[QUE/EM-02022] EM-PROBLEM

A solid sphere of radius \(R\) carries a charge density \(\rho(\vec{r})\).
Show that the average of the electric field inside the sphere is
\[\vec{E}= - \frac{1}{4\pi\epsilon_0} \frac{\vec{p}}{R^3},\]
where \(\vec{p}\) is the total dipole moment of the sphere.