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.

A conic surface is placed in a uniform electric field $E$ as shown in the figure such that the field is perpendicular to the surface on the side $AB$. The base of the cone is of the radius $R$, and the height of the cone is $h$. The angle of the cone is $\mathrm{\theta }$. Find the magnitude of the flux that enters the cone’s curved surface from the left side. Do not count the outgoing flux $\left(\mathrm{\theta }<45°\right)$.