= Force on a current loop in a bilinear magnetic field
{title2=$\mathbf F=I\alpha a^3(\hat{\mathbf x}+\hat{\mathbf y})/2$}
For a square spanning $0\leq x,y\leq a$, with current counterclockwise as seen from positive $z$, an applied field $B_z=\alpha xy$ vanishes on two edges. Integrating $I\,d\boldsymbol\ell\times\mathbf B$ on the other two gives the displayed force. Its direction reverses with the current. The formula concerns the loop, not unspecified supply leads, and cannot be replaced by a small-loop approximation without checking the field variation.
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