Induced magnetic bead force
= Induced magnetic bead force
For a linear isotropic unsaturated effective susceptibility contrast $\Delta\chi$, the induced-moment energy is $-V\Delta\chi B^2/(2\mu_0)$, giving $\mathbf F=V\Delta\chi\nabla B^2/(2\mu_0)$. The one-half differs from the fixed permanent-dipole energy because the applied field creates the moment. Demagnetization and saturation are absorbed into or replace the assumed response model.