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A square loop of side 2a, 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 the z-axis and passing through the point (0,b,0),(b> > a). The magnitude of the torque on the loop about z-axis is given by :
Option: 1 \frac{\mu _{0}I^{2}a^{2}}{2\pi b}  
Option: 2 \frac{\mu _{0}I^{2}a^{3}}{2\pi b^{2}}
Option: 3 \frac{2\mu _{0}I^{2}a^{2}}{\pi b}
Option: 4 \frac{2\mu _{0}I^{2}a^{3}}{\pi b^{2}}

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\begin{array}{l} \vec{\tau}=\overrightarrow{\mathrm{M}} \times \overrightarrow{\mathrm{B}} \\ \\ =4 \mathrm{a}^{2} \mathrm{I} \times \frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{b}} \end{array}

= \frac{2\mu _{0}I^{2}a^{2}}{\pi b}

 

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Deependra Verma

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