The field due to an infinite dielectric cylinder between two parallel conducting planes

Abstract

This paper shows that, whatever the distance of the cylinder from the planes, this field can be calculated by first solving an infinite set of linear equations with comparatively simple coefficients. By neglecting all except the first few unknowns, a good approximation to the correct solution is obtained. The simplest approximation is sufficient for most practical purposes, and it is shown that the increase in capacity between the planes due to the presence of the cylinder is nearly proportional to the cylinder radius squared times a simple function of its dielectric constant, provided that this radius is small compared with the distance between the planes.