Question 1

A charge of 20 nC is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +3 m on the x axis?

Accepted Answer

A) 
 
B) 
 
C) 
 
D) 
 
E)

Question 2

Four identical point charges (+6.0 nC) are placed at the corners of a rectangle which measures 6.0 m × 8.0 m. If the electric potential is taken to be zero at infinity, what is the potential at the geometric center of this rectangle?

Accepted Answer

A)  58 V 
B)  63 V 
C)  43 V 
D)  84 V 
E)  11 V

Question 3

A series of 3 uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the third shell, at distance r from the center, and relative to V = 0 at ∞, is

Accepted Answer

A) 
 . 
B) 
 . 
C) 
 . 
D) 
 . 
E) 
 .

Question 4

Points A [at (2, 3) m] and B [at (5, 7) m] are in a region where the electric field is uniform and given by  N/C. What is the potential difference VA − VB?

Accepted Answer

A)  33 V 
B)  27 V 
C)  30 V 
D)  24 V 
E)  11 V

Question 5

A linear charge of nonuniform density λ = bx, where b = 2.1 nC/m2, is distributed along the x axis from x = 2.0 m to x = 3.0 m. Determine the electric potential (relative to zero at infinity) of the point y = 4.0 m on the y axis.

Accepted Answer

A)  36 V 
B)  95 V 
C)  10 V 
D)  17 V 
E)  15 V

Question 6

Through what potential difference must an electron (starting from rest) be accelerated if it is to reach a speed of 3.0 × 107 m/s?

Accepted Answer

A)  5.8 kV 
B)  2.6 kV 
C)  7.1 kV 
D)  8.6 kV 
E)  5.1 kV

Question 7

Two large parallel conducting plates are 8.0 cm apart and carry equal but opposite charges on their facing surfaces. The magnitude of the surface charge density on either of the facing surfaces is 2.0 nC/m2. Determine the magnitude of the electric potential difference between the plates.

Accepted Answer

A)  36 V 
B)  27 V 
C)  18 V 
D)  45 V 
E)  16 V

Question 8

What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV?

Accepted Answer

A)  1.1 × 106 m/s 
B)  9.8 × 105 m/s 
C)  8.8 × 105 m/s 
D)  1.2 × 106 m/s 
E)  6.2 × 105 m/s

Question 9

A particle (m = 2.0 μg, q = −5.0 μC) has a speed of 30 m/s at point A and moves (with only electric forces acting on it) to point B where its speed is 80 m/s. Determine the electric potential difference VA − VB.

Accepted Answer

A)  −2.2 kV 
B)  +1.1 kV 
C)  −1.1 kV 
D)  +2.2 kV 
E)  +1.3 kV

Question 10

Point charges q and Q are positioned as shown. If q = +2.0 nC, Q = −2.0 nC, a = 3.0 m, and b = 4.0 m, what is the electric potential difference, VA − VB?

Accepted Answer

A)  8.4 V 
B)  6.0 V 
C)  7.2 V 
D)  4.8 V 
E)  0 V

Question 11

Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 m on the y axis, a −80-nC charge at x = −4 m on the x axis, and a 70-nc charge at y = −6 m on the y axis. What is the electric potential (relative to a zero at infinity) at the point x = 8 m on the x axis?

Accepted Answer

A)  +81 V 
B)  +48 V 
C)  +5.8 V 
D)  −72 V 
E)  −18 V

Question 12

Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 m to x = 5.0 m. What is the electric potential (relative to zero at infinity) at the origin (x = 0)?

Accepted Answer

A)  91 V 
B)  99 V 
C)  82 V 
D)  74 V 
E)  140 V

Question 13

A particle (charge = 40 μC) moves directly toward a second particle (charge = 80 μC) which is held in a fixed position. At an instant when the distance between the two particles is 2.0 m, the kinetic energy of the moving particle is 16 J. Determine the distance separating the two particles when the moving particle is momentarily stopped.

Accepted Answer

A)  0.75 m 
B)  0.84 m 
C)  0.95 m 
D)  0.68 m 
E)  0.56 m

Question 14

A rod (length = 2.0 m) is uniformly charged and has a total charge of 5.0 nC. What is the electric potential (relative to zero at infinity) at a point which lies along the axis of the rod and is 3.0 m from the center of the rod?

Accepted Answer

A)  22 V 
B)  19 V 
C)  16 V 
D)  25 V 
E)  12 V

Question 15

A charge of uniform density (0.80 nC/m) is distributed along the x axis from the origin to the point x = 10 cm. What is the electric potential (relative to zero at infinity) at a point, x = 18 cm, on the x axis?

Accepted Answer

A)  7.1 V 
B)  5.8 V 
C)  9.0 V 
D)  13 V 
E)  16 V

Question 16

Two identical particles, each with a mass of 2.0 μg and a charge of 25 nC, are released simultaneously from rest when the two are 4.0 cm apart. What is the speed of either particle at the instant when the two are separated by 10 cm?

Accepted Answer

A)  7.3 m/s 
B)  9.8 m/s 
C)  9.2 m/s 
D)  6.5 m/s 
E)  4.6 m/s

Question 17

A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformly on its surface. If point A is located at the center of the sphere and point B is 15 cm from the center, what is the magnitude of the electric potential difference between these two points?

Accepted Answer

A)  23 V 
B)  30 V 
C)  15 V 
D)  45 V 
E)  60 V

Question 18

A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown. Where is the induced charge density greatest in magnitude and what is its sign?

Accepted Answer

A)  A; negative. 
B)  A; positive. 
C)  B; negative. 
D)  B; positive. 
E)  C; negative.

Question 19

Two particles, each having a mass of 3.0 μg and having equal but opposite charges of magnitude 5.0 nC, are released simultaneously from rest when the two are 5.0 cm apart. What is the speed of either particle at the instant when the two are separated by 2.0 cm?

Accepted Answer

A)  2.1 m/s 
B)  1.5 m/s 
C)  1.8 m/s 
D)  2.4 m/s 
E)  3.2 m/s

Question 20

An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station. Which statement is correct?

Accepted Answer

A)  The astronaut must abandon the chamber immediately to avoid being electrocuted. 
B)  The astronaut will be safe only if she is wearing a spacesuit made of non-conducting materials. 
C)  The astronaut does not need to worry: the charge will remain on the outside surface. 
D)  The astronaut must abandon the chamber if the electric field on the outside surface becomes greater than the breakdown field of air. 
E)  The astronaut must abandon the chamber immediately because the electric field inside the chamber is non-uniform.

Exam 25: Electric Potential

A charge of 20 nC is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +3 m on the x axis?

Four identical point charges (+6.0 nC) are placed at the corners of a rectangle which measures 6.0 m × 8.0 m. If the electric potential is taken to be zero at infinity, what is the potential at the geometric center of this rectangle?

A series of 3 uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the third shell, at distance r from the center, and relative to V = 0 at ∞, is

Points A [at (2, 3) m] and B [at (5, 7) m] are in a region where the electric field is uniform and given by N/C. What is the potential difference V_A − V_B?

A linear charge of nonuniform density λ = bx, where b = 2.1 nC/m², is distributed along the x axis from x = 2.0 m to x = 3.0 m. Determine the electric potential (relative to zero at infinity) of the point y = 4.0 m on the y axis.

Through what potential difference must an electron (starting from rest) be accelerated if it is to reach a speed of 3.0 × 10⁷ m/s?

Two large parallel conducting plates are 8.0 cm apart and carry equal but opposite charges on their facing surfaces. The magnitude of the surface charge density on either of the facing surfaces is 2.0 nC/m². Determine the magnitude of the electric potential difference between the plates.