Forces and torque on a pair of uncharged conducting cylinders in an external electric field

Exact results are given for the forces per unit length acting on each of a pair of parallel conducting cylinders when polarized by an external electric field perpendicular to the cylinders. Simple analytic results are obtained at small and large separations of the cylinders. The torque on the cylinders (which acts to align them with the electric field) is proportional to the difference between the longitudinal and transverse polarizabilities. The forces acting on the cylinders (which are equal and opposite) are given by the derivatives of the polarizabilities with respect to their separation.