Full analytical solution for the magnetic field of uniformly magnetized cylinder tiles

TL;DR

This paper provides a comprehensive analytical solution for calculating the magnetic field of uniformly magnetized cylinder tiles and related geometries, using direct integration and elliptic integrals, with practical Python implementation.

Contribution

It introduces a closed-form analytical method for magnetic field computation of various magnetized cylinder geometries, including special cases, with an accompanying Python implementation.

Findings

Validated the analytical solutions against numerical methods.

Demonstrated application to a Halbach cylinder configuration.

Provided performance analysis of the implementation.

Abstract

We present an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and by extension solutions for full cylinders, rings, cylinder sectors and ring segments. The derivation is done by direct integration in the magnetic surface charge picture. Results are closed-form expressions and elliptic integrals. All special cases are treated individually, which enables the field computation for all possible position arguments. An implementation is provided in Python together with a performance analysis. The implementation is tested against numerical solutions and applied to compute the magnetic field in a discrete Halbach cylinder.