An infinitely long current-carrying wire and a small current-carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is $\mathrm{d}\left(\mathrm{d}>>\mathrm{a}\right)$ . If the loop applies a force F on the wire, then

For motion of the loop along  x-direction, P.E. is $\mathrm{U}\left(\mathrm{x}\right)=-\overrightarrow{\mathrm{m}}\cdot \overrightarrow{\mathrm{B}}$
As both $\overrightarrow{\mathrm{m}}$ (of loop) and $\overrightarrow{\mathrm{B}}$(of wire at loop) point normally into the plane of paper,
$\mathrm{U}\left(\mathrm{x}\right)=-\mathrm{mB}=-{\mathrm{\pi a}}^2\mathrm{i}\cdot \frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{\pi x}}=-\frac{{\mathrm{\mu }}_0{\mathrm{iIa}}^2}{2\mathrm{x}}$
P.E. decrease as loop moves closer to the wire. Force on the loop is attractive.
$\mathrm{F}=\frac{\mathrm{dU}}{\mathrm{dx}}=-\frac{{\mathrm{\mu }}_0{\mathrm{iIa}}^2}{2}\left(\frac{1}{{\mathrm{x}}^2}\right)$

$$\begin{gathered} \text{ At x }=\mathrm{d},\mathrm{F}=\frac{{\mathrm{\mu }}_0{\mathrm{iI}}^2{\mathrm{a}}^2}{2{\mathrm{d}}^2}\left(\text{ Attraction }\right) \\ \Rightarrow \mathrm{F}\propto \frac{{\mathrm{a}}^2}{{\mathrm{d}}^2} \end{gathered}$$