d
Force on arm \(A B\) due to current in conductor \(X Y\) is

\({F_1} = \frac{{{\mu _0}}}{{4\pi }}\frac{{2IiL}}{{(L/2)}} = \frac{{{\mu _0}Ii}}{\pi }\)

acting towards \(X Y\) in the plane of loop. Force on arm \(C D\) due to current in conductor \(X Y\) is

\({F_2} = \frac{{{\mu _0}}}{{4\pi }}\frac{{2IiL}}{{3(L/2)}} = \frac{{{\mu _0}Ii}}{{3\pi }}\)

acting away from \(X Y\) in the plane of loop.

\(\therefore\) Net force on the loop \(=F_{1}-F_{2}\)

\(=\frac{\mu_{0} I i}{\pi}\left[1-\frac{1}{3}\right]=\frac{2}{3} \frac{\mu_{0} I i}{\pi}\)