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

$A$ long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. Then

Three infinitely long charge sheets are placed as shown in the figure. The electric field at point $P$ is

In the figure,a very large plane sheet of positive charge is shown. $P_{1}$ and $P_{2}$ are two points at distances $l$ and $2l$ 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:

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R/2$ with its centre on the axis of the cylinder,as shown in the figure. The magnitude of the electric field at the point $P$,which is at a distance $2R$ from the axis of the cylinder,is given by the expression $\frac{23\rho R}{16K\varepsilon_0}$. The value of $K$ is

If $q$ is the charge per unit area on the surface of a conductor,then the electric field intensity at a point on the surface is