Electromagnetic Induction and Alternating Currents: JEE Main 2026 Physics question

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I=10\sin(\omega t)$ A, where $\omega=1000$ rad./s. A circular conducting loop ($B$) of radius 1 cm coaxially slided through the solenoid at a speed $v=1$ cm/s. The r.m.s. current through the loop when the coil $B$ is inserted 10 cm inside the solenoid is $\alpha/\sqrt2$ μA. The value of $\alpha$ is ______. [Resistance of the loop = 10 Ω]