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  4. A square 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 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:

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Q. A square 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 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:

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Solution:

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$\vec{\tau}=\overrightarrow{ M } \times \overrightarrow{ B }$
$=4 a ^{2} I \times \frac{\mu_{0} I }{2 \pi b }$