A long solenoid of diameter 0.1 m has 2 × 10^4 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with…

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