$A$ 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:

If a solid and a hollow conducting sphere have the same radius, then:

The radius of a charged metal sphere $(R)$ is $10 \, cm$ and its potential is $300 \, V$. Find the charge density on the surface of the sphere.

Write an equation for the electric potential due to a linear charge distribution.

$A$ solid sphere of radius $R_1$ and volume charge density $\rho = \frac{\rho_0}{r}$ is enclosed by a hollow sphere of radius $R_2$ with negative surface charge density $\sigma$, such that the total charge in the system is zero. $\rho_0$ is a positive constant and $r$ is the distance from the centre of the sphere. The ratio $R_2/R_1$ 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