An air-cored solenoid with length 30 cm, area of cross-section `25 cm^(2)` and number of turus 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 emf induced across the ends of the open switch in the circuit ? Ignore the variation in magnetie field near the ends of the solenoid.

Explanation

Given, length of solenoid `l=30" cm "30 xx 10^(-2)m`
Area of cross-section `A=25"cm "25 xx 10^(-4)m^(2)`
Number of turns N=500, Current `I_1=2.5A, I_(2)=0`, Brief time `dt=10^(-3)s`.
Induced emf in the solenoid `e=(dphi)/(dt)=(d(BA))/(dt) (therefore phi=BA)`
Magnetic field induction B at a point well inside the long solenoid carrying cuurent I is
`B=mu_(0)nI("where, n"=N/l)`
`e=NA (dB)/(dt)=A(d)/(dt)(mu_(0)N/l.I)`
`e=A(m_(0)N)/(l).(dI)/(dt)`
`e=500xx25xx10^(-4)xx4xx3.14xx10^(-7) xx (500)/(30xx10^(-2))xx(2.5)/(10^(-3)) Rightarrow e=6.5V`