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 counter clockwise 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 $ω$ . List-II gives the torques experienced by the circular loop at time $t = \frac{π}{6 ω}$ . Let $α = \frac{A^{2} μ_{0}^{2} m^{2} I^{2} ω}{R}$ .
List-I List-2
I) $(\sin ω t \hat{j} + \cos ω t \hat{k})$ P) 0
II) $(\sin ω t \hat{i} + \cos ω t \hat{j})$ Q) $- \frac{α}{4} \hat{i}$
III) $(\sin ω t \hat{i} + \cos ω t \hat{k})$ R) $\frac{3 α}{4} \hat{i}$
IV) $(\cos ω t \hat{j} + \sin ω t \hat{k})$ S) $\frac{α}{4} \hat{j}$
T) $- \frac{3 α}{4} \hat{i}$
Which one of the following options is correct?

Question

Infinity Learn · Accepted Answer

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

Detailed Solution