A wire $AB$ of length $L$ has linear charge density $\lambda =kx$, where $x$ is measured from the end $A$ of the wire. This wire is enclosed by a Gaussian hollow surface. Find the expression for the electric flux through this surface.

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).