Question 1

A negative charge, if free, will tend to move

Accepted Answer

A)  from high potential to low potential. 
B)  from low potential to high potential. 
C)  toward infinity. 
D)  away from infinity. 
E)  in the direction of the electric field. 
A)  from high potential to low potential. 
B)  from low potential to high potential. 
C)  toward infinity. 
D)  away from infinity. 
E)  in the direction of the electric field.

Question 2

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?

Accepted Answer

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

Question 3

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? (mel = 9.11 x 10-31 kg, e = 1.60 × 10-19 C, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

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 
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

Question 4

A conducting sphere 45 cm in diameter carries an excess of charge, and no other charges are present. You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) The excess charge on this sphere is closest to

Accepted Answer

A)  0.35 nC. 
B)  79 nC. 
C)  315 nC. 
D)  350 nC. 
E)  700 nC. 
A)  0.35 nC. 
B)  79 nC. 
C)  315 nC. 
D)  350 nC. 
E)  700 nC.

Question 5

Four point charges of magnitude 6.00 μC and of varying signs are placed at the corners of a square 2.00 m on each side, as shown in the figure. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)
(a) What is the electric potential (relative to infinity) at the center of this square due to these charges?
(b) What is the magnitude of the electric field due to these charges at the center of the square?

Accepted Answer

(a) zero

Question 6

A half-ring (semicircle) of uniformly distributed charge Q has radius R. What is the electric potential at its center?

Accepted Answer

The answer of A half-ring (semicircle) of uniformly distributed charge...

Question 7

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?

Accepted Answer

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 
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

Question 8

When the electric field is zero at a point, the potential must also be zero there.

Accepted Answer

A) True 
 B)False

Question 9

A -3.0-μC point charge and a -9.0-μC point charge are initially extremely far apart. How much work does it take to bring the -3.0-μC charge to x = 3.0 mm, y = 0.00 mm and the -9.0-μC charge to x = -3.0 mm, y = 0.00 mm? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  40 J 
B)  81 J 
C)  27 J 
D)  6.8 J 
A)  40 J 
B)  81 J 
C)  27 J 
D)  6.8 J

Question 10

A sphere with radius 2.0 mm carries +1.0 μC of charge distributed uniformly throughout its volume. What is the potential difference, VB - VA, between point B, which is 4.0 m from the center of the sphere, and point A, which is 9.0 m from the center of the sphere? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  1200 V 
B)  -1200 V 
C)  140 V 
D)  -0.45 V 
A)  1200 V 
B)  -1200 V 
C)  140 V 
D)  -0.45 V

Question 11

Consider the group of three+2.4 nC point charges shown in the figure. What is the electric potential energy of this system of charges relative to infinity? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  4.1 × 10-6 J 
B)  4.6 × 10-6 J 
C)  4.2 × 10-6 J 
D)  4.4 × 10-6 J 
A)  4.1 × 10-6 J 
B)  4.6 × 10-6 J 
C)  4.2 × 10-6 J 
D)  4.4 × 10-6 J

Question 12

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

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

A charge Q = -610 nC is uniformly distributed on a ring of 2.4-m radius. A point charge q = +480 nC is fixed at the center of the ring, as shown in the figure. An electron is projected from infinity toward the ring along the axis of the ring. This electron comes to a momentary halt at a point on the axis that is 5.0 m from the center of the ring. What is the initial speed of the electron at infinity? (e = 1.60 × 10-19 C, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2, mel = 9.11 x 10-31 kg)

Accepted Answer

A)  6.6 × 106 m/s 
B)  4.5 × 106 m/s 
C)  3.4 × 106 m/s 
D)  2.2 × 106 m/s 
E)  1.1 × 106 m/s 
A)  6.6 × 106 m/s 
B)  4.5 × 106 m/s 
C)  3.4 × 106 m/s 
D)  2.2 × 106 m/s 
E)  1.1 × 106 m/s

Question 15

Two parallel conducting plates are separated by 1.0 mm and carry equal but opposite surface charge densities. If the potential difference between them is 2.0 V, what is the magnitude of the surface charge density on each plate? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)  18 nC/m2 
B)  0.13 mC/m2 
C)  35 nC/m2 
D)  0.27 mC/m2 
A)  18 nC/m2 
B)  0.13 mC/m2 
C)  35 nC/m2 
D)  0.27 mC/m2

Question 16

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? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

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

Question 17

If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10-19 C, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2, mel = 9.11 x 10-31 kg)

Accepted Answer

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

Question 18

Two +6.0-μC point charges are placed at the corners of the base of an equilateral triangle, as shown in the figure. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) At the vertex, P, of the triangle   
(a) what is the electric potential (relative to infinity) due to these charges?
(b) what is the magnitude of the electric field due to these charges?

Accepted Answer

(a) 54 kV

Question 19

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

Accepted Answer

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

Question 20

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?

Accepted Answer

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. 
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.

Exam 22: Electric Potential

A negative charge, if free, will tend to move

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?

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? (mel = 9.11 x 10-31 kg, e = 1.60 × 10-19 C, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

A conducting sphere 45 cm in diameter carries an excess of charge, and no other charges are present. You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) The excess charge on this sphere is closest to

A half-ring (semicircle) of uniformly distributed charge Q has radius R. What is the electric potential at its center?

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?

When the electric field is zero at a point, the potential must also be zero there.

A -3.0-μC point charge and a -9.0-μC point charge are initially extremely far apart. How much work does it take to bring the -3.0-μC charge to x = 3.0 mm, y = 0.00 mm and the -9.0-μC charge to x = -3.0 mm, y = 0.00 mm? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Consider the group of three+2.4 nC point charges shown in the figure. What is the electric potential energy of this system of charges relative to infinity? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

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 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?

Two parallel conducting plates are separated by 1.0 mm and carry equal but opposite surface charge densities. If the potential difference between them is 2.0 V, what is the magnitude of the surface charge density on each plate? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

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? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10-19 C, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2, mel = 9.11 x 10-31 kg)

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

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?

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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? (mel = 9.11 x 10^-31 kg, e = 1.60 × 10^-19 C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A conducting sphere 45 cm in diameter carries an excess of charge, and no other charges are present. You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The excess charge on this sphere is closest to

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 -3.0-μC point charge and a -9.0-μC point charge are initially extremely far apart. How much work does it take to bring the -3.0-μC charge to x = 3.0 mm, y = 0.00 mm and the -9.0-μC charge to x = -3.0 mm, y = 0.00 mm? (k = 1/4πε₀ = 8.99 × 10⁹N ∙ m²/C²)

Consider the group of three+2.4 nC point charges shown in the figure. What is the electric potential energy of this system of charges relative to infinity? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two parallel conducting plates are separated by 1.0 mm and carry equal but opposite surface charge densities. If the potential difference between them is 2.0 V, what is the magnitude of the surface charge density on each plate? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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_A - V_B, between points A and B? (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²)

If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10^-19C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², mel = 9.11 x 10^-31 kg)