Relation between surface curvature and electrostatic potential of a long charged isolated conductor

Abstract

In this paper, we analyze the relation between the surface curvature of an isolated charged conductor and resultant electrostatic potential. The study will be performed for a long conductor with uniform cross section. It will be demonstrated by geometric arguments that a correlation between curvature and potential exists. This relation will be obtained for a set of polar coordinates that parameterize the surface of the isolated conductor. Two examples will be discussed based on quasi-circular conducting cylinders, whose cross sections are obtained firstly perturbing the equation of the circle by a cosine function and secondly by a more general function including a Fourier series expansion.