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A long solenoid having 200 turns per cen...

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

Text Solution

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`B=mu_(0)n I =(4 pi xx 10^(-7))(200xx10^(-2))xx1.5`
`=3.8xx10^(-2)Wb//m^(2)`
Magnetic flux through each turn of the coil
`phi=BA=(3.8xx10^(-2))(3.14xx10^(-4))=1/2xx10^(-5)` weber
When the curent in the solenoid is reversed the change the magnetic flux
`=2xx(1.2xx10^(-5))=2.4xx10^(-5)` Weber
Induced emf `=N (d phi)/(dt)=100xx(2.4xx10^(-5))/0.05=0.048V`
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