The electric intensity due to an infinite cylinder of radius $R$ and having charge $q$ per unit length at a distance $r(r > R)$ from its axis is

Shown in the figure are two point charges $+Q$ and $-Q$ inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If $\sigma _1$ is the surface charge on the inner surface and $Q_1$ net charge on it and $\sigma _2$ the surface charge on the outer surface and $Q_2$ net charge on it then

In the figure, a very large plane sheet of positive charge is shown. $P _{1}$ and $P _{2}$ are two points at distance $l$ and $2 \,l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields $E_{1}$ and $E_{2}$ at $P _{1}$ and $P _{2}$ respectively are

Let $E_1(r), E_2(r)$ and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$, an infinitely long wire with constant linear charge density $\lambda$, and an infinite plane with uniform surface charge density $\sigma$. if $E_1\left(r_0\right)=E_2\left(r_0\right)=E_3\left(r_0\right)$ at a given distance $r_0$, then

Electric field at a point varies as ${r^o}$ for

A sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre, for $x < R$, the electric field is directly proportional to