# The magnetic field from a homogeneously magnetized cylindrical tile

Source: [The magnetic field from a homogeneously magnetized cylindrical tile](<https://www.sota2.com/research/paper/68fa3bef1e209131ce8d6aae>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T00:51:50.098Z

Authors: K. K. Nielsen, R. Bj{\\o}rk

Published: 2020-04-15T17:31:10.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2004.11701>)

[PDF](<https://arxiv.org/pdf/2004.11701.pdf>)