Magnetism PYQ — JEE Advanced 2022 · Shift 1 · Q51 with Solution

A small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $x y$ -plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counterclockwise as shown in the figure. The magnetic field due to the solenoid is in $\hat{n}$ direction. List-I gives time dependences of $\hat{n}$ in terms of a constant angular frequency $\omega$ . List-II gives the torques experienced by the circular loop at time $t=\frac{\pi}{6 \omega}$ . Let $\alpha=\frac{A^{2} \mu_{0}^{2} m^{2} I^{2} \omega}{2 R}$ .

JEE Advanced 2022 Paper 1 Online Physics - Magnetism Question 12 English

List-I	List-II
(I) $\frac{1}{\sqrt{2}}(\sin \omega t \hat{\jmath}+\cos \omega t \hat{k})$	(P) 0
(II) $\frac{1}{\sqrt{2}}(\sin \omega t \hat{\imath}+\cos \omega t \hat{\jmath})$	(Q) $-\frac{\alpha}{4} \hat{\imath}$
(III) $\frac{1}{\sqrt{2}}(\sin \omega t \hat{\imath}+\cos \omega t \hat{k})$	(R) $\frac{3 \alpha}{4} \hat{\imath}$
(IV) $\frac{1}{\sqrt{2}}(\cos \omega t \hat{\jmath}+\sin \omega t \hat{k})$	(S) $\frac{\alpha}{4} \hat{\jmath}$
	(T) $-\frac{3 \alpha}{4} \hat{\imath}$

Which one of the following options is correct?

A
I $\rightarrow$ Q, II $\rightarrow$ P, III $\rightarrow$ S, IV $\rightarrow$ T
B
$\mathrm{I} \rightarrow \mathrm{S}, \mathrm{II} \rightarrow \mathrm{T}$ , III $\rightarrow \mathrm{Q}$ , IV $\rightarrow \mathrm{P}$
C
$\mathrm{I} \rightarrow \mathrm{Q}, \mathrm{II} \rightarrow \mathrm{P}$ , III $\rightarrow \mathrm{S}$ , IV $\rightarrow \mathrm{R}$
D
$\mathrm{I} \rightarrow \mathrm{T}$ , II $\rightarrow \mathrm{Q}$ , III $\rightarrow \mathrm{P}$ , IV $\rightarrow \mathrm{R}$

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