The magnetic scalar potential and demagnetization vector for a cylinder tile

TL;DR

This paper derives an exact analytical solution for the magnetic scalar potential of a uniformly magnetized cylinder and its slice, expressed via elliptic integrals, and validates it against finite element simulations.

Contribution

It provides a closed-form solution for the magnetic scalar potential of cylindrical magnets using elliptic integrals, including a demagnetization vector formulation.

Findings

Analytical expressions match finite element simulations perfectly.

Solution applies to both cylindrical slices and full cylinders.

Demagnetization vector encapsulates geometric information.

Abstract

A closed-form solution for the magnetic scalar potential generated by a uniformly magnetized cylindrical slice and a full cylinder is determined by solving Poisson's equation analytically. The solution is given in terms of elliptic integrals of the first, second and third kind. We show that the magnetic scalar potential can be written as the dot product of a demagnetization vector, containing all the geometric information of the generating cylinder, and the magnetization. We validate the derived analytical expressions for the magnetic scalar potential by comparing with a finite element simulation and show that these agree perfectly for both the cylindrical slice and the full cylinder.