Consider the four surfaces $S_1, S_2, S_3,$ and $S_4$ enclosing the same charge $q_1$ as shown in the figure. Compare the electric flux through these surfaces.

$A$ charged particle $q$ is placed at the centre $O$ of a cube of side length $L$ $(A, B, C, D, E, F, G, H)$. Another identical charge $q$ is placed at a distance $L$ from $O$, outside the cube, as shown in the figure. The electric flux through the face $BGFC$ is

Two surfaces $S_1$ and $S_2$ are shown in the figure. The electric flux associated with $S_1$ is $\phi_1$ and with $S_2$ is $\phi_2$. Which of the following is correct?

$A$ spherical rubber balloon carries a charge $q$ uniformly distributed over its surface. As the balloon is inflated,the total electric flux coming out of the surface:

$A$ charged shell of radius $R$ carries a total charge $Q$. Let $\Phi$ be the flux of the electric field through a closed cylindrical surface of height $h$,radius $r$,with its center coinciding with that of the shell. The center of the cylinder is a point on the axis of the cylinder equidistant from its top and bottom surfaces. Which of the following option$(s)$ is/are correct? [$\epsilon_0$ is the permittivity of free space]
$(1)$ If $h > 2R$ and $r > R$,then $\Phi = \frac{Q}{\epsilon_0}$
$(2)$ If $h < \frac{8R}{5}$ and $r = \frac{3R}{5}$,then $\Phi = 0$
$(3)$ If $h > 2R$ and $r = \frac{4R}{5}$,then $\Phi = \frac{2Q}{5\epsilon_0}$
$(4)$ If $h > 2R$ and $r = \frac{3R}{5}$,then $\Phi = \frac{Q}{5\epsilon_0}$

The electric field ( $\overrightarrow{E}$ in $N C^{-1}$ ) in a region is given by $\overrightarrow{E} = 3 \hat{i} + 5 \hat{j}$. The net electric flux through a square area of side $2 \ m$ parallel to the $y-z$ plane is: