Legendre polynomial expansion of the potential of a uniformly charged disk

TL;DR

This paper presents a method using Legendre polynomial expansion to analytically compute the electrostatic potential and electric field of a uniformly charged disk, providing a precise mathematical approach.

Contribution

The paper introduces a novel application of Legendre polynomial expansion to derive the potential and electric field of a charged disk, enhancing analytical techniques in electrostatics.

Findings

Derived explicit formulas for potential and electric field

Validated the expansion method against known solutions

Provided a mathematical framework for similar charge distributions

Abstract

We use a Legendre polynomial expansion to find the electrostatic potential of a uniformly charged disk. We then use the potential to find the electric field of the disk.