# Proceedings of the Forum "Math-for-Industry" 2019The Magnetic Field About a Three-Dimensional Cylindrical Magnet

Proceedings of the Forum "Math-for-Industry" 2019: The Magnetic Field About a Three-Dimensional... [Cylindrical magnets are widely used in industrial applications. We calculate the 3D magnetic field for a cylindrical magnet, assuming uniform magnetisation along the cylinder axis. The exact solution for the components of the magnetic field in the axial (radial) direction involves complete elliptic integrals of the first and third (second) kinds. The fixed points of the magnetic field are associated with a coaxial circle on the magnet surface and centred on the magnet midpoint. Away from this region, the corresponding magnetic field will approximate that from a circular disk. The only unknown is the magnetisation, with all other model parameters defined by the corresponding geometry. The vertical component of the magnetic field is bounded everywhere, but the radial component is logarithmically divergent about the upper and lower magnet edges. Because most commercially available cylindrical neodymium magnets have heights somewhat smaller than their radius, the magnetic field is locally sensitive to spatial variations in magnetisation, which will produce a variable surface magnetic field, over the length scale of the magnetic domains.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Proceedings of the Forum "Math-for-Industry" 2019The Magnetic Field About a Three-Dimensional Cylindrical Magnet

Part of the Mathematics for Industry Book Series (volume 36)
Editors: McKibbin, Robert; Wake, Graeme; Saeki, Osamu
14 pages

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Publisher
Springer Nature Singapore
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022
ISBN
978-981-19-1153-8
Pages
65 –79
DOI
10.1007/978-981-19-1154-5_3
Publisher site
See Chapter on Publisher Site

### Abstract

[Cylindrical magnets are widely used in industrial applications. We calculate the 3D magnetic field for a cylindrical magnet, assuming uniform magnetisation along the cylinder axis. The exact solution for the components of the magnetic field in the axial (radial) direction involves complete elliptic integrals of the first and third (second) kinds. The fixed points of the magnetic field are associated with a coaxial circle on the magnet surface and centred on the magnet midpoint. Away from this region, the corresponding magnetic field will approximate that from a circular disk. The only unknown is the magnetisation, with all other model parameters defined by the corresponding geometry. The vertical component of the magnetic field is bounded everywhere, but the radial component is logarithmically divergent about the upper and lower magnet edges. Because most commercially available cylindrical neodymium magnets have heights somewhat smaller than their radius, the magnetic field is locally sensitive to spatial variations in magnetisation, which will produce a variable surface magnetic field, over the length scale of the magnetic domains.]

Published: Sep 11, 2022

Keywords: 3D magnetic field; Cylindrical magnet; Magnetisation; Conceptual model; MCS2000 primary 74C99 and secondary 52C35 and 74A45