The electric field intensity at a point at a distance $r$ from the axis of an infinitely long pipe having a linear charge density $q$ is proportional to:

The electric field in a region is radially outward with magnitude $E = A r_0$. The charge contained in a sphere of radius $r_0$ centered at the origin is

The figure shows a hollow hemisphere of radius $R$ in which two charges $3q$ and $5q$ are placed symmetrically about the centre $O$ on the planar surface. The electric flux over the curved surface is

Two infinite parallel metal planes contain electric charges with charge densities $+\sigma$ and $-\sigma$ respectively, and they are separated by a small distance in air. If the permittivity of air is $\varepsilon_{0}$, then the magnitude of the field between the two planes with its direction will be:

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ is carved out of it,as shown,the ratio $\frac{|\overrightarrow{E}_{A}|}{|\overrightarrow{E}_{B}|}$ of the magnitude of the electric field $\overrightarrow{E}_{A}$ and $\overrightarrow{E}_{B}$ respectively,at points $A$ and $B$ due to the remaining portion is

Let $\rho (r) = \frac{Q}{\pi R^4} r$ be the volume charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $p$ inside the sphere at distance $r_1$ from the centre of the sphere,the magnitude of the electric field is: