A long solenoid of diameter $0.1\text{m}$ has $2\times 10^4$ turns per meter. 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:

1. A
   $32\pi \mu \text{C}$
2. B
   $16\mu \text{C}$
3. C
   $32\mu \text{C}$
4. D
   $16\pi \mu \text{C}$