Q: Three Gaussian surfaces enclose charges as follows: Surface 1 encloses $+q$, Surface 2 encloses $-q$, and Surface 3 encloses both $+q$ and $-q$. Rank the net electric flux through these surfaces from smallest to largest.

Surface 2 < Surface 3 < Surface 1

Q: If the electric field is not uniform over a surface, how is the total electric flux $\Phi_E$ through the surface calculated?

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

Q: Which of the following statements is true regarding the electric field at a point on a Gaussian surface surrounding a point charge?

The electric field at a point depends only on the distance from the charge, not on the size or shape of the Gaussian surface.

Q: If a charge inside a Gaussian surface is removed, which of the following will remain unchanged?

Neither the net electric flux nor the electric field at all points will remain unchanged.

Q: Which symmetry is possessed by the electric field of a uniformly charged cube centered at the origin?

Rotation by $90^\circ$ about the $x$, $y$, and $z$ axes, and reflection in any plane containing the center and parallel to the axes.

Q: Which of the following is a correct statement about a Gaussian surface?

It is an imaginary closed surface used to apply Gauss's law.

Question 1

A large sheet of positive charge lies in the $xz$ plane at $y=0$. Which of the following symmetries must the electric field produced by this sheet possess?

Accepted Answer

Translation symmetry along the $x$ and $z$ axes, rotation symmetry about the $y$ axis, and reflection symmetry in the $xz$ plane.

Question 2

Which electric field pattern is consistent with the symmetries of a uniformly charged infinite plane located at $y=0$ in the $xz$ plane?

Accepted Answer

A uniform field pointing in the $+y$ direction above the plane and $-y$ direction below the plane.

Question 3

A spherical shell and a cubical shell are both centered at the origin and have uniform surface charge. Which electric field pattern is consistent with the symmetry of the spherical shell?

Accepted Answer

A radial field pointing outward from the center, with magnitude depending only on the distance from the origin.

Question 4

Which of the following statements about the electric flux through a closed surface is correct according to Gauss's law?

Accepted Answer

The net electric flux through a closed surface is proportional to the net charge enclosed within the surface.

Question 5

A closed surface surrounds a region of space with no net charge inside. What is the net electric flux through the surface?

Accepted Answer

$0$

Question 6

Three Gaussian surfaces enclose charges as follows: Surface 1 encloses $+q$, Surface 2 encloses $-q$, and Surface 3 encloses both $+q$ and $-q$. Rank the net electric flux through these surfaces from smallest to largest.

Accepted Answer

Surface 2 < Surface 3 < Surface 1

Question 7

The electric flux $\Phi_E$ through a flat surface of area $A$ in a uniform electric field $E$ is given by which formula?

Accepted Answer

$\Phi_E = E A \cos 	heta$

Question 8

A uniform electric field of $3000\,\mathrm{N/C}$ points in the $x$ direction. A flat surface of area $1.0\,\mathrm{m}^2$ is tilted $30^\circ$ from the $xy$ plane. What is the magnitude of the electric flux through the surface?

Accepted Answer

$1500\,\mathrm{N\cdot m^2/C}$

Question 9

If the electric field is not uniform over a surface, how is the total electric flux $\Phi_E$ through the surface calculated?

Accepted Answer

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

Question 10

A point charge $q$ is at the center of a spherical Gaussian surface of area $A$. What is the magnitude of the electric field at the surface?

Accepted Answer

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

Question 11

A cylindrical rod of radius $r$ has uniform volume charge density $\rho$. Two coaxial cylindrical Gaussian surfaces are drawn, one with radius $r$ and one with radius $2r$. What is the ratio of the electric flux through the larger surface to the smaller surface?

Accepted Answer

$2$

Question 12

Which of the following statements is true regarding the electric field at a point on a Gaussian surface surrounding a point charge?

Accepted Answer

The electric field at a point depends only on the distance from the charge, not on the size or shape of the Gaussian surface.

Question 13

If a charge inside a Gaussian surface is removed, which of the following will remain unchanged?

Accepted Answer

Neither the net electric flux nor the electric field at all points will remain unchanged.

Question 14

Which symmetry is possessed by the electric field of a uniformly charged cube centered at the origin?

Accepted Answer

Rotation by $90^\circ$ about the $x$, $y$, and $z$ axes, and reflection in any plane containing the center and parallel to the axes.

Question 15

A flat surface of area $A$ is placed in a uniform electric field $E$ at an angle $	heta$ to the field. What is the component of the electric field passing normal to the surface?

Accepted Answer

$E \cos 	heta$

Question 16

Which of the following is a correct statement about a Gaussian surface?

Accepted Answer

It is an imaginary closed surface used to apply Gauss's law.

Question 17

A spherical shell of charge is centered at the origin. Which of the following electric field patterns is inconsistent with the shell's symmetry?

Accepted Answer

A field with different magnitudes along the $x$, $y$, and $z$ axes.

Question 18

Which of the following is true about the electric flux through a closed surface surrounding a net negative charge?

Accepted Answer

The net electric flux is inward and negative.

Electric Fields, Symmetry, and Electric Flux: Study Notes

Study Guide - Practice Questions

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