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. How much is the average back e.m.f. induced across the ends of the open switch in the cuicuit ? Ignore the variation in magnetic field near the ends of the solenoid.

Explanation

`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