A long solenoid has $20$ turns per cm. A small loop of area $\pi\,\text{cm}^2$ is placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $1.0\,\text{A}$ to $3.0\,\text{A}$ in $0.2\,\text{s}$, what is the magnitude of the induced emf in the loop while the current is changing?