Question 1

What is the electric potential $$V at a $$distance $$r \u003e R$$ from the center of a sphere of radius $$R$$ carrying a total charge $$Q$$?

Accepted Answer

$$V = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{Q}{r}$$

Question 2

A parallel-plate capacitor is charged by a battery and then disconnected. If the plates are pulled farther apart, what happens to the potential difference $$\Delta V_C$$ between the plates?

Accepted Answer

$$\Delta V_C$$ increases

Question 3

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

Accepted Answer

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

Question 4

A parallel-plate capacitor has plate area $$A$$ and separation $$d. $$What is its capacitance $$C in $$terms of $$\$$epsilon_0$$, A$, and d$?

Accepted Answer

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

Question 5

A proton is shot into a parallel-plate capacitor with an initial speed $$v_i = 2.0 	imes 10^5$ m/s toward the positive plate. The plates are 2.00 mm apart and the potential difference is 500 V. What is the farthest distance x_f$ from the negative plate the proton reaches before stopping?

Accepted Answer

$$x_f = \dfrac{m_p v_i^2$}{2e \Delta V}$$

Question 6

Which of the following statements about the energy stored in a capacitor is correct?

Accepted Answer

The energy stored is $$U = \dfrac{1}{2} C (\Delta V)^2$

Question 7

A dielectric material with dielectric constant $$k is $$inserted between the plates of a capacitor. What happens to the capacitance?

Accepted Answer

It increases by a factor of $$k$$

Question 8

Which of the following is the correct unit for capacitance?

Accepted Answer

Farad (F)

Question 9

Four charges $$+q$$ are placed at the corners of a square of side $$a. $$What is the electric potential at the center of the square?

Accepted Answer

$$V = \dfrac{4kq}{a\sqrt{2}}$$

Question 10

A capacitor is connected to a battery and becomes fully charged. If the battery is then removed, what happens to the voltage across the capacitor?

Accepted Answer

It remains equal to the battery voltage

Question 11

The energy density $$u of $$the electric field in a parallel-plate capacitor with dielectric constant $$k is $$given by:

Accepted Answer

$$u = \dfrac{1}{2} k \$$epsilon_0$$ E^2$

Question 12

If the spacing $$d$$ between the plates of a parallel-plate capacitor is doubled while keeping the charge $$Q$$ constant, what happens to the electric field $$E$$ between the plates?

Accepted Answer

$$E$$ remains the same

Question 13

A capacitor with capacitance $$C is $$charged to a potential difference $$\Delta V. $$What is the charge $$Q$$ stored on the capacitor?

Accepted Answer

$$Q = C \Delta V$$

Question 14

Which of the following best describes the effect of inserting a dielectric between the plates of a charged, isolated capacitor?

Accepted Answer

The capacitance increases and the voltage decreases

Question 15

The electric potential energy $$U_{elec} of $$two point charges $$q$$ and $$q'$$ separated by a distance $$r is$$:

Accepted Answer

$$U_{elec} = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{qq'}{r}$$

Question 16

A parallel-plate capacitor is constructed with a plate area of $$0.40\ \mathrm{m}^2$$ and a plate separation of $$0.10\ \mathrm{mm}. It is $$charged to a potential difference of $$12\ \mathrm{V}. $$What is the charge stored on each plate? ($$\$$epsilon_0$$ = 8.85 	imes 10$$^{-12}$$\ \mathrm{C}^2/\mathrm{N} \cdot \mathrm{m}^2)$$

Accepted Answer

$$Q = 4.25 	imes 10$$^{-9}$$\ \mathrm{C}$$

Question 17

Which of the following is true about the direction of the electric field $$\vec{E}$$ relative to the direction of decreasing electric potential $$V$$?

Accepted Answer

$$\vec{E}$$ points in the direction of decreasing $$V$$

Electric Potential and Capacitance: Concepts, Formulas, and Applications

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