# A squre loop of side 2 a and carrying current I is kept in $xz$ plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point $(0,b,0), (b>>a)$. The magnitude of torque on the loop about z-axis will be:   Option: 1   Option: 2 Option: 3   Option: 4

$\begin{array}{l} \mathrm{F}=\mathrm{BI} 2 \mathrm{a}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}} \mathrm{I} \times 2 \mathrm{a} \\ \\ \mathrm{F}=\frac{\mu_{0} \mathrm{I}^{2} \mathrm{a}}{\pi \sqrt{\mathrm{b}^{2}+\mathrm{a}^{2}}} \\ \\ \tau=\mathrm{F} \cos \theta \times 2 \mathrm{a} \\ \\ =\frac{\mu_{0} \mathrm{I}^{2} \mathrm{a}}{\pi \sqrt{\mathrm{b}^{2}+\mathrm{a}^{2}}} \times \frac{\mathrm{b}}{\sqrt{\mathrm{b}^{2}+\mathrm{a}^{2}}} \times 2 \mathrm{a} \\ \\ \tau=\frac{2 \mu_{0} \mathrm{I}^{2} \mathrm{a}^{2} \mathrm{~b}}{\pi\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)} \end{array}$

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