Question

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:

• A. $\frac{2{\mu }_0{I}^2{a}^2}{\pi b}$
• B. $\frac{{\mu }_0{I}^2{a}^3}{2\pi b^2}$
• C. $\frac{{\mu }_0{I}^2{a}^2}{2\pi b}$
• D. $\frac{2{\mu }_0{I}^2{a}^3}{\pi b^2}$

Answer 1

Answer: (A)

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