Answer
${\bf 0.123}\;\rm T$
Work Step by Step
We need the magnetic force to make the net torque exerted on the loop zero.
$$\sum \tau=0\;\rm N$$
So the magnetic force should force the loop to move counterclockwise since the block is forcing the loop to move clockwise.
Hence, the net torque around the nonmagnetic axle is then
$$\mu B\sin90^\circ-mg (d/2)=0$$
where $d$ is the distance between the two long wires,
$$(NIA)B =\dfrac{mgd}{2}$$
Hence,
$$B=\dfrac{mgd}{2NIA}$$
Plug the known;
$$B=\dfrac{(50\times 10^{-3})(9.8)(0.05)}{2(10)(2)(0.05\times 0.10)}$$
$$B=\color{red}{\bf 0.123}\;\rm T$$
