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THE MAGNETIC FIELD ABOUT A THREE-DIMENSIONAL BLOCK NEODYMIUM MAGNET

Part of: Discrete geometry Generalities, axiomatics, foundations of continuum mechanics of solids Plastic materials, materials of stress-rate and internal-variable type

Published online by Cambridge University Press:  22 June 2020

GRAHAM WEIR Open the ORCID record for GRAHAM WEIR [Opens in a new window] ,
GEORGE CHISHOLM Open the ORCID record for GEORGE CHISHOLM [Opens in a new window]  and
JEROME LEVENEUR Open the ORCID record for JEROME LEVENEUR [Opens in a new window]
GRAHAM WEIR*
Affiliation:
Massey University Manawatu, Private Bag 11 222, Palmerston North4442, New Zealand
GEORGE CHISHOLM
Affiliation:
GNS Science, PO Box 30-368, Lower Hutt5040, New Zealand; e-mail G.Chisholm@gns.cri.nz, J.Leveneur@gns.cri.nz
JEROME LEVENEUR
Affiliation:
GNS Science, PO Box 30-368, Lower Hutt5040, New Zealand; e-mail G.Chisholm@gns.cri.nz, J.Leveneur@gns.cri.nz
*
e-mail: grahamweir@xtra.co.nz
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Abstract

Neodymium magnets were independently discovered in 1984 by General Motors and Sumitomo. Today, they are the strongest type of permanent magnets commercially available. They are the most widely used industrial magnets with many applications, including in hard disk drives, cordless tools and magnetic fasteners. We use a vector potential approach, rather than the more usual magnetic potential approach, to derive the three-dimensional (3D) magnetic field for a neodymium magnet, assuming an idealized block geometry and uniform magnetization. For each field or observation point, the 3D solution involves 24 nondimensional quantities, arising from the eight vertex positions of the magnet and the three components of the magnetic field. The only unknown in the model is the value of magnetization, with all other model quantities defined in terms of field position and magnet location. The longitudinal magnetic field component in the direction of magnetization is bounded everywhere, but discontinuous across the magnet faces parallel to the magnetization direction. The transverse magnetic fields are logarithmically unbounded on approaching a vertex of the magnet.

Keywords

3D magnetic fieldblock magnetneodymiummagnetization

MSC classification

Primary: 74C99: None of the above, but in this section
Secondary: 52C35: Arrangements of points, flats, hyperplanes 74A45: Theories of fracture and damage
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 4 , October 2020 , pp. 386 - 405
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Copyright
© Australian Mathematical Society 2020

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References

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