Question

Using Gauss's law derive an expression for the electric field intensity due to a uniform charged thin spherical shell at a point.
(i) Outside the shell
(ii) Inside the shell

Answer 1

Let, R be the radius of the shell and Q be the charge uniformly distributed on the surface.

i) For a point outside the shell :

By Gauss's law, $E.4\pi r^2=\frac{Q_{en}}{{ϵ}_0}$

here $r$ be the distance from centre of shell $(r>R)$ and charge enclosed by surface $Q_{eq}=Q$

So, $E_{out}=E=\frac{Q}{4\pi {ϵ}_0{r}^2}$

ii) For a point inside the shell :

By Gauss's law, $E.4\pi r^2=\frac{Q_{en}}{{ϵ}_0}$

here $r$ be the distance from centre of shell $(r<R)$ and charge inside the shell, $Q_{eq}=0$

So, $E_{in}=E=0$