A long solenoid of diameter $0.1\, m$ has $2 \times 10^4$ turns per meter. At the centre of the solenoid, a coil of $100$ turns and radius $0.01\, m$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $0\,A$ from $4\, A$ in $0.05 \,s$. If the resistance of the coil is $10\pi^2 \Omega$ . the total charge flowing through the coil during this time is :