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A long solenoid with 1.5 turns per cm ha...

A long solenoid with `1.5` turns per `cm` has a small loop of area `2.0 cm^(2)` placed inside the solenoid normal to its axis. If the current in the solenoid changes steadily from `2.0 A` to `4.0 A` in `1.0 s`. The emf induced in the loop is

Text Solution

Verified by Experts

The magnetic field along the axis of solenoid is `B=mu_0ni` where n is no. of turns per unit length.
flux through the smaller loop placed in solenoid is
`phi=BxxA` since current in solenoid is changing.
emf induced in loop is `e=(dphi)/(dt)=d/(dt) [mu_0niA]`
`e=mu_0 nA ((di)/(dt))`
`=4pi xx10^(-7)xx1.5 xx 10^2 xx2 xx 10^(-4) xx ((4-2)/(1-0))`
`=0.75 xx 10^(-6) V `
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