Magnetic dipole — UPSC Physics Optional CSE 2008 Paper I

Show that the interaction energy of two magnetic dipoles \bar{m}_1 and \bar{m}_2 separated by a displacement \bar{r} is given by U = \frac{\mu_0}{4\pi} \cdot \frac{1}{r^3} \left[ \bar{m}_1 \cdot \bar{m}_2 - 3(\bar{m}_1 \cdot \hat{r})(\bar{m}_2 \cdot \hat{r}) \right]. If two magnetic dipoles are held at a fixed distance apart, but allowed to rotate freely, what would be the configuration for stable equilibrium ?