Calculation of the electrostatic-potential distribution in ohmic elliptical cylinders fed by a dipole source

Abstract

A simplified representation of anisotropic charge distributions within proteinsWe have developed an analytical method based on Mathieu functions to solve Poisson's equation in homogeneous right elliptical cylinders. We apply the method to a detailed study of the electric-potential distribution in the bulk and on the surface of ohmic conductors of such a shape, fed by a current dipole located at any inside position. Contrary to a common opinion in electrocardiology, the potential contour map on the surface of cylinders of pronounced ellipticity has more than one maximum and one minimum if the dipole is located close and parallel to the symmetry plane containing the axes of greatest lengths, i.e., the ellipse major axis and the cylinder axis. The extrema are located near the intersection with the plane normal to the previous one and containing the dipole axis. We discuss the cases of cylinders with different ellipticity and dimension ratio, focusing on the evolution of the number and position of the surface-potential extrema as a function of the location and orientation of the dipole with respect to the nearby boundary.