 Solution

Define $\mathbf{d}$ to point from the negative charge to the positive charge. The electric dipole moment is $\mathbf{p}=q\mathbf{d}$. In a uniform electric field, the two forces cancel, so the net force is zero. They nevertheless form a couple with torqueFor a positive angular displacement increasing $\theta$, the restoring torque component is $-pE\sin \theta$. Thus $dU/d\theta =pE\sin \theta$ andwith the additive constant chosen to make $U=0$ at $\theta =\pi /2$. Alignment is a stable minimum and antialignment an unstable maximum. The zero-force result uses a uniform field; a field gradient can exert a net force on a dipole.