Fig. $\left(a\right)$ shows a square loop, $20 \mathrm{cm}$ on each side in the $x-y$ plane with its Centre at the origin. The loop carries a current of $78 \mathrm{A}$. above it at $y=0, z=12 \mathrm{cm}$ is an infinitely long wire parallel to the $\mathrm{x}$$-$axis carrying a current of 10 A. Find the torque on the loop.

Torque on the coil

       $=\left(\frac{{\mu }_0{I}_1{I}_2}{2\pi r}a\cos \theta \right)\text{a}$

       $=2\times {10}^{-7}\times 65\times 78\times {\left(10\times {10}^{-2}\right)}^2\times \frac{12\times 100}{{\left(13\right)}^2}$

       $={7.210}^{-5}\text{Nm}$

The magnitudes of forces ${\overrightarrow{F}}_1$ and ${\overrightarrow{F}}_2$ are same,

$\left|{\overrightarrow{F}}_1\right|=\left|{\overrightarrow{F}}_2\right|=F=\frac{{\mu }_0{I}_1{I}_2}{2\pi r}\times a$

The components $F_1\sin \theta$ and $F_2\sin \theta$ do not exert torque; torque is due to components $F_1\cos \theta$ and $F_2\cos \theta$.