Introduction to Electrodynamics · Problem 3.36

Potentials — David J. Griffiths

Physics · electric-field-dipole

Problem

Show that the electric field of a (perfect) dipole (Eq. 3.103) can be written in the coordinate-free form

\mathbf{E}_{\text{dip}}(\mathbf{r}) = \frac{1}{4\pi\epsilon_0}\frac{1}{r^3}[3(\mathbf{p}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}} - \mathbf{p}].