A long slenoid of radius 2 cm has 100 turns/cm and carries a current of 5A. A coil of radus 1 cm having 100 turns and a total resistance of 20 Omega is placed inside the solenoid coxially. The coil is conneted to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer.

Explanation

Here `r=2 cm =2xx10^(-2)m`
`n=turns//cm`
`= turns//m`
`i-5A`
`B=mu_0 ni=4 pi xx^(-7)xx10000xx5`
`=20 pixx10^(-3) T`
`n^(2)= 100 turns, R=20 Omega`
`r=1 cm =10^(-2)m`
`flux linking per turm the second coil`
`=B pi r^2= B pixx10^(-4)`
`phi(Total flux linking)`
`=Bn_(2)pi r^2`
`=100xxpi xx10^(-4)xx20 pixx10^(-3)`
`Where current is reversed `
`d phi=phi_2-phi_1`
`=2xx100xxpixx10^(-4)xx20 pi xx10^(-3)`
`e=(-d phi)/(dt)=(4 pi^2xx10^(-4))/(dt)`
`I=(e/R)=(4 pi^2 xx10^(-4))/(dtxx20)`
`q=Idt=(4 pi^2xx10^(-4))/(20xxdt)xxdt`
`=2xx10^(-4)C.`