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A long solenoid of diameter 0.1m has 2$×{10}^{-4}$ turns per metre. At the centre of the solenoid, a coil of 100 turns and radius 0.01m is placed with its axis coinciding with the solenoids axis. The current in the solenoid axis. The current in the solenid reduces at a constant rate to 0 A 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

(a)32$\mathrm{\pi \mu C}$

(b)16$\mu C$

(c)32$\mu C$

(d)16$\mathrm{\pi \mu C}$

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