Closed-form solution for a pair of touching cylindrical conductors in an external electric field

We give expressions for the electric potential and field around two conducting cylinders in contact, in closed form and in terms of elementary functions. The polarizability tensor, and hence the torque acting on the cylinder pair, follow from these results. The surface charge density, and the total charge per unit length on each cylinder, can also be evaluated in closed form. The equal and opposite forces on the two cylinders are found in the case of equal cylinder radii.