Q: Refer to the parallel plate capacitor with equipotential surfaces at 0.0 V, 0.5 V, 1.0 V, and 1.5 V. What is the magnitude of the electric field between the plates if the distance between the plates is 3 mm?

$$E = \frac{1.5\ \mathrm{V}}{3 \times 10$$^{-3}$$\ \mathrm{m}} = 500\ \mathrm{V/m}$$

Question 1

A proton and an electron are both released from rest in a uniform electric field between two parallel plates separated by 3 mm, with the left plate at 0 V and the right plate at 1.5 V. Which particle experiences the greater magnitude of acceleration, and why?

Accepted Answer

The electron, because it has a smaller mass.

Question 2

Refer to the parallel plate capacitor with equipotential surfaces at 0.0 V, 0.5 V, 1.0 V, and 1.5 V. What is the magnitude of the electric field between the plates if the distance between the plates is 3 mm?

Accepted Answer

$$E = \frac{1.5\ \mathrm{V}}{3 	imes 10$$^{-3}$$\ \mathrm{m}} = 500\ \mathrm{V/m}$$

Question 3

A positive charge moves from the 0.5 V equipotential to the 1.0 V equipotential in a parallel plate capacitor. What is the work done by the electric field on the charge?

Accepted Answer

$$W = -q \Delta V = -q (1.0\ \mathrm{V} - 0.5\ \mathrm{V})$$

Question 4

Which of the following statements about equipotential surfaces in a parallel plate capacitor is correct?

Accepted Answer

Equipotential surfaces are always parallel to the plates.

Question 5

Given the graph of electric potential $$V$$ versus position $$x$$ between two plates (as shown in the third image), what is the direction of the electric field?

Accepted Answer

From higher $$V to $$lower $$V$$

Question 6

A charged particle moves along an equipotential line. What is the work done by the electric field?

Accepted Answer

$$W = 0$$

Question 7

Which of the following is true for a conductor in electrostatic equilibrium?

Accepted Answer

The potential is constant throughout the conductor.

Question 8

Two conducting spheres of different radii are connected by a wire. Which of the following quantities must be the same for both spheres?

Accepted Answer

Electric potential

Question 9

A proton is launched from point A to point B in a uniform electric field, and another proton is launched from A to C, where B and C have the same $$y-$$coordinate. If the paths are different but endpoints have the same potential, how do the changes in potential energy compare?

Accepted Answer

The change in potential energy is the same for both paths.

Question 10

At which point is the magnitude of the electric field the largest: where equipotential lines are closest together or farthest apart?

Accepted Answer

Where equipotential lines are closest together.

Question 11

A battery is connected to a wire loop as shown. What is the potential difference between points 1 and 2 on the wire?

Accepted Answer

Zero, because the wire is an ideal conductor.

Question 12

For a charged conducting sphere of radius $$R$$ and total charge $$Q$$, what is the electric potential at the surface?

Accepted Answer

$$V = \frac{kQ}{R}$$

Question 13

Which of the following best describes the relationship between electric field $$\vec{E}$$ and electric potential $$V$$?

Accepted Answer

$$\vec{E} is $$always perpendicular to equipotential surfaces.

Question 14

A positive charge is moved from a point at 20 V to a point at 0 V. What is the change in its electric potential energy?

Accepted Answer

$$\Delta U = q (0\ \mathrm{V} - 20\ \mathrm{V}) = -20q$$

Question 15

In the potential graph $$V vs$$ $$r$$ for a point charge, what is the mathematical relationship for $$V$$ outside the charge?

Accepted Answer

$$V = \frac{kQ}{r}$$

Question 16

At which labeled location (M, N, or O) on the $$V vs$$ $$y$$ graph is the magnitude of the electric field the largest?

Accepted Answer

At M, where the slope is steepest.

Question 17

Which of the following is NOT a property of a conductor in electrostatic equilibrium?

Accepted Answer

The surface is not an equipotential.

Question 18

If a positive test charge is placed near a positive point charge, what is the direction of the electric field at the test charge's location?

Accepted Answer

Away from the positive charge.

Question 19

A metal sphere is placed in a region of space with a nonzero electric field. After reaching electrostatic equilibrium, what is the electric field inside the sphere?

Accepted Answer

Zero.

Equipotentials, Electric Potential, and Conductors in Electrostatics

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