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