The torque on a loop of wire (a magnetic dipole) in a uniform magnetic field is τ = NIAB sin θ, where θ is the angle between B and a line perpendicular to the loop of wire. Suppose an electric dipole, consisting of two charges ±q a fixed distance d apart is in a uniform electric field E.
(a) Show that the net electric force on the dipole is zero.
(b) Let θ be the angle between E and a line running from the negative to the positive charge. Show that the torque on the electric dipole is τ = qdE sin θ for all angles −180° ≤ θ ≤ 180°. (Thus, for both electric and magnetic dipoles, the torque is the product of the dipole moment times the field strength times sin θ. The quantity qd is the electric dipole moment; the quantity NIA is the magnetic dipole moment.)