Electric Charges & Fields: Gauss's Law

A point charge $+Q$ is enclosed by a spherical Gaussian surface. If the charge is doubled to $+2Q$, what happens to the electric flux through the surface?

A cube with side length $a$ encloses a point charge $q$ at its center. What is the electric flux through one face of the cube?

The electric flux through a closed cylindrical surface is given by $\Phi_E = kA$, where $A$ is the area of the curved surface and $k$ is a constant. If the electric field is not uniform, what is the enclosed charge?

Which Gaussian surface is most appropriate for calculating the electric field due to a point charge?

Why is a cylindrical Gaussian surface suitable for calculating the electric field of an infinitely long charged wire?

A charge distribution has a complex, non-symmetric shape. Which of the following Gaussian surfaces would be most effective for simplifying the calculation of the electric field?

A charge $q$ is enclosed within a spherical Gaussian surface of radius $r$. If the radius of the Gaussian surface is increased to $2r$, what happens to the electric flux through the surface?

A point charge is enclosed by two different Gaussian surfaces, one a small sphere and the other a large cube. How does the electric flux through the two surfaces compare?

Two charges, $+q$ and $-q$, are enclosed within separate Gaussian surfaces. Surface A encloses $+q$, and surface B encloses both charges. What is the net electric flux through surface B?

An electric field is given by $\vec{E} = E_0 \hat{i}$, where $E_0$ is a constant. A rectangular Gaussian surface is oriented such that its faces are either parallel or perpendicular to the x-axis. On which faces of the rectangle is the integral $\oint \vec{E} \cdot d\vec{A}$ equal to zero?