Deck 25: Electric Charges and Forces

Question 1

Three point charges are placed on the x-axis. A charge of +2.0 μC is placed at the origin, -2.0 μC to the right at x = 50 cm, and +4.0 μC at the 100 cm mark. What are the magnitude and direction of the electrostatic force that acts on the charge at the origin? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Answer 1

0.072 N, toward the right

Question 2

A positive point charge Q is fixed on a very large horizontal frictionless tabletop. A second positive point charge q is released from rest near the stationary charge and is free to move. Which statement best describes the motion of q after it is released?

A) Its speed will be greatest just after it is released.
B) Its acceleration is zero just after it is released.
C) As it moves farther and farther from Q, its acceleration will keep increasing.
D) As it moves farther and farther from Q, its speed will decrease.
E) As it moves farther and farther from Q, its speed will keep increasing.

Answer 2

As it moves farther and farther from Q, its speed will keep increasing.

Question 3

Two small insulating spheres are attached to silk threads and aligned vertically as shown in the figure. These spheres have equal masses of 40 g, and carry charges q₁ and q₂ of equal magnitude 2.0 μC but opposite sign. The spheres are brought into the positions shown in the figure, with a vertical separation of 15 cm between them. Note that you cannot neglect gravity. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The tension in the lower thread is closest to

A) 1.2 N.
B) 1.4 N.
C) 1.6 N.
D) 1.8 N.
E) 2.0 N.

Answer 3

1.2 N.

Question 4

In the figure, all the charges are point charges and the charge in the middle is Q = -3.1 nC. For what charge q₁ will charge q₂ be in static equilibrium?

A) 12 nC
B) 6.2 nC
C) 3.1 nC
D) 25 nC

Question 5

One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure. The balls are in equilibrium a distance d apart. If the charge on each ball is doubled, the distance between the balls in the test tube would become

A) d.
B) 2d.
C) 4d.
D) 8d.

Question 6

Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually leaks off of both spheres. When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be

A) 1/16 F.
B) 1/8 F.
C) 1/4 F.
D) 1/2 F.

Question 7

A piece of plastic has a net charge of +2.00 μC. How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10^-19 C)

A) 1.25 × 10¹³
B) 1.25 × 10¹⁹
C) 2.50 × 10¹³
D) 2.50 × 10¹⁹

Question 8

When two point charges are a distance d part, the electric force that each one feels from the other has magnitude F. In order to make this force twice as strong, the distance would have to be changed to

A) 2d.
B) d.
C) d/
D) d/2.
E) d/4.

Question 9

In the figure Q = 5.8 nC and all other quantities are accurate to 2 significant figures. What is the magnitude of the force on the charge Q? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 1.8 × 10^-3 N
B) 1.0 × 10^-3 N
C) 9.0 × 10^-4 N
D) 1.2 × 10^-3 N

Question 10

In the figure, charge q₁ = 3.1 × 10^-6 C is placed at the origin and charge q₂ = -8.7 × 10^-6 C is placed on the x-axis, at x = -0.20 m. Where along the x-axis can a third charge Q = -8.3 µC be placed such that the resultant force on this third charge is zero?

Question 11

Two identical small conducting spheres are separated by 0.60 m. The spheres carry different amounts of charge and each sphere experiences an attractive electric force of 10.8N. The total charge on the two spheres is -24 μC. The two spheres are now connected by a slender conducting wire, which is then removed. The electric force on each sphere is closest to

A) zero.
B) 3.6 N, attractive.
C) 5.4 N, attractive.
D) 3.6 N, repulsive.
E) 5.4 N, repulsive.

Question 12

X and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A positively charged rod R is brought close to X as shown in Figure (a). Sphere Y is now moved away from X, as in Figure (b).
What are the final charge states of X and Y?

A) Both X and Y are neutral.
B) X is positive and Y is neutral.
C) X is neutral and Y is positive.
D) X is negative and Y is positive.
E) Both X and Y are negative.

Question 13

When two point charges are 2.0 cm apart, each one experiences a 1.0-N electric force due to the other charge. If they are moved to a new separation of 8.0 cm, the electric force on each of them is closest to

A) 1.0 N.
B) 4.0 N.
C) 16 N.
D) 0.25 N.
E) 0.063 N.

Question 14

A point charge Q is located a short distance from a point charge 3Q, and no other charges are present. If the electrical force on Q is F, what is the electrical force on 3Q?

A) F/3
B) F/
C) F
D) F
E) 3F

Question 15

A +7.00 μC point charge and -9.00 μC point charge are placed along the x-axis at x = 0.000 cm and x = 40.0 cm, respectively. Where must a third charge, q, be placed along the x-axis so that it does not experience any net electric force due to the other two charges?

A) -0.200 m
B) 2.99 m
C) -0.187 m
D) -2.99 m
E) 0.187 m

Question 16

Charge Q₁ = 6.0 nC is at (0.30 m, 0), charge Q₂ = -1.0 nC is at (0, 0.10 m), and charge Q₃ = 5.0 nC is at (0, 0). What are the magnitude and direction of the net electrostatic force on the 5.0-nC charge due to the other charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Question 17

The point charge at the bottom of the figure is Q = +17 nC, and the curve is a circular arc. What is the magnitude of the force on the charge Q due to the other point charges shown? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 1.9 × 10^-4 N
B) 1.2 × 10^-4 N
C) 1.6 × 10^-4 N
D) 2.3 × 10^-4 N

Question 18

A 1.0-C point charge is 15 m from a second point charge, and the electric force on one of them due to the other is 1.0 N. What is the magnitude of the second charge? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 25 C
B) 1.0 C
C) 10 nC
D) 0.025 C
E) 25 nC

Question 19

In the figure, a small spherical insulator of mass 6.00 × 10^-2 kg and charge +0.400 μC is hung by a thin wire of negligible mass. A charge of -0.220 μC is held 0.290 m away from the sphere and directly to the right of it, so the wire makes an angle θ with the vertical, as shown. What is the angle θ? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 0.917°
B) 1.10°
C) 1.30°
D) 1.50°
E) 1.70°

Question 20

The figure shows two tiny 5.0-g spheres suspended from two very thin 1.0-m-long threads. The spheres repel each other after being charged to +91 nC and hang at rest as shown. What is the angle θ? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 4.1°
B) 8.2°
C) 12°
D) 16°

Question 21

The electric field 1.5 cm from a very small charged object points toward the object with a magnitude of 180,000 N/C. What is the charge on the object? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) -4.5 nC
B) +4.5 nC
C) -5.0 nC
D) +5.0 nC

Question 22

A point charge Q of mass 8.50 g hangs from the horizontal ceiling by a light 25.0-cm thread. When a horizontal electric field of magnitude 1750 N/C is turned on, the charge hangs away from the vertical as shown in the figure. The magnitude of Q is closest to

A) 27.5 µC.
B) 47.6 µC.
C) 55.0 µC.
D) 3.0 µC.
E) 3.5 µC.

Question 23

A metal sphere of radius 10 cm carries a charge of +2.0 μC uniformly distributed over its surface. What is the magnitude of the electric field due to this sphere at a point 5.0 cm outside the sphere's surface? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 4.0 × 10⁵ N/C
B) 8.0 × 10⁵ N/C
C) 4.2 × 10⁶ N/C
D) 4.0 × 10⁷ N/C
E) 8.0 × 10⁷ N/C

Question 24

A small sphere with a mass of 441 g is moving upward along the vertical +y-axis when it encounters an electric field of 5.00 N/C . If, due to this field, the sphere suddenly acquires a horizontal acceleration of 13.0 m/s²

, what is the charge that it carries?

A) 1.15 C
B) -1.15 C
C) 1150 C
D) -1150 C

Question 25

A small glass bead has been charged to 8.0 nC. What is the magnitude of the electric field 2.0 cm from the center of the bead? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 1.8 × 10⁵ N/C
B) 3.6 × 10³ N/C
C) 1.4 × 10^-3 N/C
D) 3.6 × 10^-6 N/C

Question 26

What is the minimum magnitude of an electric field that balances the weight of a plastic sphere of mass 6.4 g that has been charged to -3.0 nC?

A) 2.1 × 10⁷ N/C
B) 2.4 × 10⁶ N/C
C) 4.5 × 10⁶ N/C
D) 6.4 × 10⁶ N/C