Question 1

A solid conducting sphere of radius $$R$$ carries a total charge $$q. $$What is the electric field $$E at a $$distance $$r$$ from the center, where $$r \u003c R$$?

Accepted Answer

$$E = 0$$

Question 2

For a solid conducting sphere of radius $$R$$ and charge $$q$$, what is the electric potential $$V at a $$distance $$r$$ from the center, where $$r \u003c R$$?

Accepted Answer

$$V = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{q}{R}$$

Question 3

A parallel-plate capacitor is connected to a battery of voltage $$V_b. If $$the plate separation $$d is $$doubled while the battery remains connected, what happens to the charge $$Q on $$the plates?

Accepted Answer

It is halved.

Question 4

The capacitance of a parallel-plate capacitor is given by $$C = \$$epsilon_0$$ \dfrac{A}{d}. $$Which change will increase the capacitance?

Accepted Answer

Doubling the plate area $$A.$$

Question 5

Two capacitors, $$C_1$$ and $$C_2$$, are connected in series. What is the equivalent capacitance $$C_{eq}$$?

Accepted Answer

$$\dfrac{1}{C_{eq}} = \dfrac{1}{C_1$} + \dfrac{1}{C_2$}$$

Question 6

A plastic disk of radius $$R is $$uniformly charged on its surface with charge density $$\sigma. $$What is the general approach to find the electric potential $$V at a $$point $$P on $$the axis a distance $$z$$ above the center?

Accepted Answer

Integrate the contributions from each ring element of charge on the disk.

Question 7

In a region with a uniform electric field $$\vec{E}$$ between two parallel plates, what is the relationship between the electric potential $$V$$ and the distance $$y$$ from the negative plate?

Accepted Answer

$$V = Ey$$

Question 8

Which statement about equipotential surfaces and electric field lines is correct?

Accepted Answer

Equipotential surfaces are always perpendicular to electric field lines.

Question 9

A camera flash uses a capacitor to store energy. Why is a capacitor used instead of a battery to deliver the flash?

Accepted Answer

A capacitor can release energy much more quickly than a battery.

Question 10

If a negative charge is moved in the direction of a uniform electric field, what happens to its electric potential and electric potential energy?

Accepted Answer

Potential increases, potential energy decreases.

Question 11

A parallel-plate capacitor is disconnected from a battery after being charged. If the plate separation is doubled, what happens to the voltage across the plates?

Accepted Answer

It doubles.

Question 12

Which of the following best describes the energy stored in a capacitor?

Accepted Answer

It is stored in the electric field between the plates.

Question 13

A capacitor is charged to a voltage $$V$$ and then disconnected from the battery. If the area of the plates is doubled while the separation remains the same, what happens to the voltage across the plates?

Accepted Answer

It decreases by a factor of four.

Question 14

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

Accepted Answer

The total capacitance is the sum of the individual capacitances.

Question 15

A spherical capacitor consists of two concentric spheres of radii $$r_a$$ and $$r_b$$ ($$r_b \u003e r_a). $$What is the capacitance?

Accepted Answer

$$C = 4\pi\$$epsilon_0$$ \dfrac{r_a r_b}{r_b - r_a}$$

Question 16

Which of the following is a real-world application of supercapacitors?

Accepted Answer

Energy storage for alternate energy systems.

Question 17

If the electric field between two parallel plates is $$E$$ and the distance between the plates is $$d$$, what is the potential difference $$V$$ between the plates?

Accepted Answer

$$V = Ed$$

Question 18

Which of the following statements about the relationship between gravitational and electric potential energy is correct?

Accepted Answer

Gravitational potential energy is analogous to electric potential energy.

Question 19

A capacitor is used in a defibrillator to deliver a quick burst of energy. Which property of capacitors makes them suitable for this application?

Accepted Answer

They can release stored energy very quickly.

Electric Potential and Capacitance: Concepts, Calculations, and Applications

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