Question 1

Which of the following best describes electric potential energy?

Accepted Answer

The energy stored in the interaction between a charged particle and an electric field.

Question 2

A proton is released from rest at the midpoint between the plates of a parallel-plate capacitor with a potential difference of $$V = 100\ \mathrm{V}. $$What is the change in electric potential energy as the proton moves to the negative plate?

Accepted Answer

$$\Delta U = -eV$$

Question 3

The electric potential energy of two point charges $$q_1$$ and $$q_2$$ separated by a distance $$r is $$given by:

Accepted Answer

$$U = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{q_1$ q_2$}{r}$$

Question 4

A water molecule with dipole moment $$p is $$aligned with an electric field $$E. $$How much energy is required to rotate the molecule by $$90^\circ$$?

Accepted Answer

$$\Delta U = pE$$

Question 5

Which statement about equipotential surfaces is correct?

Accepted Answer

Equipotential surfaces are always perpendicular to the electric field.

Question 6

A parallel-plate capacitor has a capacitance $$C = 1.0\ \mathrm{pF}$$ and is charged to $$V = 1.5\ \mathrm{V}. $$What is the charge stored on the plates?

Accepted Answer

$$Q = CV = 1.5\ \mathrm{pC}$$

Question 7

A proton is fired from far away at a glass sphere of diameter $$1.0\ \mathrm{mm}$$ charged to $$+100\ \mathrm{nC}. $$What initial kinetic energy must the proton have to just reach the surface?

Accepted Answer

$$K = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{qQ}{r}$$

Question 8

Which of the following is true for capacitors connected in series?

Accepted Answer

They all have the same charge.

Question 9

The energy stored in a capacitor of capacitance $$C$$ charged to voltage $$V is$$:

Accepted Answer

$$U = \dfrac{1}{2}CV^2$

Question 10

A parallel-plate capacitor is filled with a dielectric of constant $$\kappa. $$How does the capacitance change compared to the empty capacitor?

Accepted Answer

It increases by a factor of $$\kappa.$$

Question 11

A conducting sphere of radius $$r is $$charged to potential $$V. $$What is the charge on the sphere?

Accepted Answer

$$Q = 4\pi\$$varepsilon_0$$ r V$$

Question 12

The relationship between electric field $$E$$ and electric potential $$V in $$one dimension is:

Accepted Answer

$$E = -\dfrac{dV}{dx}$$

Question 13

A capacitor is constructed using a dielectric with $$\kappa = 3.00$$ and dielectric strength $$2.0 	imes 10^7$\ \mathrm{V/m}. If $$the desired capacitance is $$0.250\ \mathrm{pF}$$ and the maximum potential difference is $$4,000\ \mathrm{V}$$, what is the minimum area required for the plates?

Accepted Answer

$$A = \dfrac{Cd}{\kappa\$$varepsilon_0$$}$$

Question 14

Which of the following statements about conductors in electrostatic equilibrium is correct?

Accepted Answer

The electric field inside the conductor is zero.

Question 15

A thin conducting spherical shell of radius $$R$$ carries a total charge $$Q. $$What is the electric potential at a point outside the shell at distance $$r$$ from the center ($$r \u003e R$$)?

Accepted Answer

$$V = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{Q}{r}$$

Question 16

A uniformly charged ring of radius $$a$$ and total charge $$Q$$ produces an electric potential at a point on its axis at distance $$x$$ from the center. Which expression gives the potential at that point?

Accepted Answer

$$V = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{Q}{\sqrt{x^2$ + a^2$}}$$

Question 17

If the electric field between the plates of a parallel-plate capacitor is $$E$$ and the plate separation is $$d$$, what is the potential difference between the plates?

Accepted Answer

$$V = Ed$$

Question 18

A Geiger counter consists of a cylindrical tube of radius $$R$$ and a wire of radius $$r$$ along its axis. The capacitance per unit length of the system is:

Accepted Answer

$$C' = \dfrac{2\pi\$$varepsilon_0$$}{\ln(R/r)}$$

Question 19

A capacitor with capacitance $$C is $$charged to voltage $$V$$ and then disconnected from the battery. If a dielectric with constant $$\kappa is $$inserted, what happens to the voltage across the plates?

Accepted Answer

The voltage decreases by a factor of $$\kappa.$$

Electric Potential, Potential Energy, and Electric Field: Study Notes for Physics

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