In a region of space, the electric field is given by $\overrightarrow{E}=8\hat{\mathrm{i}}+4\hat{\mathrm{j}}+3\hat{\mathrm{k}}$. The electric flux through the surface of the area $100 \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}$ in the $xy$ plane is

A dielectric in the form of a sphere is introduced into a homogeneous electric field. $A$, $B$ and $C$ are three points as shown in the figure. Then

The electric field on two sides of a large charged plate is shown in the figure. The charge density on the plate in SI units is given by (${\epsilon }_0$ is the permittivity of free space in SI units)

An uncharged conducting large plate is placed as shown. Now an electric field $E$ towards the right is applied. Find the induced charge density on the right surface of the plate.

Figure shows a uniformly charged hemisphere of radius $R$. It has a volume charge density $\rho$. If the electric field at a point $2R$ above its centre is $E$, then what is the electric field at the point $2R$ below its centre?

Four very large metal plates are given charges as shown in the figure. The middle two are then connected through a wire. Find the charge that will flow through the wire.