A Closed-Form Solution for the Polarizability of a Dielectric Double Half-Cylinder

Abstract

Using the bipolar coordinate system, the electrostatic scattering problem of a dielectric double half-cylinder is solved. In particular, an expression for the polarizability of the half-cylinder is obtained in terms of two dilogarithm functions. Also the nonuniqueness of the solution is proven in a certain range of negative values of the permittivity.