A long solenoid of diameter `0.1 m` has `2xx 10^(4)` turns per metre. 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 `4A` in `0.05` .If the resistance of the coil is `10 pi^(2) ohm`, the total charge (in `mu C` ) flowing through the coil during this time is

Options

A. `32pimuC`
B. `16muC`
C. `32muC`
D. `16pimuC`

Answer

C

Explanation

`q=(Deltavarphi)/R=(mu_(0)n(i-0)NA)/R`
N = Number of loops in coil
A = Area of coil having radius 0.01 m
n = Number of turns per unit length of solenoid
`Q=(4pixx10^(-7)xx2xx10^(4)xx4xx100xxpixx10^(-4))/(10pi^(2))=32muC`.