A square loop $ABCD$ carrying a current $i,$ is placed near and coplanar with a long straight conductor $XY$ carrying a current $I,$ the net force on the loop will be
NEET 2016, Medium
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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 $=F_{1}-F_{2}$
$=\frac{\mu_{0} I i}{\pi}\left[1-\frac{1}{3}\right]=\frac{2}{3} \frac{\mu_{0} I i}{\pi}$
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