We use simple symmetry arguments suitable for undergraduate students to demonstrate that the magnetic energy, forces, and torques between two uniformly magnetized spheres are identical to those between two point magnetic dipoles. These arguments exploit the equivalence of the field outside of a uniformly magnetized sphere with that of a point magnetic dipole, and pertain to spheres of arbitrary sizes, positions, and magnetizations. The point dipole/sphere equivalence for magnetic interactions may be useful in teaching and research, where dipolar approximations for uniformly magnetized spheres can now be considered to be exact. The work was originally motivated by interest in the interactions between collections of small neodymium magnetic spheres used as desk toys.
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February 2017
February 01 2017
Interactions between uniformly magnetized spheres
Boyd F. Edwards;
Boyd F. Edwards
Department of Physics,
Utah State University
, Logan, Utah 84322
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D. M. Riffe;
D. M. Riffe
Department of Physics,
Utah State University
, Logan, Utah 84322
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Jeong-Young Ji;
Jeong-Young Ji
Department of Physics,
Utah State University
, Logan, Utah 84322
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William A. Booth
William A. Booth
Department of Physics,
Utah State University
, Logan, Utah 84322
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Am. J. Phys. 85, 130–134 (2017)
Article history
Received:
May 31 2015
Accepted:
December 14 2016
Citation
Boyd F. Edwards, D. M. Riffe, Jeong-Young Ji, William A. Booth; Interactions between uniformly magnetized spheres. Am. J. Phys. 1 February 2017; 85 (2): 130–134. https://doi.org/10.1119/1.4973409
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