Question 1

A point charge $$q is $$placed at the center of a conducting spherical shell of radius $$R. $$What is the magnitude of the electric field just outside the shell?

Accepted Answer

$$E = \dfrac{q}{4\pi\$$epsilon_0$$ R^2$}$$

Question 2

Which of the following correctly expresses the electric field at a distance $$z$$ above the center of a charged disk of radius $$R$$ and uniform surface charge density $$\sigma$$?

Accepted Answer

$$E = \dfrac{\sigma}{2\$$epsilon_0$$} \left(1 - \dfrac{z}{\sqrt{z^2$ + R^2$}} \right)$$

Question 3

A parallel plate capacitor is filled with a dielectric of constant $$\kappa. If $$the original capacitance was $$C_0$$, what is the new capacitance?

Accepted Answer

$$C = \kappa C_0$

Question 4

Which equation gives the electric potential $$V at a $$distance $$r$$ from a point charge $$q$$?

Accepted Answer

$$V = \dfrac{q}{4\pi\$$epsilon_0$$ r}$$

Question 5

A dipole with moment $$p is $$placed in a uniform electric field $$E. $$What is the potential energy of the dipole when it makes an angle $$	heta$$ with the field?

Accepted Answer

$$U = -pE \cos 	heta$$

Question 6

A charged ring of radius $$R$$ carries a total charge $$q. $$What is the electric field at a point on the axis of the ring, a distance $$z$$ from its center?

Accepted Answer

$$E = \dfrac{qz}{4\pi\$$epsilon_0$$ (z^2$ + R^2$)^{3/2}$$}$

Question 7

If $$n$$ capacitors, each of capacitance $$C$$, are connected in parallel, what is the equivalent capacitance?

Accepted Answer

$$C_{eq} = nC$$

Question 8

A uniformly charged infinite sheet produces an electric field. What is the magnitude of the field at a point near the sheet?

Accepted Answer

$$E = \dfrac{\sigma}{2\$$epsilon_0$$}$$

Question 9

Which of the following correctly expresses Gauss's Law in integral form?

Accepted Answer

$$\Phi = \oint \vec{E} \cdot d\vec{A} = \dfrac{q_{enc}}{\$$epsilon_0$$}$$

Question 10

A parallel plate capacitor has plates of area $$A$$ separated by distance $$d. $$What is its capacitance?

Accepted Answer

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

Question 11

A spherical conductor of radius $$R is $$charged to potential $$V. $$What is the total charge on the sphere?

Accepted Answer

$$q = 4\pi\$$epsilon_0$$ R V$$

Question 12

A capacitor stores charge $$q at $$potential difference $$V. $$What is the energy stored in the capacitor?

Accepted Answer

$$U = \dfrac{1}{2} q V$$

Question 13

A line of charge with linear charge density $$\lambda$$ produces an electric field at a distance $$r. $$What is the magnitude of the field?

Accepted Answer

$$E = \dfrac{\lambda}{2\pi\$$epsilon_0$$ r}$$

Question 14

Which of the following is the correct expression for the electric field due to a point charge $$q at a $$distance $$r$$?

Accepted Answer

$$E = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{|q|}{r^2$}$$

Question 15

A cylindrical capacitor has inner radius $$a$$ and outer radius $$b. $$What is its capacitance per unit length?

Accepted Answer

$$C = \dfrac{2\pi\$$epsilon_0$$}{\ln(b/a)}$$

Question 16

Which of the following correctly expresses the potential energy of a capacitor in terms of its capacitance $$C$$ and voltage $$V$$?

Accepted Answer

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

Question 17

A parallel plate capacitor is connected to a battery and then disconnected. If the plates are pulled apart, what happens to the energy stored in the capacitor?

Accepted Answer

The energy increases because $$U = \dfrac{1}{2} \dfrac{q^2$}{C}$$ and $$C$$ decreases.

Question 18

Which of the following is the correct expression for the electric field inside a parallel plate capacitor with a dielectric of constant $$\kappa$$?

Accepted Answer

$$E = \dfrac{\sigma}{\kappa \$$epsilon_0$$}$$

Question 19

A conducting sphere of radius $$R is $$isolated in space. What is its capacitance?

Accepted Answer

$$C = 4\pi\$$epsilon_0$$ R$$

Electrostatics and Capacitance: Key Equations and Concepts

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