Magnetic Forces in Systems of Dipoles and Polarized Matter in Isolated and Dispersed States

Magnetic forces, associated with magnetic dipoles and isolated polarized matter in nonuniform magnetic fields, are considered. Thermodynamic intensive formulation of magnetic energy is used to derive the forces and related stress tensors. It is shown that the total magnetic force acting on magnetizable matter in isolated as well as dispersed states is given by the negative gradient of magnetic potential energy, whereas the force given by the magnetic dipole model, being part of the former, holds for the isolated state, provided that ∇× H = 0. Magnetic forces that act on magnetizable particulates in dispersed states are derived using both intensive and extensive formulations of magnetic energy and also by direct use of gradient of magnetic energy. These forces are shown to differ from the dipole model and to depend on magnetization of particulates, field gradients, and on gradients of magnetic energy density of the dispersion, which thus can be linked to diffusion effects.