The two point charges, q and −q, are 2d apart. We form a z-axis through both charges. Let the two charges be at (0,0,d) and (0,0,—d) in the figure. Let's say that p is any point in space which is very distant (r>>d).

(a) Show that the electric potential at point P is \Phi(\overrightarrow{\mathrm{r}})=\frac{1}{4 \pi \epsilon_{0}} \frac{\overrightarrow{\mathrm{p}} \cdot \hat{\mathrm{r}}}{r^{2}} (b) Use equation (11) to prove that the field \overrightarrow{\mathrm{E}}(\overrightarrow{\mathrm{r}})=\frac{1}{4 \pi \epsilon_{0}} \frac{3(\overrightarrow{\mathrm{p}} \cdot \hat{\mathbf{r}}) \hat{\mathbf{r}}-\overrightarrow{\mathrm{p}}}{r^{3}}