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  • A squre loop of side 2 a and carrying current I is kept in plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through

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 \frac{2\mu _{0}I^{2}a^{2}}{\pi b}
 
Option: 2 \frac{2\mu _{0}I^{2}a^{2}b}{\pi (a^{2}+b^{2})}
Option: 3 \frac{\mu _{0}I^{2}a^{2}b}{2\pi (a^{2}+b^{2})}  
Option: 4 \frac{\mu _{0}I^{2}a^{2}}{2\pi b}

Answers (1)

best_answer

\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}

Posted by

Deependra Verma

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