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.