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

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 r is an element of R-3. 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 and a rotation sensor system.

Automated summary

This paper presents an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and extends it to solutions for full cylinders, rings, cylinder sectors, and ring segments. The solution is derived by direct integration in the magnetic surface charge picture, resulting in closed-form expressions and elliptic integrals. All special cases are treated individually, allowing the computation of the magnetic field for all possible position arguments r ∈ R-3. A Python implementation and performance analysis are provided, and the implementation is tested against numerical solutions and applied to compute the magnetic field in a discrete Halbach cylinder and a rotation sensor system.