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

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Correct answer · Option B

\( 32\;\mu\text{C} \)

Charge \( Q = \frac{\Delta\Phi}{R} = \frac{N B A}{R} = \frac{N (\mu_0 n \Delta I) \pi r^2}{R} = 32\;\mu\text{C} \).