(a) (i) Derive an expression for potential energy of an electric dipole $\vec{p}$ in an external uniform electric field $\vec{E}$. When is the potential energy of the dipole (1) maximum, and (2) minimum ? (ii) An electric dipole consists of point charges $-1.0\text{ pC}$ and $+1.0\text{ pC}$ located at $(0, 0)$ and $(3\text{ mm}, 4\text{ mm})$ respectively in x - y plane. An electric field $\vec{E} = \left(\frac{1000\text{ V}}{\text{m}}\right)\hat{i}$ is switched on in the region. Find the torque $\vec{\tau}$ acting on the dipole.