Nondipole interaction between two uniformly magnetized spheres and its relation to superconducting levitation

TL;DR

This paper analytically investigates the magnetic interaction between two uniformly magnetized spheres, revealing that it differs from point dipole interactions and explaining implications for superconducting levitation.

Contribution

It provides an exact analytical solution to the magnetostatic problem for two magnetized spheres and clarifies misconceptions about their interaction compared to point dipoles.

Findings

Magnetic interaction between spheres is not equivalent to point dipole interaction.

Nonzero levitation force demonstrates the difference in interactions.

Analytical solution in bispherical coordinates confirms non-equivalence.

Abstract

Analytically solving the magnetostatic Maxwell equations in the bispherical coordinates, we calculate the magnetic field around two uniformly magnetized spheres oriented so that their magnetic moments are parallel to the axis passing through the centers of the spheres. We demonstrate that, contrary to what is often claimed in the literature, the magnetic interaction between such spheres is not equivalent to the interaction between two point magnetic dipoles placed in the centers of the spheres. The nonzero levitation force acting on a uniformly magnetized sphere or a point magnetic dipole above a superconducting sphere in the ideal Meissner state is a clear manifestation of the non-equivalence.