Force on arm AB due to current in conductor XY is

${F_1} = {{{\mu _0}} \over {4\pi }}{{2IiL} \over {\left( {L/2} \right)}} = {{{\mu _0}Ii} \over \pi }$

acting towards XY in the plane of loop.

Force on arm CD due to current in conductor XY is

${F_2} = {{{\mu _0}} \over {4\pi }}{{2IiL} \over {3\left( {L/2} \right)}} = {{{\mu _0}Ii} \over {3\pi }}$

acting away from XY in the plane of loop.

$\therefore$ Net force on the loop = F₁ – F₂

$= {{{\mu _0}Ii} \over {3\pi }}\left[ {1 - {1 \over 3}} \right] = {2 \over 3}{{{\mu _0}Ii} \over \pi }$