The magnetic field from a homogeneously magnetized cylindrical tile
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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.
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