Introduction to Electrodynamics · Problem 5.34

Magnetic Fields in Matter — David J. Griffiths

Physics · magnetic-dipole

Problem

Show that the magnetic field of a dipole can be written in coordinate-free form:

\mathbf{B}_{\text{dip}}(\mathbf{r}) = \frac{\mu_0}{4\pi} \frac{1}{r^3}\left[3(\mathbf{m} \cdot \hat{r})\hat{r} - \mathbf{m}\right].