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

Answer

C

Explanation

Thinking Process Current induced in the coil is given by
`=1/R(dphi)/(dt)rArr(triangleq)/(trianglet)=1/r(trianglephi)/(trianglet)`
Given, resistacne of the solenoid,`R=10pi^(2)omega`
Radius of second and coil `r=10^(-2)`
`trianglet=0.05s, triagneli=4-0=4A`
Charge flowing thrrough the coil is given by
`triangleq=((trianglephi))/(trianglet)1/R(trianglet)=mu_(0)N_(1)N_(2)pir^(23)(trianglei)/((trianglet)) 1/R(trianglet)
`=4pixx10^(-7)xx2xx10^(4)xx100xxpi`
`" "x(10^(-2))^(2)xx((4)/(0.05))xx(1)/(10p^(2)xx0.05`
`=32xx10^(-6)C=32muC`