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The magnetic field from a homogeneously magnetized cylindrical tile

The magnetic field of a homogeneously magnetized cylindrical tile geometry, i.e. an angular section of a finite hollow cylinder, is found. The field is expressed as the product between a tensor field describing the geometrical part of the problem and a column vector holding the magnetization of the tile. Outside the tile, the tensor is identical to the demagnetization tensor. We find that four components of the tensor, $N_{xy},N_{xz},N_{yz}$ and $N_{zy}$, can be expressed fully analytically, while the five remaining components, $N_{xx},N_{yx},N_{yy},N_{zx}$ and $N_{zz}$, contain integrals that have to be evaluated numerically. When evaluated numerically the tensor is symmetric. A comparison between the found solution, implemented in the open source magnetic framework MagTense, and a finite element calculation of the magnetic flux density of a cylindrical tile shows excellent agreement.