A charge $Q$ is distributed uniformly on a ring of radius $r$. A sphere of equal radius $r$ is constructed with its centre at the periphery of the ring. Find the flux of the electric field through the surface of the sphere.

Figure (a) shows an imaginary cube of edge $L/2$. A uniformly charged rod of length $L$ moves towards left at a small but constant speed $v.$ At $t=0,$ the left end of the rod just touches the right face of the cube. Which of the graphs in the Figure (b) represents the flux of the electric field through the cube as the rod goes through it?

A hemispherical body is placed in a uniform electric field $E$. What is the flux linked with the curved surface if the field is $\left(\mathrm{i}\right)$ parallel to the base of the body [Figure (a)]; $\left(\mathrm{ii}\right)$ perpendicular to base of the body [Figure (b)] and $\left(\mathrm{iii}\right)$ perpendicular to the curved surface at every points as in Figure (c).

In which position ($A,B,C$ or $D$) of the second charge, the flux of the electric field through the hemisphere remains unchanged?

 A point charge $Q$ is located just above the center of the flat face of a hemisphere of radius $R$ as in figure. What is the flux

(a) through the curved surface, and

(b) through the flat face?

(c) Repeat parts (a) and (b) if the charge is exactly at the centre.

In figure, a cone lies in a uniform electric field $E$. Determine the electric flux entering the cone.

(a) A point charge $q$ is located at distance $d$ from an infinite plane. Determine the electric flux through the plane due to the point charge.

(b) A point charge $q$ is located at a very small distance from the center of a very large square on the line perpendicular to the square passing through its center. Determine the approximate electric flux through the square due to the point charge.

Calculate the total electric flux through the paraboloidal surface due to a uniform electric field of magnitude $E_0$ in the direction shown in figure.