Question 1

A parallel-plate capacitor has a uniform electric field $$E$$ between its plates. If the distance from the negative plate is $$s$$, what is the electric potential at that point relative to the negative plate?

Accepted Answer

$$V = Es$$

Question 2

An electron is released from rest just above the negative plate of a parallel-plate capacitor with a potential difference of $$2.4 	imes 10^4$ V. What is its speed when it reaches the positive plate? (Given: q_e = -1.6$$ 	imes $$10^{-19} C$$, $$m_e = 9.1 	imes 10$$^{-31}$$ kg)

Accepted Answer

$$9.2 	imes 10^7$ m/s

Question 3

Which of the following best describes an equipotential surface?

Accepted Answer

A surface where the electric potential is the same at every point

Question 4

The electric potential at a distance $$r$$ from a point charge $$q ($$assuming $$V=0 at $$infinity) is given by:

Accepted Answer

$$V = \frac{q}{4\pi \$$varepsilon_0$$ r}$$

Question 5

Two metal spheres, A and B, are separated by a large distance. The radius of sphere A is twice that of sphere B. If both spheres have the same electric potential at their surfaces, how does the charge on sphere A ($$Q_A) $$compare to that on sphere B ($$Q_B$$)?

Accepted Answer

$$Q_A = 2Q_B$$

Question 6

The electric potential at a point in space due to multiple point charges $$q_1$$, $$q_2$$, ..., q_n$$ is given by:

Accepted Answer

$$V = \sum \frac{q_i}{4\pi \$$varepsilon_0$$ r_i}$$

Question 7

Three different arrangements of two protons are shown, each with a point P at the same distance from both protons. How do the net electric potentials at P compare?

Accepted Answer

$$V_A = V_B = V_C$$

Question 8

The relationship between electric potential difference $$\Delta V$$ and electric field $$\vec{E} is $$given by:

Accepted Answer

$$\Delta V = - \int \vec{E} \cdot d\vec{s}$$

Question 9

Given a graph of electric potential $$V(x) as a $$function of $$x$$, how is the electric field $$E_x$$ related to the graph?

Accepted Answer

$$E_x = -\frac{dV}{dx}$$

Question 10

Metal rods are arranged so that the potential is constant along each rod, and there is a potential difference between the rods. At which point between the rods is the electric field the greatest?

Accepted Answer

Where the rods are closest together

Question 11

Equipotential lines are shown for a region. At which point is the magnitude of the electric field the greatest?

Accepted Answer

Where the equipotential lines are closest together

Question 12

What is the direction of the electric field at a point on an equipotential map?

Accepted Answer

Perpendicular to the equipotential line, pointing toward lower potential

Question 13

Two metal spheres of different radii are connected by a conducting wire. After electrostatic equilibrium is reached, which of the following is true?

Accepted Answer

The potential at the surface of both spheres is equal

Question 14

A parallel-plate capacitor is fully charged by a battery and then disconnected. If the separation between the plates is doubled, what happens to the charge on the plates?

Accepted Answer

The charge remains the same

Question 15

A parallel-plate capacitor is fully charged by a battery and then disconnected. If the separation between the plates is doubled, what happens to the electric field between the plates?

Accepted Answer

The electric field remains the same

Question 16

A parallel-plate capacitor is fully charged by a battery and then disconnected. If the separation between the plates is doubled, what happens to the potential difference between the plates?

Accepted Answer

The potential difference doubles

Question 17

A parallel-plate capacitor is fully charged by a battery and then disconnected. If the area of the plates is halved (with the charge remaining the same), what happens to the potential difference between the plates?

Accepted Answer

The potential difference doubles

Question 18

A parallel-plate capacitor is fully charged by a battery. If the separation between the plates is doubled while the battery remains connected, what happens to the charge on the plates?

Accepted Answer

The charge halves

Question 19

The energy stored in a capacitor is given by which of the following expressions?

Accepted Answer

$$U_c = \frac{1}{2} C (\Delta V)^2$

Question 20

A parallel-plate capacitor is fully charged by a battery and then disconnected. The plates are then pulled apart until they are separated by a distance $$2d. $$What is the ratio of the final to initial electrostatic energies, $$U_f/U_i$$?

Accepted Answer

2

Electric Potential, Field, and Capacitance: Study Notes ch 26

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