A long solenoid of diameter 0.1 m has 2 × 10⁴ 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 $10 \pi^2 \Omega$, then the total charge flowing through the coil during this time is _________.

Fill in the blank with the correct answer from the options given below.

$32 \mu C$

Initial flux is $ \phi_i = 0$

$ B_f = \mu_0 nI = 4\pi \times 10^{-7} \times 2\times 10^4 \times 4 = 32\pi \times 10^{-3} T$

Final flux is $ \phi_f = NBA = 100 \times 32\times 10^{-3}\times \pi \times 10.^2 = 32\pi^2 \times 10^{-5} Wb$

Induced charge $ q = \frac{\Delta \phi}{R} = \frac{32\pi^2 \times 10^{-5}}{10\pi^2} = 32\mu C$

The correct answer is Option (2) → $32 \mu C$