An infinitely long current $(I_{1})$ carrying wire is placed along the z-axis as shown in the figure. A current $(I_{2})$ carrying square loop of side length a is placed with its centre at $(x_{0}, 0, 0)$ where $(x_{0} >>a)$ . If the normal to the loop through its centre is in the x-y plane and inclined at angle $37^{0}$ with the x-axis, then

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Magnetic moment of the loop is ${2a}^{2} I_{2}$

The magnitude of torque on the loop is $\frac{2 μ_{0} a^{2} l_{1} l_{2}}{5 π x_{0}}$

The magnitude of torque on the loop is $\frac{3 μ_{0} a^{2} l_{1} l_{2}}{10 π x_{0}}$

Magnetic moment of the loop is $a^{2} I_{2}$

answer is B, C.

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Detailed Solution

$\vec{μ} = i \vec{A}$

$(\bar{τ}) = \vec{μ} \times \vec{B} = i_{2} a^{2} . \frac{μ_{2} i_{1}}{2 π x_{0}} \sin 53^{0}$

$\Rightarrow | \bar{τ} | = \frac{2 μ_{0} i_{1} i_{2} a^{2}}{5 π x_{0}}$

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