= Force on a small linearly magnetizable body
{title2=$\mathbf F=\alpha_B\nabla B_0^2/2$}
For constant scalar response $\mathbf m=\alpha_B\mathbf B_0$ and a body small compared with the applied field's spatial variation scale, the gradient of the <induced magnetic dipole> energy gives $\mathbf F=\alpha_B\nabla B_0^2/2$. Along an axis this is $F_z=m\,dB_0/dz$. For an ellipsoidal body, put $\chi_{\rm eff}=\chi/(1+N_d\chi)$ to obtain $F_z=\mu_0V\chi_{\rm eff}H_0H'_0$. Positive effective <magnetic susceptibility> attracts the body towards stronger field; a negative response repels it. Reversing the source current leaves the force unchanged because both the induced moment and the field gradient reverse. Shape and orientation enter through the <demagnetizing factor>, not merely through volume.
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