Electromagnetic Induction and Alternating Currents: JEE Main 2026 Physics question

A circular loop of radius 20 cm and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec B=(2t^2+2t+3)$ T. At $t=0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t=3$ s is $\frac{\alpha}{50}$ A. The value of $\alpha$ is ______. (Take $\pi=22/7$)