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

Options

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

Answer

B

Explanation

`q=[((Deltaphi)/(Deltat))(1)/(R )]Deltat`
`q=[mu_(0)nNpir^(2)(Deltai)/(Deltat)](1)/(R )Deltat`
`q=[4xx10^(-7)xx2xx10^(4)xx100xxpixx(10^(-2))^(2)xx((4)/(0.05))](1)/(10pi^(2))xx0.05`
`q=32muC`