 Induced magnetic dipole

A small linearly magnetizable sample has a magnetic dipole moment induced by its applied field. In a fixed principal direction, write $m={\alpha }_B{B}_0$; this convention gives ${\alpha }_B$ units $\mathrm{A}{\mathrm{m}}^2{\mathrm{T}}^{-1}$. A uniformly magnetized ellipsoid of volume $V$ has ${\alpha }_B=V\chi /[{\mu }_0(1+N_d\chi )]$. The effective interaction potential energy at fixed source current is $-{\alpha }_B{B}_0^2/2$. The factor one half arises because the moment must be induced as the field is raised; differentiating $-m(B_0)B_0$ as though it described a permanent moment would count the response twice. The response model excludes remanence, nonlinear saturation and hysteresis.