An air cored solenoid with length `20` cm area of cross section `2` A. The current is suddenly switched off within `10^(-3)` s. The average back emf induced across the ends of the open switch in the circuit is (ignore the variation in magnetic field near the ends of the solenoid)

Options

A. 2 V
B. 4 V
C. 3 V
D. 5 V

Answer

B

Explanation

Here, `l=20cm=20xx10^(-3)m`,
`A=20cm^(2)=20xx10^(-4)m^(2)`
`N=400,I_(1)=2A,l_(2)=0,dt=10^(-3)s`
As `epsi=(dphi)/(dt)=(d(BAN))/(dt)`
`=(mu_(0)NdlAN)/(ldt)" "(":. "B=(mu_(0)NI)/(l))`
`=(mu_(0)N(I_(1)-I_(2))AN)/(ldt)`
`=(4pixx10^(-7)xx(400)^(2)xx2xx20xx10^(-4))/(20xx10^(-2)xx10^-3)`
`=4V`