Polarizability of two parallel conducting circular cylinders

We give exact results for the polarizabilities, longitudinal and transverse, of two parallel cylinders of the same radius. The expressions are infinite sums, which converge rapidly if the cylinders are separated by a radius or more. In close approach the sums converge slowly, but are replaced by equivalent integral expressions, which give simple analytical results in this limit. The contact values of the longitudinal and transverse polarizabilities are π2/6 and π2/12 times the large-separation values. The longitudinal contact value is approached infinitely rapidly as the separation tends to zero, while the approach of the transverse polarizability to its contact value is regular.