Question

Find ampere force acting on the frame

Answer 1

Force of attraction between parallel currents
$F_1=\left[\frac{{\mu }_0}{2\pi }\frac{2I{I}_0}{(2\eta +1)\frac{a}{2}}\right]a$
Similarly force of repulsion between antiparallel currents
$F_2=\left[\frac{{\mu }_0}{2\pi }\frac{2I{I}_0}{(\eta +1)\frac{a}{2}}\right]a$
Net force of attraction between the square frame and the long straight wire
$F=F_1-F_2=\frac{{\mu }_0}{2\pi }\frac{I{I}_0}{4{\eta }^2-1}$
Putting values: $F=4\times {10}^{9}N=40nN$