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.

Development of a unified FDTD-FEM library for electromagnetic analysis with CPU and GPU computing

“…where a is the radius of the cylinder, n is an integer parameter and is an small number [3]. The analytical expression developed by Neipp et al in [3] relates the curvature of an infinite conductor and the electrostatic potential.…”

“…The analytical expression developed by Neipp et al in [3] relates the curvature of an infinite conductor and the electrostatic potential.…”

“…where r and θ are the cylindrical coordinates, φ 0 is the potential at the surface of the conductor and b 0 is a constant coefficient defined in [3]. Therefore, the Laplace's equation ∇ 2 φ = 0 is considered.…”