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

$$Q = 4.25 \times 10$$^{-8}$$\ \mathrm{C}$$

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 connected to a battery and fully charged. If the battery is then disconnected and the plate separation is increased, what happens to the voltage across the plates?

Accepted Answer

The voltage increases.

Question 3

Which of the following best describes the relationship between electric field lines and equipotential surfaces?

Accepted Answer

Electric field lines are always perpendicular to equipotential surfaces.

Question 4

A parallel-plate capacitor has plates of area $$A$$ and separation $$d. $$What is its capacitance?

Accepted Answer

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

Question 5

If a dielectric with dielectric constant $$k is $$inserted between the plates of a capacitor, what happens to the capacitance?

Accepted Answer

The capacitance increases by a factor of $$k.$$

Question 6

A proton is shot into a parallel-plate capacitor with a potential difference of $$500\ \mathrm{V}$$ and plate separation $$2.00\ \mathrm{mm}. If $$its initial speed is $$2.0 	imes 10^5$\ \mathrm{m/s}$$, what is the farthest distance from the negative plate it reaches before stopping?

Accepted Answer

$$x_f = \dfrac{m v_i^2$}{2 e \Delta V} \cdot d + 0$$

Question 7

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

Accepted Answer

$$U = \dfrac{1}{2} C (\Delta V)^2$

Question 8

Which of the following is true about the electric potential at the center of a square formed by four identical charges $$q at $$the corners, with side length $$a$$?

Accepted Answer

$$V = \dfrac{4 k q}{a \sqrt{2}}$$

Question 9

A capacitor is charged to a potential difference $$\Delta V_C$$ using a battery. What happens to the charge on the capacitor if the battery is removed?

Accepted Answer

The charge remains constant.

Question 10

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

Accepted Answer

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

Question 11

Which of the following statements about the electric field $$\vec{E}$$ and potential $$V is $$correct?

Accepted Answer

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

Question 12

A parallel-plate capacitor with area $$0.40\ \mathrm{m}^2$$ and separation $$0.10\ \mathrm{mm} is $$charged to $$12\ \mathrm{V}. $$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

$$Q = 4.25 	imes 10$$^{-8}$$\ \mathrm{C}$$

Question 13

Which of the following best describes the effect of increasing the plate area $$A of a $$parallel-plate capacitor while keeping the separation $$d$$ constant?

Accepted Answer

The capacitance increases.

Question 14

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{q q'}{r}$$

Question 15

A capacitor is charged to a potential difference $$\Delta V$$ and then disconnected from the battery. If a dielectric is inserted between the plates, what happens to the stored energy?

Accepted Answer

The stored energy decreases.

Question 16

Which of the following is the correct unit for capacitance?

Accepted Answer

Farad ($$\mathrm{F})$$

Question 17

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

The electric field remains constant.

Question 18

A $$1\ \mathrm{eV} ($$electron volt) is equivalent to:

Accepted Answer

$$1.60 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 19

Which of the following best describes the effect of inserting a dielectric into a capacitor connected to a battery?

Accepted Answer

The charge on the plates increases.

Electric Potential and Capacitance: Study Notes

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