= Induced magnetic dipole
{title2=$\mathbf m=\alpha_B\mathbf B_0,\quad U_{\rm eff}=-\alpha_BB_0^2/2$}
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 $\mathrm{A\,m^2\,T^{-1}}$. 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 $-\alpha_BB_0^2/2$. 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.
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