Conducting cylinders in an external electric field: Polarizability and field enhancement

We obtain a simple and exact expression for the average field Eave in the gap between cylinders of arbitrary radii and separation. For given external field E0 parallel to the plane of the cylinder axes, Eave/E0 increases in proportion to s-1/2 as the separation s of the cylinders tends to zero. In addition, exact expressions are derived for the longitudinal and transverse polarizabilities of a pair of cylinders, and for their contact values.