Problem 3.96

A dielectric ball is polarized uniformly and statically. Its polarization equals P. Taking into account that a ball polarized in this way may be represented as a result of a small shift of all positive charges of the dielectric relative to all negative charges, (a) find the electric field strength E inside the ball; (b) demonstrate that the field outside the ball is that of a dipole located at the centre of the ball, the potential of that field being equal to $\varphi=\mathbf{p}_ {0} \mathbf{r} / 4 \pi \varepsilon_{0},$ where $\mathbf{p}_{0}$ is the electric moment of the ball, and $\mathbf{r}$ is the distance from its centre.