Q: A $$2.0 \text{ cm} \times 2.0 \text{ cm}$$ parallel-plate capacitor is connected to a $$100 \text{ V}$$ battery. If the plate separation is $$1.0 \text{ mm}$$, what is the capacitance? ($$\$$epsilon_0$$ = 8.85 \times 10$$^{-12}$$ \text{ F/m})$$

$$C = 3.54 \times 10$$^{-12}$$ \text{ F}$$

Question 1

Which of the following statements best describes the relationship between electric potential energy and electric potential for a point charge $$q at a $$location with electric potential $$V$$?

Accepted Answer

$$U = qV$$, where $$U is $$the electric potential energy.

Question 2

A proton is released from rest in a region of space where the electric potential decreases in the direction of motion. What happens to the proton's kinetic energy as it moves?

Accepted Answer

Its kinetic energy increases.

Question 3

Which of the following is true about equipotential surfaces in an electric field?

Accepted Answer

Equipotential surfaces are always perpendicular to electric field lines.

Question 4

A parallel-plate capacitor has plates of area $$A$$ separated by distance $$d. $$What is the capacitance $$C of $$the capacitor in terms of the permittivity of free space $$\$$epsilon_0$$?

Accepted Answer

$$C = \frac{\$$epsilon_0$$ A}{d}$$

Question 5

If a dielectric material with dielectric constant $$k is $$inserted between the plates of a capacitor that has been disconnected from the battery, what happens to the capacitance and the potential difference across the plates?

Accepted Answer

Capacitance increases by a factor of $$k$$, and the potential difference decreases.

Question 6

A charged particle moves from point A to point B in an electric field, and the electric potential at A is higher than at B. If the particle is positively charged, what can be said about the work done by the electric field?

Accepted Answer

The electric field does positive work on the particle.

Question 7

What is the energy stored in a capacitor with charge $$Q$$ and potential difference $$V$$?

Accepted Answer

$$U = \frac{1}{2} QV$$

Question 8

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

Accepted Answer

The electric field inside the conductor is zero.

Question 9

A $$2.0 	ext{ cm} 	imes 2.0 	ext{ cm}$$ parallel-plate capacitor is connected to a $$100 	ext{ V}$$ battery. If the plate separation is $$1.0 	ext{ mm}$$, what is the capacitance? ($$\$$epsilon_0$$ = 8.85 	imes 10$$^{-12}$$ 	ext{ F/m})$$

Accepted Answer

$$C = 3.54 	imes 10$$^{-12}$$ 	ext{ F}$$

Question 10

The electron volt (eV) is defined as:

Accepted Answer

The energy gained by an electron when it moves through a potential difference of $$1 	ext{ V}.$$

Question 11

A $$1.0 	ext{ nC}$$ point charge is located $$0.03 	ext{ m}$$ from a $$-1.0 	ext{ nC}$$ point charge. What is the electric potential at a point $$0.04 	ext{ m}$$ from the $$+1.0 	ext{ nC}$$ charge and $$0.03 	ext{ m}$$ from the $$-1.0 	ext{ nC}$$ charge? ($$k = 9.0 	imes 10^9$ 	ext{ N} \cdot 	ext{m}^2/	ext{C}^2)$$

Accepted Answer

$$V = 435 	ext{ V}$$

Question 12

Which of the following best explains why high voltage is not always dangerous?

Accepted Answer

It is the amount of current (charge per unit time) that is dangerous, not just the voltage.

Question 13

The electric field $$E$$ between the plates of a parallel-plate capacitor is related to the potential difference $$V$$ and plate separation $$d by$$:

Accepted Answer

$$E = \frac{V}{d}$$

Question 14

If a capacitor is connected to a battery and a dielectric is inserted between the plates, what happens to the charge on the plates?

Accepted Answer

The charge increases.

Question 15

Which of the following is true about the energy density $$u$$ stored in the electric field between the plates of a capacitor?

Accepted Answer

$$u = \frac{1}{2} \$$epsilon_0$$ E^2$

Question 16

A negative charge moves from a region of lower electric potential to higher electric potential. What happens to its kinetic energy?

Accepted Answer

Its kinetic energy increases.

Question 17

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

Accepted Answer

The electric field inside the conductor is nonzero.

Question 18

The capacitance of a parallel-plate capacitor can be increased by:

Accepted Answer

Decreasing the separation between the plates.

Question 19

Which equation correctly relates the electric field $$E to $$the rate of change of electric potential $$V$$ with respect to position $$x$$?

Accepted Answer

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

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