Electric dipole — UPSC Physics Optional CSE 2011 Paper I

Determine the torque experienced by an electric dipole of moment \vec{p} if placed in an electric field \vec{E} in nonaligned state. Also show that the interaction energy of two dipoles of moments \vec{p}_1 and \vec{p}_2 separated by a displacement \vec{r} is U=\frac{1}{4\pi\epsilon_0}\frac{1}{r^3}\left[\vec{p}_1\cdot\vec{p}_2-3(\vec{p}_1\cdot\hat{r})(\vec{p}_2\cdot\hat{r})\right] assuming the expression for field due to a dipole.