A Novel Variational Principle in Electrostatics and its Consequences

TL;DR

This paper introduces a new variational principle in electrostatics that enables deriving the mirror equation for image problems and connects to Green's differential equation, offering a fresh theoretical framework.

Contribution

It presents a novel variational principle in electrostatics and demonstrates its ability to derive classical equations like the mirror and Green's equations.

Findings

Derivation of mirror equation from the new variational principle

Connection between the variational principle and Green's differential equation

Potential for new analytical methods in electrostatics

Abstract

We propose a novel variational principle in electrostatics and show that one can derive mirror equation in the context of image problem starting from this principle. The corresponding Euler-Lagrange equation is seen to lead to Green's differential equation (also known as Thomson's equation).