Analytical Solution for the Electric Field Response Generated by a Nonconducting Ellipsoid (Prolate Spheroid) in a Conducting Fluid Subject to an External Electric Field

Abstract

An analytical solution is presented for the electric field response generated by a nonconducting ellipsoid (prolate spheroid) in a homogeneous conducting fluid subject to an external primary electric field, including surface charge distribution. Such a solution might be useful for different purposes, including cell modeling subject to an external quasistatic electromagnetic stimulus. The solution utilizes the well-known analogy between the electrostatics of dielectrics and DC conduction. The solution obtained includes an expression for the volumetric fields and an expression for the induced surface charge density at the membrane.