Deck 28: The Electric Potential

Question 1

Which statements are true for an electron moving in the direction of an electric field? (There may be more than one correct choice.)

A) Its electric potential energy increases as it goes from high to low potential.
B) Its electric potential energy decreases as it goes from high to low potential.
C) Its potential energy increases as its kinetic energy decreases.
D) Its kinetic energy decreases as it moves in the direction of the electric field.
E) Its kinetic energy increases as it moves in the direction of the electric field.

Answer 1

Its electric potential energy increases as it goes from high to low potential.
Its potential energy increases as its kinetic energy decreases.
Its kinetic energy decreases as it moves in the direction of the electric field.

Question 2

A negative charge is moved from point A to point B along an equipotential surface. Which of the following statements must be true for this case?

A) The negative charge performs work in moving from point A to point B.
B) Work is required to move the negative charge from point A to point B.
C) No work is required to move the negative charge from point A to point B.
D) The work done on the charge depends on the distance between A and B.
E) Work is done in moving the negative charge from point A to point B.

Answer 2

No work is required to move the negative charge from point A to point B.

Question 3

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)
(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?

Answer 3

(a) +8.99 × 10⁴ V
(b) 1.12 × 10⁵ V

Question 4

If the electrical potential in a region is constant, the electric field must be zero everywhere in that region.

Question 5

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.

Question 6

The figure shows two arcs of a circle on which charges +Q and -Q have been spread uniformly. What is the value of the electric potential at the center of the circle?

Question 7

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)

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

Question 8

Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively. Where should a third charge of +3.0-μC be placed on the +x-axis so that the potential at the origin is equal to zero? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) x = 4.0 cm
B) x = 1.0 cm
C) x = 2.0 cm
D) x = 3.0 cm
E) x = 5.0 cm

Question 9

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

Question 10

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?
(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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

Question 11

Two equal positive charges are held in place at a fixed distance. If you put a third positive charge midway between these two charges, its electrical potential energy of the system (relative to infinity) is zero because the electrical forces on the third charge due to the two fixed charges just balance each other.

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

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

Question 13

Suppose you have two negative point charges. 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.

Question 14

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)

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

Question 15

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?

Question 16

A negative charge, if free, will tend to move

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 17

If the electric field is zero everywhere inside a region of space, the potential must also be zero in that region.

Question 18

Four equal +6.00-μC point charges are placed at the corners of a square 2.00 m on each side. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)
(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?

Question 19

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

Question 20

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?

Question 21

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, ^m_el = 9.11 x 10^-31 kg)

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 22

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)

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

Question 23

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC, and no other charges are present. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The potential (relative to infinity) due to this sphere at a point 12.0 cm from its center is closest to

A) zero.
B) 674 kV.
C) 1130 kV.
D) 3380 kV.
E) 9380 kV.

Question 24

An alpha particle is a nucleus of helium. It has twice the charge and four times the mass of the proton. When they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 0.0030c, where c is the speed of light. What is their distance of closest approach? Hint: There are two conserved quantities. Make use of both of them.
(c = 3.00 × 10⁸ m/s, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19 C, m_proton = 1.67 x 10^-27 kg)

A) 2.1 × 10^-13 m
B) 3.3 × 10^-13 m
C) 2.6 × 10^-13 m
D) 2.9 × 10^-13 m

Question 25

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

Question 26

Two large conducting parallel plates A and B are separated by 2.4 m. A uniform field of 1500 V/m, in the positive x-direction, is produced by charges on the plates. The center plane at x = 0.00 m is an equipotential surface on which V = 0. An electron is projected from x = 0.00 m, with an initial velocity of 1.0 × 10⁷ m/s 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? (e = 1.60 × 10^-19 C, m_el = 9.11 x 10^-31 kg)

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

Question 27

Two point charges of +1.0 μC and -2.0 μC are located 0.50 m apart. What is the minimum amount of work needed to move the charges apart to double the distance between them? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) -36 mJ
B) +18 mJ
C) 0 mJ
D) +36 mJ
E) -18 mJ

Question 28

Two equal point charges Q are separated by a distance d. One of the charges is released and moves away from the other due only to the electrical force between them. When the moving charge is a distance 3d from the other charge, what is its kinetic energy?

Question 29

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

Question 30

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

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 31

A sphere with radius 2.0 mm carries +1.0 μC of charge distributed uniformly throughout its volume. What is the potential difference, V_B - V_A, 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)

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

Question 32

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

Question 33

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, m_el = 9.11 x 10^-31 kg)

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 34

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

Question 35

A charge Q = -820 nC is uniformly distributed on a ring of 2.4 m radius. A point charge q = +530 nC is fixed at the center of the ring. Points A and B are located on the axis of the ring, as shown in the figure. What is the minimum work that an external force must do to transport an electron from B to A?
(e = 1.60 × 10^-19 C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) -8.7 × 10^-17 J
B) +7.2 × 10^-18 J
C) +1.0 × 10^-16 J
D) +8.7 × 10^-17 J
E) -7.2 × 10^-18 J

Question 36

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? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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

Question 37

A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart. If it takes 29.0 J of work to bring them to a final configuration in which the +3.0.0-μC object i is at x = 1.00 mm, y = 1.00 mm, and the other charged object is at x = 1.00 mm, y = 3.00 mm, find the magnitude of the charge on the second object. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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

Question 38

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.

Question 39

The figure shows an arrangement of two -4.5 nC charges, each separated by 5.0 mm from a proton. If the two negative charges are held fixed at their locations and the proton is given an initial velocity v as shown in the figure, what is the minimum initial speed v that the proton needs to totally escape from the negative charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19 C, m_proton = 1.67 x 10^-27 kg)

A) 1.8 × 10⁶ m/s
B) 3.5 × 10⁶ m/s
C) 6.8 × 10⁶ m/s
D) 1.4 × 10⁷ m/s

Question 40

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)

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