Question 1

Which of the following best expresses Gauss's Law in integral form for a closed surface $$S$$ enclosing a net charge $$q_{in}$$?

Accepted Answer

$$\oint_S \vec{E} \cdot d\vec{A} = \frac{q_{in}}{\epsilon_0}$$

Question 2

A point charge $$q is $$placed at the center of a spherical Gaussian surface of radius $$r. $$What is the electric flux through the surface?

Accepted Answer

$$\frac{q}{\epsilon_0}$$

Question 3

For a continuous charge distribution with charge density $$\rho(\vec{x})$$, what is the total charge enclosed by a volume $$V$$?

Accepted Answer

$$q_{in} = \int_V d^3x\, \rho(\vec{x})$$

Question 4

Which of the following is the correct expression for the electric field outside a long, straight line of charge with linear charge density $$\lambda$$?

Accepted Answer

$$E = \frac{\lambda}{2\pi \epsilon_0 y}$$

Question 5

The electric field between the plates of a parallel-plate capacitor is given by which of the following?

Accepted Answer

$$E = \frac{V}{d}$$

Question 6

A planar sheet of charge has a surface charge density $$\sigma. $$What is the magnitude of the electric field just outside the sheet?

Accepted Answer

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

Question 7

What is the potential energy of a system of two point charges $$q_1$$ and $$q_2$$ separated by a distance $$r$$?

Accepted Answer

$$U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r}$$

Question 8

Which of the following correctly relates the electric field $$\vec{E} to $$the electric potential $$V$$?

Accepted Answer

$$\vec{E} = -
abla V$$

Question 9

A spherical conductor of radius $$R$$ carries a total charge $$Q. $$What is the electric field just outside its surface?

Accepted Answer

$$E = \frac{Q}{4\pi\epsilon_0 R^2}$$

Question 10

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

Accepted Answer

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

Question 11

Which of the following is the correct expression for the electric potential $$V at a $$distance $$r$$ from a point charge $$q$$?

Accepted Answer

$$V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$$

Question 12

If the electric field in a region is constant and points in the $$x-$$direction, what is the potential difference $$V_B - V_A$$ between two points $$A$$ and $$B$$ separated by a distance $$d$$ along the $$x-$$axis?

Accepted Answer

$$V_B - V_A = -E d$$

Question 13

Which of the following is the correct unit for capacitance?

Accepted Answer

$$1\,\mathrm{F} = 1\,\mathrm{C}/\mathrm{V}$$

Question 14

A parallel-plate capacitor is filled with a dielectric material of dielectric constant $$\kappa. $$What is the new capacitance?

Accepted Answer

$$C = \kappa \epsilon_0 \frac{A}{d}$$

Question 15

Which of the following best describes the relationship between electric flux $$\Phi_E$$ and electric field $$\vec{E}$$ through a surface $$A$$?

Accepted Answer

$$\Phi_E = \int \vec{E} \cdot d\vec{A}$$

Question 16

In spherical coordinates, what is the correct expression for the differential volume element $$d^3x$?

Accepted Answer

$$d^3x = r^2 \sin	heta\, dr\, d	heta\, d\phi$$

Study Notes: Gauss's Law, Electric Potential, and Capacitance

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