Question 1

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?

Accepted Answer

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. 
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.

Question 2

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, mel = 9.11 x 10-31 kg)

Accepted Answer

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 
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 3

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 4

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 5

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

Accepted Answer

A) True 
 B)False

Question 6

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?

Accepted Answer

(a) 153 kV

Question 7

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)

Accepted Answer

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

Question 8

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

Accepted Answer

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. 
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.

Question 9

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)

Accepted Answer

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 
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 10

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)

Accepted Answer

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

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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)

Accepted Answer

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

Question 13

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 14

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

Accepted Answer

A) True 
 B)False

Question 15

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)

Accepted Answer

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

Question 16

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, mproton = 1.67 x 10-27 kg)

Accepted Answer

A)  2.1 × 10-13 m 
B)  3.3 × 10-13 m 
C)  2.6 × 10-13 m 
D)  2.9 × 10-13 m 
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 17

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?

Accepted Answer

(a) +8.99

Question 18

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 19

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 20

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?

Accepted Answer

The answer of The figure shows two arcs of a...

Exam 28: The Electric Potential

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?

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)

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

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

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)

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

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)

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

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 negative charge, if free, will tend to move

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?

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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? (m_el= 9.11 x 10^-31 kg, e = 1.60 × 10^-19 C, 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 = 1/4πε₀ = 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)

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)