IMAGE THEORY FOR A POINT-CHARGE INSIDE A LAYERED DIELECTRIC SPHERE

Following the approach of Neumann and Lindell [i] we derive an image line source that produces in a homogeneous medium the same electric field as a point charge inside a layered dielectric sphere. The image charge density function for the sphere with two interfaces is solved analytically, and approximations are derived in the case of a thin layer and a low-contrast layer. An image expression for the thin-layered sphere with three interfaces is developed. We suggest that point charge approximations of the image charge may be used to speed up computations of the electric potential on the scalp due to sources in the brain.