A square loop of side 2 a and carrying current I is kept in xz plane… | JEE Main 2020 (6 Sep, Shift 2)

Q64JEE Main 2020 · 6 SEP · SHIFT 2Difficult

Current Loop as a Magnetic Dipole

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 z-axis and passing through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will be:

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Answer: (a)

Since $b \gg a$ , the wire's field at the loop is nearly uniform: $B = \frac{\mu_0 I}{2\pi b}$ , along the $x$ -axis.
Loop in the xz plane: $m = I(2a)^2 = 4a^2I$ along the $y$ -axis, so $\vec m \perp \vec B$ .
$\tau = mB = 4a^2I\cdot\frac{\mu_0 I}{2\pi b} = \frac{2\mu_0 I^2a^2}{\pi b}$
So the answer is (a).

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