Analogy of the grounded conducting sphere image problem with mirror optics

TL;DR

This paper demonstrates that the grounded conducting sphere image problem can be understood using mirror optics principles, providing a new approach to solve for extended charge distributions near the sphere.

Contribution

It introduces a novel analogy between electrostatic image problems and mirror optics, offering a new method for solving extended charge distributions.

Findings

Image charge information derived from mirror equation

Method for extended charge distributions near grounded sphere

Unified approach linking electrostatics and optics

Abstract

We show that in the grounded conducting sphere image problem, all the necessary information about the image charge can be found from a mirror equation and a magnification formula. Then, we propose a method to solve the image problem for an extended charge distribution near a grounded conducting sphere.