A circular loop of radius $$r = 20$$ cm and resistance $$R = 2\,\Omega$$ is placed in a time varying  magnetic field $$B = (2t^2 + 2t + 3)$$ 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 $$\pi = 22/7$$)