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

Answer

B

Explanation

`DeltaQ=(Deltaphi)/R=(Delta(NBA))/R`
`=(Nmu_(0)nA(i_(1)-i_(2)))/R`
`=(100xx4pixx10^(-7)xx2xx10^(4)xxpi(0.05)^(2)xx(4-0))/(10pi^(2))`
`=32xx10^(-6) C=32 muC`