A long solenoid having `200` turns per centimeter carries a current of `1.5 A`. At the center of the solenoid a coil is placed of `100` turns of cross-sectional area `3.14 xx 10^(-4) m^(2)` having its axis parallel to the field produced by the solenoid. When the direction of current in the solenoid is reversed within `0.05 s`, the induced emf in the coil is

Explanation

Solenoid
`n=200 turns//cm=200xx10^(-2)turns//m`
`i=1.5A`
coil: `N=100,A=3.14xx10^(-4)m^(2)`
Magnetic field due to solenoid `B=mu_(0)ni` , along the axis
When the current in one direction, flux through coil
`phi_(1)=NBAcos0=Nmu_(0)niA`
When direction of current is reversed, direction of field reserses, flux through the cooil
`phi_(2)=NBAcos180^(@)=-Nmu_(0)niA`
`Deltaphi=|phi_(2)-phi_(1)|=2Nmu_(0)niA`
`Deltat=0.05sec`
`bar(e)=(Deltaphhi)/(Deltat)=(2Nmu_(0)niA)/(Deltat)`
`=(2xx100xx4pixx10^(-7)xx200xx10^(2)xx1.5xx3.14xx10^(-4))/(0.05)`
`=4.8xx10^(-2)V`