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 :

Question

( A ) 32 $\pi \mu$C
( B ) 16 $\mu$C
( C ) 32 $\mu$C
( D ) 16 $\pi \mu$C