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

$$Q = \$$epsilon_0$$ \dfrac{A}{d} V = 4.25 \times 10$$^{-8}$$ C

Question 1

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

Accepted Answer

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

Question 2

Which of the following statements about electric field lines and equipotential surfaces is correct?

Accepted Answer

Electric field lines are always perpendicular to equipotential surfaces.

Question 3

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

Accepted Answer

The voltage remains equal to the battery voltage.

Question 4

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 separated by d = 2.00$ mm and the potential difference is 500$ V. What is the farthest distance from the negative plate the proton reaches before stopping?

Accepted Answer

$$x_f = \dfrac{m v_i^2$}{2 e (\Delta V)}$$

Question 5

The capacitance $$C of a $$parallel-plate capacitor with plate area $$A$$ and separation $$d is $$given by:

Accepted Answer

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

Question 6

If a dielectric 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 7

The energy stored in a capacitor with capacitance $$C$$ and voltage $$V is$$:

Accepted Answer

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

Question 8

Which of the following best describes the electric field inside a parallel-plate capacitor?

Accepted Answer

It is uniform and points from the positive to the negative plate.

Question 9

A capacitor is charged to a voltage $$V$$ and then disconnected from the battery. If the plate separation is doubled, what happens to the stored energy?

Accepted Answer

It increases by a factor of 2.

Question 10

The electric potential at a point due to multiple point charges is:

Accepted Answer

$$V = \sum_i \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{q_i}{r_i}$$

Question 11

Which of the following is true about the relationship between electric field $$\vec{E}$$ and electric potential $$V$$?

Accepted Answer

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

Question 12

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

Accepted Answer

$$Q = \$$epsilon_0$$ \dfrac{A}{d} V = 4.25 	imes 10$$^{-8}$$ C

Question 13

Which of the following best describes the effect of inserting a dielectric between the plates of a charged capacitor (battery disconnected)?

Accepted Answer

The voltage across the plates decreases.

Question 14

The energy density $$u of $$the electric field in a capacitor is given by:

Accepted Answer

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

Question 15

A capacitor is charged to a voltage $$V$$ and then the battery is removed. If the area of the plates is doubled while keeping the separation constant, what happens to the stored energy?

Accepted Answer

It doubles.

Question 16

Which of the following is the correct unit for capacitance?

Accepted Answer

Farad (F)

Question 17

If the spacing between equipotential surfaces increases, what happens to the electric field strength?

Accepted Answer

It decreases.

Question 18

A capacitor is connected to a battery and then the separation between the plates is increased. What happens to the charge and the electric field between the plates?

Accepted Answer

The charge decreases and the electric field remains constant.

Electric Potential and Capacitance: Study Notes

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