Physics Question from JEE Main 2026 · 23 January, Shift 2

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