Potential, Field, and Interactions of Multipole Spheres: Coated Spherical Magnets
Journal of Magnetism and Magnetic Materials
Elsevier BV * North-Holland
NSF, Division of Chemistry (CHE) 1808225
NSF, Division of Chemistry (CHE)
We show that the energy, force, and torque between two spherically symmetric multipole density distributions are identical to those between two point multipoles, and apply this point-sphere equivalence to coated spherical dipole magnets. We also show that the potential and field of such a distribution are equivalent to those due to point multipoles located at the center of the distribution. We expand the inverse-distance potential in terms of harmonic (Hermite irreducible) tensors, whose properties enable us to express the potential energy, force, and torque for two arbitrary source distributions in a series of point-multipole interactions. This work generalizes recent work on interactions between uniformly magnetized dipole spheres [B. F. Edwards, D. M. Riffe, J.-Y. Ji, and W. A. Booth, Am. J. Phys. 85, 130 (2017)] to interactions between spherically-symmetric multipole spheres.
Ji, Jeong-Young, et al. “Potential, Field, and Interactions of Multipole Spheres: Coated Spherical Magnets.” Journal of Magnetism and Magnetic Materials, vol. 529, July 2021, p. 167861, doi:10.1016/j.jmmm.2021.167861.