Question

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 $\alpha=\frac{A^2 \mu_0^2 m^2 I^2 \omega}{2 R}$ 

Column I		Column 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	$\frac{\alpha}{4} \hat{j}$
		T	$-\frac{3 \alpha}{4} \hat{i}$

Which one of the following options is correct?

• A. $I \rightarrow Q , II \rightarrow P , III \rightarrow S , IV \rightarrow T$
• B. $I \rightarrow S , II \rightarrow T, III \rightarrow Q, IV \rightarrow P$
• C. $I \rightarrow Q , II \rightarrow P , III \rightarrow S , IV \rightarrow R$
• D. $I \rightarrow T , II \rightarrow Q , III \rightarrow P , IV \rightarrow R$

Answer 1

The Correct Option is C

$I \rightarrow Q , II \rightarrow P , III \rightarrow S , IV \rightarrow R$