Given: Edge length of a square loop kept in $XZ$ plane with its centre at origin is $2a$,

current through the loop is I,

current through a wire kept parallel to $z$ axis at $(0,\text{\ }b,0)$ is also $I,b > > a$.

To find: $\tau$, the magnitude of torque on the square loop about the $z$ axis.

As $b > > a$, the distance between the wire and the square loop is $b$.

Magnitude of magnetic field due to the wire at the location of square loop:

$$B = \frac{\mu_{0}I}{2\pi b}$$

Magnetic moment of the square loop:

$$M = I(2a)^{2}$$

Torque on the square loop

$$\tau = MBsin\theta = I(2a)^{2}\frac{\mu_{0}I}{2\pi b}sin90$$

$$\tau = \frac{2\mu_{0}I^{2}a^{2}}{\pi b}$$