A very long solenoid of radius R is carrying current $I\left(t\right)=kt{e}^{-\alpha t}\left(k>0\right)$, as a function of time$\left(t\ge 0\right)$. Counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted,as a function of time, by: