A conductor AB of length l carrying current i is placed perpendicular to a long straight conductor carrying a current I as shown. Force on AB will be

Consider an element of length dx on AB at a distance x from XY.

Force on this element, $\mathrm{dF}=\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{\pi x}}\mathrm{idx}$

Total force on the conductor AB

$=\frac{{\mathrm{\mu }}_0\mathrm{Ii}}{2\mathrm{\pi }}\underset{\mathrm{l}/2}{\overset{3\mathrm{l}/2}{\int }}\frac{1}{\mathrm{x}}\mathrm{dx}=\frac{{\mathrm{\mu }}_0\mathrm{Ii}}{2\mathrm{\pi }}{\log }_{\mathrm{e}}3$