An Invariant General Solution for the Magnetic Fields within and Surrounding a Small Spherical Particle in an Imposed Arbitrary Magnetic Field and the Resulting Magnetic Force and Couple

摘要

A general coordinate-system invariant solution for the magnetic field and flux density within and surrounding a spherical particle in a linearly magnetizable medium in an arbitrary, externally applied field is developed for cases where the particle possesess homogeneous permanent and/or linear magnetization. The solution is consistent with the equations of magnetostatics and asymptotically exact in a regular perturbation sense, where the expansion parameter is the ratio of particle radius a to characteristic length scale L for variations in the externally applied field. Expressions for the magnetic field and flux, accurate to O(a/L), are used to determine the magnetic force and couple exerted on the particle by integration of the Maxwell stress tensor over the particle surface. This result is shown to be the same for some of the various reported expressions for the magnetic body force density (e.g., the Kelvin, Helmholtz, and Korteweg-Helmholtz) and is consistent with previously derived expressions for the magnetic force. It is further shown that the effective dipole method yields results consistent with these calculations. The results may be applied to the analogous electrostatic situation by replacing the magnetic quantities by their electric analogues.