Capacitance between Two Points in an Infinite Grid

TL;DR

This paper analyzes the capacitance between two points in an infinite grid of capacitors by solving difference equations using separation of variables, providing a mathematical approach to a classic problem.

Contribution

It introduces a method to solve the capacitance problem in an infinite capacitor grid through difference equations and symmetry exploitation.

Findings

Capacitance can be derived using superposition and symmetry.

Solution involves infinite linear difference equations.

Method provides a systematic approach to similar problems.

Abstract

The capacitance between two adjacent nodes on an infinite square grid of identical capacitors can easily be found by superposition, and the solution is found by explotting the symmetry of the grid. The mathematical problem presented in this work involves the solution of an infinite set of linear, inhomogenous difference equations which are solved by the method of separation of variables.