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 full cylinders, rings, sectors ring segments. The derivation is done direct integration in surface charge picture. Results are closed-form expressions elliptic integrals. All special cases treated individually, which enables computation all possible position arguments r?R3. An implementation provided Python together with performance analysis. tested against numerical applied to compute discrete Halbach rotation sensor system.