Potential, field, and interactions of multipole spheres: Coated spherical magnets

• Published in: Journal of magnetism and magnetic materials 2021-07, Vol.529 (C), p.167861, Article 167861
• Main Authors: Ji, Jeong-Young, Edwards, Boyd F., Spencer, J. Andrew, Held, Eric D.
• Format: Article
• Language: English
• Subjects: Dipoles; Equivalence; Magnets; Materials Science; Multipoles; Physics; Potential energy; Spheres; Spherically symmetric dipole multipole magnets; Tensors; Torque
• ISSN: 0304-8853; 1873-4766
• DOI: 10.1016/j.jmmm.2021.167861

•Interactions between uniformly magnetized dipole spheres are generalized to multipoles.•Potentials and fields of multipole distributions are expressed by harmonic tensors.•Force and torque between two multipole distributions are presented.•Equivalence of spherically symmetric distribution and a point multipole is shown. 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.