Theory of perturbation of electric potential by a 3D object made of an anisotropic dielectric material

TL;DR

This paper extends the boundary condition method to analyze how a 3D anisotropic dielectric object perturbs an electric potential, providing a new theoretical framework for electrostatic problems involving complex materials.

Contribution

The paper formulates the extended boundary condition method for anisotropic dielectric objects, deriving a transition matrix independent of the source potential.

Findings

Derived a Green's identity-based formulation for anisotropic media

Established a transition matrix depending on geometry and material properties

Provided a theoretical basis for electrostatic perturbation analysis

Abstract

The extended boundary condition method (EBCM) was formulated for the perturbation of a source electric potential by a 3D object composed of a homogeneous anisotropic dielectric medium whose relative permittivity dyadic is positive definite. The formulation required the application of Green's second identity to the exterior region to deduce the electrostatic counterpart of the Ewald--Oseen extinction theorem. The electric potential inside the object was represented using a basis obtained by implementing an affine bijective transformation of space to the Gauss equation for the electric field. The EBCM yields a transition matrix that depends on the geometry and the composition of the 3D object, but not on the source potential.