What will be the total flux through the faces of the cube as shown in the figure with side of length $a$ if a charge $q$ is placed at:
$(a)$ $C$: centre of a face of the cube.
$(b)$ $D$: midpoint of $B$ and $C$.

$A$ point charge causes an electrical flux of $-1.0 \times 10^3 \ Nm^2 \ C^{-1}$ to pass through a spherical Gaussian surface of $10 \ cm$ radius centered on the charge. If the radius of the Gaussian surface were $3$ times,how much flux would pass through the surface?

$A$ positive charge $q$ is kept at the center of a thick shell of inner radius $R_1$ and outer radius $R_2$ which is made up of conducting material. If $\phi_1$ is the flux through a closed Gaussian surface $S_1$ whose radius is just less than $R_1$ and $\phi_2$ is the flux through a closed Gaussian surface $S_2$ whose radius is just greater than $R_1$,then:

Four closed surfaces $S_1, S_2, S_3$ and $S_4$ together with charges $+q, -q$ and $-2q$ are shown. Through which one of the surfaces is the net flux zero?

Let the electrostatic field $E$ at distance $r$ from a point charge $q$ not be an inverse square but instead an inverse cubic, e.g., $E = k \cdot \frac{q}{r^3} \hat{r}$, where $k$ is a constant.
Consider the following two statements:
$(I)$ Flux through a spherical surface enclosing the charge is $\phi = q_{\text{enclosed}} / \varepsilon_0$.
$(II)$ $A$ charge placed inside a uniformly charged shell will experience a force.
Which of the above statements are valid?

What is the net flux of the uniform electric field of $E = 3 \times 10^{3} \hat{i} \; N/C$ through a cube of side $20 \; cm$ oriented so that its faces are parallel to the coordinate planes?