Electrostatic potential of a uniformly charged disk through Green's theorem

TL;DR

This paper demonstrates that using Green's theorem simplifies the calculation of the electrostatic potential of a uniformly charged disk, making it a straightforward process compared to traditional complex methods.

Contribution

It revisits and applies Duffin and McWhirter's method, showing it significantly simplifies potential calculations for planar charged bodies.

Findings

Green's theorem simplifies potential calculations

Method reduces computational complexity

Potential of a disk can be obtained easily

Abstract

All existing derivations of the electrostatic potential of a uniformly charged disk are technically rather involved. In an old and now almost forgotten publication, Duffin and McWhirter proposed a method for calculating the electrostatic potentials of planar bodies by a skillful application of Green's theorem. It is shown that this method significantly simplifies the problem of calculating the electrostatic potential of a uniformly charged disk and makes it an almost trivial task.