$A$ 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:

$A$ charge is spread non-uniformly on the surface of a hollow sphere of radius $R$,such that the charge density is given by $\sigma = \sigma_0(1 - \sin \theta)$,where $\theta$ is the usual polar angle. The potential at the centre of the sphere is

Electric charge is transferred to an irregular metallic disk as shown in the figure. If $\sigma_1, \sigma_2, \sigma_3$ and $\sigma_4$ are surface charge densities at the given points,then choose the correct answer from the options given below:

$A$ 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

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

$A$ non-uniformly shaped conductor is charged. Then,at its sharpest point: