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

• A

  $32\pi \mathrm{\mu C}$
• B

  $16 \mathrm{\mu C}$
• Correct answer
  C

  $32 \mathrm{\mu C}$
• D

  $16\pi \mathrm{\mu C}$

Hence, the correct answer is option: 'C'.