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

A long solenoid with 15 turns per cm has small loop of area `2.0 cm^(2)` placed inside, normal to the axis of the soleniod. If current carried by the solenoid changes steadily from 2 A to 4 A in 0.1 s, what is the induced voltage in the loop, while the current is changing ?

Text Solution

Verified by Experts

Here, `(N)/(l) = 15 turns//cm = 1500 tunrs//metre., A = 2.0 cm^(2) = 2 xx 10^(-4) m^(2)`
`(di)/(dt) = (4 - 2)/(0.1) = 20 A s^(-1)`
`e = (d phi)/(dt) = (d)/(dt)(BA) = A (d)/(dt) (mu_(0) (N)/(l)i) = A mu_(0) ((N)/(l)) (di)/(dt) = (2 xx 10^(-4)) xx 4 pi xx 10^(-7) xx 1500 xx 20 V`
`e = 7.5 xx 10^(-6) V`
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