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

• Published in: Journal of magnetism and magnetic materials Vol. 559; p. 169482
• Main Authors: Slanovc, F., Ortner, M., Moridi, M., Abert, C., Suess, D.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-10-2022
• Subjects: Analytical expression; Cylinder; Cylinder tile; Halbach; Magnetic field; Surface charge; Surface integral; Uniformly magnetized; Cylinder; Halbach; Surface charge; Surface integral; Cylinder tile; Analytical expression; Uniformly magnetized; Magnetic field
• ISSN: 0304-8853
• DOI: 10.1016/j.jmmm.2022.169482

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∈R3. 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.
•Derivation of analytical formulas for magnetic field of cylinder tile.•Inclusion of special cases cylinder rings, sectors and full cylinders.•Implementation in open source library Magpylib.