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

The linear charge density on the upper half of a segment of a ring is $\lambda$ and on the lower half,it is $-\lambda$. The direction of the electric field at the centre $O$ of the ring is:

Obtain the expression for the electric field at any point due to a continuous distribution of charge on a $(i)$ line,$(ii)$ surface,and $(iii)$ volume.

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:

$A$ 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?

The surface charge density $\sigma$ on a charged conducting sphere of radius $R$ in terms of the electric field intensity $E$ at a distance $r$ $(r > R)$ in free space is (where $\varepsilon_{0}$ is the permittivity of free space):