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