JEE Main 2026 · 5 Apr · Shift 2, Physics question 50

A circular loop of radius 20 cm and resistance 2 Ω is placed in a time varying magnetic field $\vec B=\left(2t^2+2t+3\right)$ 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 $\dfrac\alpha{50}$ A. The value of $\alpha$ is ________.

(Take $\pi=22/7$)