following plots correctly shows the potential as a function of distance from the center of the sphere? A) plot W B) plot X C) plot Y D) plot Z A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity) .Which of the following plots correctly shows the potential as a function of distance from the center of the sphere? A) plot W B) plot X C) plot Y D) plot Z A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity) .Which of the following plots correctly shows the potential as a function of distance from the center of the sphere? A) plot W B) plot X C) plot Y D) plot Z A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity) .Which of the following plots correctly shows the potential as a function of distance from the center of the sphere? A) plot W B) plot X C) plot Y D) plot Z


A) plot W
B) plot X
C) plot Y
D) plot Z

E) B) and C)
F) None of the above

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Suppose you have two point charges of opposite sign.As you move them farther and farther apart,the potential energy of this system relative to infinity


A) increases.
B) decreases.
C) stays the same.

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

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In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y) = 2xy - x2 - y,where x and y are measured in meters and V is in volts.At which point is the electric field equal to zero?


A) x = 0.5 m, y = 1 m
B) x = 1 m, y = 1 m
C) x = 1 m, y = 0.5 m
D) x = 0.5 m, y = 0.5 m
E) x = 0 m, y = 0 m

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

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If an electron is accelerated from rest through a potential difference of 9.9 kV,what is its resulting speed? If an electron is accelerated from rest through a potential difference of 9.9 kV,what is its resulting speed? , = ,<sup> </sup> <sup> </sup> A) 5.9 × 10<sup>7</sup> m/s B) 4.9 × 10<sup>7</sup> m/s C) 3.9 × 10<sup>7</sup> m/s D) 2.9 × 10<sup>7</sup> m/s , If an electron is accelerated from rest through a potential difference of 9.9 kV,what is its resulting speed? , = ,<sup> </sup> <sup> </sup> A) 5.9 × 10<sup>7</sup> m/s B) 4.9 × 10<sup>7</sup> m/s C) 3.9 × 10<sup>7</sup> m/s D) 2.9 × 10<sup>7</sup> m/s = If an electron is accelerated from rest through a potential difference of 9.9 kV,what is its resulting speed? , = ,<sup> </sup> <sup> </sup> A) 5.9 × 10<sup>7</sup> m/s B) 4.9 × 10<sup>7</sup> m/s C) 3.9 × 10<sup>7</sup> m/s D) 2.9 × 10<sup>7</sup> m/s , If an electron is accelerated from rest through a potential difference of 9.9 kV,what is its resulting speed? , = ,<sup> </sup> <sup> </sup> A) 5.9 × 10<sup>7</sup> m/s B) 4.9 × 10<sup>7</sup> m/s C) 3.9 × 10<sup>7</sup> m/s D) 2.9 × 10<sup>7</sup> m/s


A) 5.9 × 107 m/s
B) 4.9 × 107 m/s
C) 3.9 × 107 m/s
D) 2.9 × 107 m/s

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

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A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity) .If the sphere's radius were twice as large,but the charge on the sphere were the same,what would be the potential on the surface relative to infinity?


A) 50 V
B) 25 V
C) 100 V
D) 200 V

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

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A

Four equal +6.00-μC point charges are placed at the corners of a square 2.00 m on each side. Four equal +6.00-μC point charges are placed at the corners of a square 2.00 m on each side. (a)What is the electric potential (relative to infinity)due to these charges at the center of this square? (b)What is the magnitude of the electric field due to these charges at the center of the square? (a)What is the electric potential (relative to infinity)due to these charges at the center of this square? (b)What is the magnitude of the electric field due to these charges at the center of the square?

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A very small object carrying -6.0 μC of charge is attracted to a large,well-anchored,positively charged object.How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is 3.0 mV? A very small object carrying -6.0 μC of charge is attracted to a large,well-anchored,positively charged object.How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is 3.0 mV? A) 18 nJ B) 0.50 kJ C) 0.50 J D) 6.0 μJ


A) 18 nJ
B) 0.50 kJ
C) 0.50 J
D) 6.0 μJ

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

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Three point charges of -2.00 μC,+4.00 μC,and +6.00 μC are placed along the x-axis as shown in the figure.What is the electrical potential at point P (relative to infinity) due to these charges? (k = 1/4πε0 = 8.99 × 109 N • m2/C2) Three point charges of -2.00 μC,+4.00 μC,and +6.00 μC are placed along the x-axis as shown in the figure.What is the electrical potential at point P (relative to infinity) due to these charges? (k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N • m<sup>2</sup>/C<sup>2</sup>) A) -307 kV B) +307 kV C) -154 kV D) +154 kV E) 0 kV


A) -307 kV
B) +307 kV
C) -154 kV
D) +154 kV
E) 0 kV

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

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B

Suppose a region of space has a uniform electric field,directed towards the right,as shown in the figure.Which statement about the electric potential is true? Suppose a region of space has a uniform electric field,directed towards the right,as shown in the figure.Which statement about the electric potential is true? A) The potential at all three locations (A, B,C) is the same because the field is uniform. B) The potential at points A and B are equal, and the potential at point C is higher than the potential at point A. C) The potential at points A and B are equal, and the potential at point C is lower than the potential at point A. D) The potential at point A is the highest, the potential at point B is the second highest, and the potential at point C is the lowest.


A) The potential at all three locations (A, B,C) is the same because the field is uniform.
B) The potential at points A and B are equal, and the potential at point C is higher than the potential at point A.
C) The potential at points A and B are equal, and the potential at point C is lower than the potential at point A.
D) The potential at point A is the highest, the potential at point B is the second highest, and the potential at point C is the lowest.

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

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A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure.What is the potential difference,VA - VB,between points A and B? A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure.What is the potential difference,V<sub>A</sub> - V<sub>B</sub>,between points A and B? A) 48 V B) 96 V C) 0.00 V D) 96 kV E) 48 kV A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure.What is the potential difference,V<sub>A</sub> - V<sub>B</sub>,between points A and B? A) 48 V B) 96 V C) 0.00 V D) 96 kV E) 48 kV


A) 48 V
B) 96 V
C) 0.00 V
D) 96 kV
E) 48 kV

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

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D

The graph in the figure shows the variation of the electric potential V(x) (in arbitrary units) as a function of the position x (also in arbitrary units) .Which of the choices below correctly describes the orientation of the x-component of the electric field along the x-axis? The graph in the figure shows the variation of the electric potential V(x) (in arbitrary units) as a function of the position x (also in arbitrary units) .Which of the choices below correctly describes the orientation of the x-component of the electric field along the x-axis? A) E<sub>x</sub> is positive from x = -2 to x = 2. B) E<sub>x</sub> is positive from x = -2 to x = 0, and negative from x = 0 to x = 2. C) E<sub>x</sub> is negative from x = -2 to x = 0, and positive from x = 0 to x = 2. D) E<sub>x</sub> is negative from x = -2 to x = 2.


A) Ex is positive from x = -2 to x = 2.
B) Ex is positive from x = -2 to x = 0, and negative from x = 0 to x = 2.
C) Ex is negative from x = -2 to x = 0, and positive from x = 0 to x = 2.
D) Ex is negative from x = -2 to x = 2.

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

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Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of ,in the positive x-direction,is produced by charges on the plates.The center plane at m is an equipotential surface on which .An electron is projected from ,with an initial velocity of perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? , A) +2.4 × 10<sup>-16</sup> J B) +3.3 × 10<sup>-16</sup> J C) -2.4 × 10<sup>-16</sup> J D) -2.9 × 10<sup>-16</sup> J E) -3.3 × 10<sup>-16</sup> J ,in the positive x-direction,is produced by charges on the plates.The center plane at Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of ,in the positive x-direction,is produced by charges on the plates.The center plane at m is an equipotential surface on which .An electron is projected from ,with an initial velocity of perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? , A) +2.4 × 10<sup>-16</sup> J B) +3.3 × 10<sup>-16</sup> J C) -2.4 × 10<sup>-16</sup> J D) -2.9 × 10<sup>-16</sup> J E) -3.3 × 10<sup>-16</sup> J m is an equipotential surface on which Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of ,in the positive x-direction,is produced by charges on the plates.The center plane at m is an equipotential surface on which .An electron is projected from ,with an initial velocity of perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? , A) +2.4 × 10<sup>-16</sup> J B) +3.3 × 10<sup>-16</sup> J C) -2.4 × 10<sup>-16</sup> J D) -2.9 × 10<sup>-16</sup> J E) -3.3 × 10<sup>-16</sup> J .An electron is projected from Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of ,in the positive x-direction,is produced by charges on the plates.The center plane at m is an equipotential surface on which .An electron is projected from ,with an initial velocity of perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? , A) +2.4 × 10<sup>-16</sup> J B) +3.3 × 10<sup>-16</sup> J C) -2.4 × 10<sup>-16</sup> J D) -2.9 × 10<sup>-16</sup> J E) -3.3 × 10<sup>-16</sup> J ,with an initial velocity of Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of ,in the positive x-direction,is produced by charges on the plates.The center plane at m is an equipotential surface on which .An electron is projected from ,with an initial velocity of perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? , A) +2.4 × 10<sup>-16</sup> J B) +3.3 × 10<sup>-16</sup> J C) -2.4 × 10<sup>-16</sup> J D) -2.9 × 10<sup>-16</sup> J E) -3.3 × 10<sup>-16</sup> J perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of ,in the positive x-direction,is produced by charges on the plates.The center plane at m is an equipotential surface on which .An electron is projected from ,with an initial velocity of perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? , A) +2.4 × 10<sup>-16</sup> J B) +3.3 × 10<sup>-16</sup> J C) -2.4 × 10<sup>-16</sup> J D) -2.9 × 10<sup>-16</sup> J E) -3.3 × 10<sup>-16</sup> J , Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of ,in the positive x-direction,is produced by charges on the plates.The center plane at m is an equipotential surface on which .An electron is projected from ,with an initial velocity of perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? , A) +2.4 × 10<sup>-16</sup> J B) +3.3 × 10<sup>-16</sup> J C) -2.4 × 10<sup>-16</sup> J D) -2.9 × 10<sup>-16</sup> J E) -3.3 × 10<sup>-16</sup> J Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of ,in the positive x-direction,is produced by charges on the plates.The center plane at m is an equipotential surface on which .An electron is projected from ,with an initial velocity of perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? , A) +2.4 × 10<sup>-16</sup> J B) +3.3 × 10<sup>-16</sup> J C) -2.4 × 10<sup>-16</sup> J D) -2.9 × 10<sup>-16</sup> J E) -3.3 × 10<sup>-16</sup> J


A) +2.4 × 10-16 J
B) +3.3 × 10-16 J
C) -2.4 × 10-16 J
D) -2.9 × 10-16 J
E) -3.3 × 10-16 J

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

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A -7.0-μC point charge has a positively charged object in an elliptical orbit around it.If the mass of the positively charged object is 1.0 kg and the distance varies from 5.0 mm to 20.0 mm between the charges,what is the maximum electric potential difference through which the positive object moves? A -7.0-μC point charge has a positively charged object in an elliptical orbit around it.If the mass of the positively charged object is 1.0 kg and the distance varies from 5.0 mm to 20.0 mm between the charges,what is the maximum electric potential difference through which the positive object moves? = A) 9.4 MV B) 3.2 MV C) 4.2 MV D) 16 MV = A -7.0-μC point charge has a positively charged object in an elliptical orbit around it.If the mass of the positively charged object is 1.0 kg and the distance varies from 5.0 mm to 20.0 mm between the charges,what is the maximum electric potential difference through which the positive object moves? = A) 9.4 MV B) 3.2 MV C) 4.2 MV D) 16 MV


A) 9.4 MV
B) 3.2 MV
C) 4.2 MV
D) 16 MV

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

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Two positive point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure.(k = 1/4πε0 = 8.99 × 109 N • m2/C2) Two positive point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure.(k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N • m<sup>2</sup>/C<sup>2</sup>) (a)What is the potential at point A (relative to infinity)due to these charges? (b)What is the potential at point B (relative to infinity)due to these charges? (a)What is the potential at point A (relative to infinity)due to these charges? (b)What is the potential at point B (relative to infinity)due to these charges?

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(a)+8.99 ×...

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If the electric potential at a point in space is zero,then the electric field at that point must also be zero.

A) True
B) False

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Two point charges,Q and -3Q,are located on the x-axis a distance d apart,with -3Q to the right of Q.Find the location of ALL the points on the x-axis (not counting infinity)at which the potential (relative to infinity)due to this pair of charges is equal to zero.

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D/4 TO THE RIGHT OF ...

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A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes of work to bring them to a final configuration in which the object i is at ,y = 1.00 mm,and the other charged object is at , ,find the magnitude of the charge on the second object. A) 2.15 μC B) 4.30 μC C) 10.74 μC D) 4.30 nC of work to bring them to a final configuration in which the A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes of work to bring them to a final configuration in which the object i is at ,y = 1.00 mm,and the other charged object is at , ,find the magnitude of the charge on the second object. A) 2.15 μC B) 4.30 μC C) 10.74 μC D) 4.30 nC object i is at A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes of work to bring them to a final configuration in which the object i is at ,y = 1.00 mm,and the other charged object is at , ,find the magnitude of the charge on the second object. A) 2.15 μC B) 4.30 μC C) 10.74 μC D) 4.30 nC ,y = 1.00 mm,and the other charged object is at A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes of work to bring them to a final configuration in which the object i is at ,y = 1.00 mm,and the other charged object is at , ,find the magnitude of the charge on the second object. A) 2.15 μC B) 4.30 μC C) 10.74 μC D) 4.30 nC , A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes of work to bring them to a final configuration in which the object i is at ,y = 1.00 mm,and the other charged object is at , ,find the magnitude of the charge on the second object. A) 2.15 μC B) 4.30 μC C) 10.74 μC D) 4.30 nC ,find the magnitude of the charge on the second object. A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes of work to bring them to a final configuration in which the object i is at ,y = 1.00 mm,and the other charged object is at , ,find the magnitude of the charge on the second object. A) 2.15 μC B) 4.30 μC C) 10.74 μC D) 4.30 nC


A) 2.15 μC
B) 4.30 μC
C) 10.74 μC
D) 4.30 nC

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

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An electron is released from rest at a distance of 9.00 cm from a proton.If the proton is held in place,how fast will the electron be moving when it is 3.00 cm from the proton? An electron is released from rest at a distance of 9.00 cm from a proton.If the proton is held in place,how fast will the electron be moving when it is 3.00 cm from the proton? , , A) 75.0 m/s B) 106 m/s C) 130 m/s D) 1.06 × 10<sup>3</sup> m/s E) 4.64 × 10<sup>5</sup> m/s , An electron is released from rest at a distance of 9.00 cm from a proton.If the proton is held in place,how fast will the electron be moving when it is 3.00 cm from the proton? , , A) 75.0 m/s B) 106 m/s C) 130 m/s D) 1.06 × 10<sup>3</sup> m/s E) 4.64 × 10<sup>5</sup> m/s , An electron is released from rest at a distance of 9.00 cm from a proton.If the proton is held in place,how fast will the electron be moving when it is 3.00 cm from the proton? , , A) 75.0 m/s B) 106 m/s C) 130 m/s D) 1.06 × 10<sup>3</sup> m/s E) 4.64 × 10<sup>5</sup> m/s


A) 75.0 m/s
B) 106 m/s
C) 130 m/s
D) 1.06 × 103 m/s
E) 4.64 × 105 m/s

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

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The graph in the figure shows the variation of the electric potential V (measured in volts) as a function of the radial direction r (measured in meters) .For which range or value of r is the magnitude of the electric field the largest? The graph in the figure shows the variation of the electric potential V (measured in volts) as a function of the radial direction r (measured in meters) .For which range or value of r is the magnitude of the electric field the largest? A) from r = 0 m to r = 3 m B) from r = 3 m to r = 4 m C) from r = 4 m to r = 6 m D) at r = 3 m E) at r = 4 m


A) from r = 0 m to r = 3 m
B) from r = 3 m to r = 4 m
C) from r = 4 m to r = 6 m
D) at r = 3 m
E) at r = 4 m

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

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