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A long solenoid with 15 turns per cm has...

A long solenoid with 15 turns per cm has a small loop of area 2.0 `cm^(2)` placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?

Text Solution

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The magnetic field along the axis of solenoid is `B = mu_0`ni where n is no. of turns per unit length.
flux through the smaller loop placed in solenoid is `phi = B xx A`
Since current in solenoid is changing, emf induced in loop is `e = (dphi)/(dt) = (d)/(dt) [mu_0 "niA"]`
` e = mu_0 nA [(di)/(dt)]`
`4pi xx 10^(-3) xx 15 xx 10^2 xx 2 xx 10^(-4) xx ((4-2)/(1-0))`
` = 0.75 xx 10^(-6) V`
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