A rigid square loop of side \(a\) and carrying current \(I_2\) is laying on a horizontal surface near a long current \(I_1\) wire in the same plane as shown in figure. The net force on the loop due to the wire will be

\({\text{Force on PQ will be }}{{\text{F}}_1} = {2_B}{\text{Ia}}\)

\({\text{ = }}{{\text{I}}_2}\frac{{{\mu _0}{I_1}}}{{2\pi {\text{a}}}}{\text{a}}\)

\( = \frac{{{\mu _0}I}}{{2\pi {\text{a}}}}{\text{a}}\)

\( = \frac{{{\mu _0}{I_1}{I_2}}}{{2\pi }}\)

Force on \(RS\) will be \(F_{2}=I_{2} B_{2} a\)

\({=\mathrm{I}_{2} \frac{\mu_{0} \mathrm{I}_{1}}{2 \pi 2 \mathrm{a}} \mathrm{a}}\)

\({=\frac{\mu_{0} I_{1} I_{2}}{4 \pi}}\)

Net force \(=\mathrm{F}_{1}-\mathrm{F}_{2}=\frac{\mu_{0} I_1 \mathrm{I}_{2}}{4 \pi}\) repulsion