Asymptotic solution for the electrostatic field around a slender conducting body

This paper deals with the electrostatic field around a slender, conducting body, not necessarily of revolution, embedded in an applied potential. In contrast to previous works devoted to a body of revolution we do not place sources on a segment inside the body. Instead we spread a source density on the boundary of the body in order to obtain a well-posed problem. More precisely, the source strength satisfies a well-known Fredholm integral equation of the first kind. This latter is asymptotically inverted with respect to the slenderness ratio by invoking a systematic formula which provides, to any order, the asymptotic estimate of certain integrals. Several comparisons with the behaviour of exact solutions are also proposed.