Two spherical hollow spheres of radii $R_1$ and $R_2$ are charged with the same charge $Q$. If $\sigma_1$ and $\sigma_2$ are their respective surface charge densities, then the ratio $\sigma_1 : \sigma_2$ is:

Two isolated metallic spheres of radii $2 \,cm$ and $4 \,cm$ are given equal charge,then the ratio of charge density on the surfaces of the spheres will be

$A$ spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a net charge $Q$. $A$ point charge $-q$ is placed at the center of the shell. Determine the surface charge density on the inner and outer surfaces of the shell.

$A$ square plate of side $a$ is placed in the $xy$-plane with its center at the origin. If the surface charge density of the square plate is given by $\sigma = xy$,then the total charge on the plate will be:

$A$ thin square plate is placed in the $x-y$ plane as shown in the figure,such that its center coincides with the origin. Its charge density at point $(x, y)$ is $\sigma = \sigma_0 xy$ (where $\sigma_0$ is a constant). Find the total charge on the plate.

$A$ particle of mass $2 \times 10^{-6} \ kg$ with a charge $5 \times 10^{-6} \ C$ is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 N^{-1} m^{-2}$ and $g = 10 \ m \ s^{-2}$)