Magnetic dipole field
= Magnetic dipole field
Outside a localized magnetic dipole $\boldsymbol\mu$, the vacuum field in Gaussian conventions is
$$
\mathbf B(\mathbf r)=\frac{3(\boldsymbol\mu\mathbin\cdot\mathbf r)\mathbf r}{r^5}-\frac{\boldsymbol\mu}{r^3}.
$$
For a dipole along the polar axis, $B_r=2\mu\cos\theta/r^3$ and $B_\theta=\mu\sin\theta/r^3$.