$A$ 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

Three concentric metallic spherical shells of radii $R, 2R, 3R$ are given charges $Q_1, Q_2, Q_3$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then,the ratio of the charges given to the shells,$Q_1 : Q_2 : Q_3$,is

In the absence of other conductors,the surface charge density is:

$A$ circle of radius $a$ has a linear charge density given by $\lambda = \lambda_0 \cos^2 \theta$ on its circumference. What will be the total charge on the circle?

If a metal cube of side $5 \, cm$ has a charge of $6 \, \mu C$,then the surface charge density is