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An air cored solenoid with length 30 cm ...

An air cored solenoid with length 30 cm , area of cross section `25 cm ^2` and number of turns 500 carries a current of 2.5 A. The current is suddenly switched off in a brief time of `10 ^(-3)s`. What is the average back emf induced across the ends of the open switch in the circuit ?

Text Solution

Verified by Experts

`B= (mu_0 NI)/(l)`
(Inside the solenoid away from the ends)
`Phi = (mu_0 NI)/(l) A`
Total flux linkage `= N Phi`
`=(mu_0 N^2 A)/(l) I`
(Ignoring end variations in B)
`|epsi| = (d)/(dt) (N Phi)`
`|epsi|_(av) = ("total change in flux")/("total time")`
`|epsi|_(av) = (4pi xx 10^(-7) xx 25 xx 10^(-4))/(0.3xx10^(-3)) xx (500)^2 xx 2.5`
=6.5 V
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