A small circular loop of area $$A$$ and resistance $$R$$ is fixed on a horizontal $$xy$$-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 $$\alpha = \frac{A^2 \mu_0^2 m^2 I^2 \omega}{2R}$$.

List-I	List-II
(I) $$\frac{1}{\sqrt{2}}(\sin \omega t \, \hat{j} + \cos \omega t \, \hat{k})$$	(P) 0
(II) $$\frac{1}{\sqrt{2}}(\sin \omega t \, \hat{i} + \cos \omega t \, \hat{j})$$	(Q) $$-\frac{\alpha}{4}\hat{i}$$
(III) $$\frac{1}{\sqrt{2}}(\sin \omega t \, \hat{i} + \cos \omega t \, \hat{k})$$	(R) $$\frac{3\alpha}{4}\hat{i}$$
(IV) $$\frac{1}{\sqrt{2}}(\cos \omega t \, \hat{i} + \sin \omega t \, \hat{k})$$	(S) $$\frac{\alpha}{4}\hat{j}$$
Which one of the following options is correct?	(T) $$-\frac{3\alpha}{4}\hat{i}$$