Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current I=10 sin (ω t ) A, where ω=1000 rad / s. A…

Suppose a long solenoid of $\displaystyle 100$ cm length, radius $\displaystyle 2$ cm having $\displaystyle 500$ turns per unit length, carries a current $\displaystyle I=10 \sin (\omega \mathrm{t}) \mathrm{A}$, where $\displaystyle \omega=1000 \mathrm{rad} / \mathrm{s}$. A circular conducting loop $\displaystyle (B)$ of radius $\displaystyle 1$ cm coaxially slided through the solenoid at a speed $\displaystyle v=1 \mathrm{~cm} / \mathrm{s}$. The r.m.s. current through the loop when the coil $\displaystyle B$ is inserted $\displaystyle 10$ cm inside the solenoid is $\displaystyle \alpha / \sqrt{2} \mu \mathrm{~A}$. The value of $\displaystyle \alpha$ is $\displaystyle \_\_\_\_$. [Resistance of the loop $\displaystyle =10 \Omega$ ]