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

Two infinite plane parallel sheets separated by a distance $d$ have equal and opposite uniform charge densities $\sigma$ and $-\sigma$. The electric field at a point between the sheets is

As shown in the figure,a ball $B$ is suspended by a string $S$ from a large charged plate $P$ such that it makes an angle $\theta$ with the plate. The surface charge density of the plate is proportional to which of the following?

$A$ solid metallic sphere has a charge $+3Q$. Concentric with this sphere is a conducting spherical shell having charge $-Q$. The radius of the sphere is $a$ and that of the spherical shell is $b$ $(b > a)$. What is the electric field at a distance $R$ $(a < R < b)$ from the center?

$A$ solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho = \kappa r^a$,where $\kappa$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r = \frac{R}{2}$ is $\frac{1}{8}$ times that at $r = R$,find the value of $a$.

If the electric field intensity in a fair weather atmosphere is $100 \, V/m$,then the total charge on the earth's surface is ............ $C$ (radius of the earth is $6400 \, km$).