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 -OA from
4A in 0.05s. If the resistance of the coil is $10 \pi^2 \Omega$ the total charge flowing through the coil during this time is :
