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 ?

Explanation

Given `l=0.30 m ,A 25xx10^(-4)m^2,N=500,i=2.5A,t=10^(-3)s,varepsilon =?`
Magnetic field in a solenoid B =`(mu_0Ni)/l`
i.e., `B=(4xx3.14xx10^(-7)xx500xx2.5)/(0.30)"tesla" =5.23 xx10^(-3)T`
Magnetic flux linked with the solenoid , `Phi_B=BAN`
i.e., `Phi_B=5.23xx10^(-3)xx25xx10^(-4)xx500 =6.537xx10^(-3) Wb`
Induced emf `e=(Phi_B)/t=(6.537xx10^(-3)V)/(10^(-3))`
i.e., e= 6.537 V