If some charge is given to a solid metallic sphere,the field inside remains zero and by Gauss's law all the charge resides on the surface. Now,suppose that Coulomb's force between two charges varies as $1 / r^{3}$. Then,for a charged solid metallic sphere

If charge $q$ is placed on one of the vertex of a cube, then total electric flux passing through the cube is . . . . . . .

$A$ charged spherical shell of radius $R$ carries a total charge $Q$. Let $\Phi$ be the electric flux through a closed cylindrical surface of height $h$ and 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 statement$(s)$ 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 $\Phi = \frac{Q}{5\epsilon_0}$

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$-axis in the $y-z$ plane at $z=\frac{\sqrt{3}}{2} a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $A B C D$ lying in the $x-y$ plane with its center at the origin is $\frac{\lambda L }{ n \varepsilon_0}$ (where $\varepsilon_0$ is the permittivity of free space),then the value of $n$ is

The charge distribution is shown in the figure below. The electric flux through the surface $S$ due to these charges is .........

Which among the following has dimensions of charge?