Question 1

Which of the following best describes the electric flux $$\Phi_E$$ through a flat surface of area $$A$$ when the electric field $$\vec{E} is $$parallel to the surface, as shown in the first image?

Accepted Answer

$$\Phi_E = 0$$

Question 2

A cube of side $$L is $$placed in a uniform electric field $$\vec{E} = -B \hat{i} + C \hat{j} - D \hat{k}$$, where $$B$$, $$C$$, and $$D$$ are constants. What is the total electric flux through the entire cube?

Accepted Answer

$$\Phi_E = 0$$

Question 3

According to Gauss's Law, what is the net electric flux through a closed surface that encloses a net charge $$Q$$?

Accepted Answer

$$\Phi_E = Q/\$$epsilon_0$$

Question 4

A point charge $$Q is $$placed at the center of a spherical Gaussian surface of radius $$R. $$What is the electric field at the surface?

Accepted Answer

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

Question 5

Which of the following statements is true regarding the electric flux through a closed surface if all charges are outside the surface?

Accepted Answer

The net electric flux is zero.

Question 6

A uniformly charged insulating sphere of radius $$R$$ has total charge $$Q. $$What is the electric field at a distance $$r \u003c R$$ from the center?

Accepted Answer

$$E = \dfrac{Q r}{4\pi \$$epsilon_0$$ R^3$}$$

Question 7

A long, straight wire carries a uniform line charge density $$\lambda. $$Using Gauss's Law, what is the electric field at a distance $$r$$ from the wire?

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

A conducting spherical shell has inner radius $$a$$ and outer radius $$b. A $$point charge $$Q is $$placed at the center. What is the electric field at a distance $$r$$ such that $$r \u003c a$$?

Accepted Answer

$$E = \dfrac{Q}{4\pi \$$epsilon_0$$ r^2$}$$

Question 10

If the net electric flux through a closed surface is zero, which of the following must be true?

Accepted Answer

The net charge enclosed by the surface is zero.

Question 11

A parallel-plate capacitor consists of two large plates with equal and opposite charges $$\pm Q$$ and area $$A. $$What is the electric field between the plates (neglecting edge effects)?

Accepted Answer

$$E = \dfrac{Q}{\$$epsilon_0$$ A}$$

Question 12

Which of the following best explains why Gauss's Law is especially useful for calculating electric fields in systems with high symmetry?

Accepted Answer

It allows the electric field to be taken out of the integral when it is constant over the Gaussian surface.

Question 13

A cube encloses a charge $$+q at $$its center. If the charge is doubled to $$+2q$$, what happens to the electric flux through the cube?

Accepted Answer

It doubles.

Question 14

A closed surface encloses both a charge $$+q$$ and a charge $$-q. $$What is the net electric flux through the surface?

Accepted Answer

$$0$$

Question 15

A Gaussian surface encloses a region of space where the electric field is zero everywhere. What can you conclude about the net charge enclosed?

Accepted Answer

The net charge enclosed is zero.

Question 16

A water flow analogy is used to explain electric flux. If more electric field lines enter a closed surface than leave, what does this indicate about the net charge inside?

Accepted Answer

There is a net negative charge inside.

Question 17

The permittivity of free space $$\$$epsilon_0$$ is a fundamental constant. Which of the following best describes its physical meaning?

Accepted Answer

It quantifies the ability of a vacuum to permit electric field lines.

Question 18

A cube of side $$L is $$placed in a uniform electric field $$\vec{E}$$ directed along the $$z-$$axis. What is the net electric flux through the cube?

Accepted Answer

$$0$$

Question 19

A point charge $$Q is $$placed at the center of a conducting spherical shell with total charge $$-3Q. $$What is the net charge on the outer surface of the shell?

Accepted Answer

$$-2Q$$

Gauss’s Law and Electric Flux: Structured Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards