Problem 3.38

A charge $q$ is uniformly distributed over the volume of a sphere of radius $R$ . Assuming the permittivity to be equal to unity throughout, find the potential (a) at the centre of the sphere; (b) inside the sphere as a function of the distance $r$ from its centre.

\text { (a) } \varphi_{0}=\frac{3 q}{8 \pi \varepsilon_{0} R} \text { (b) } \varphi=\varphi_{0}\left(1-\frac{r^{2}}{3 R^{2}}\right), r \leqslant R

Constant Electric Field in a Vacuum