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. `32 pi mu C`
B. `16 mu C`
C. `32 mu C`
D. `16 pi mu C`

Answer

C

Explanation

Emf induced in the small solenoid
`epsilon=-N(dphi)/(dt) :. epsilon=I_(av)R=(dQ)/(dt)R`
`I_(av)=|(epsilon)/(R)|=(N)/(R)(dphi)/(dt)`
`(dQ)/(dt)=(N)/(R)(dphi)/(dt)`
`DeltaQ=I_(av)R=(N(Deltaphi))/(R)=(N(BA))/(R)=(N(mu_(0)ni)pir^(2))/(R)`
`=(100 xx [(4pi xx 10^(-7)) xx (2 xx 10^(4)) xx 100 xx 4 xx pi xx (0.01)^(2)])/(10pi^(2))`
`DeltaQ=32 muC`