JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Magnetic Effects of Current

The long wire's field at distance $r$ is $B=\frac{{\mu }_0{I}_1}{2\pi r}$. The loop's near side, at distance $a$, feels $F_1=I_{2}Ba=\frac{{\mu }_0{I}_1{I}_2}{2\pi }$, while the far side at $2a$ feels $F_2=\frac{{\mu }_0{I}_1{I}_2}{4\pi }$; the two sides perpendicular to the wire give equal and opposite pulls that cancel. The near side dominates, and with the currents there running opposite to the wire it is pushed away, so the net force is $F_1-F_2=\frac{{\mu }_0{I}_1{I}_2}{2\pi }-\frac{{\mu }_0{I}_1{I}_2}{4\pi }=\frac{{\mu }_0{I}_1{I}_2}{4\pi }$, directed away from the wire.