Use Gauss's law to prove that the electric field inside a uniformly charged spherical shell is zero.

Given the electric field in the region $\overrightarrow{E}=2x\hat{i}$, find the net electric flux through the cube and the charge enclosed by it.

Using Gauss's law, deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius $R$ at a point outside the shell.

Plot a graph showing variation of electric field as a function of $r>R$ and $r<R$ ($r$ being the distance from the centre of the shell).

Using Gauss's law, deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius $R$ at a point inside the shell.

Plot a graph showing variation of electric field as a function of $r>R$ and $r<R$($r$ being the distance from the centre of the shell).

Define electric flux quantity?

A point charge $q$ is at a distance of $\frac{d}{2}$ directly above the centre of a square of side $d$, as shown in Fig. 1.163. Use Gauss' law to obtain the expression for the electric flux through the square.