A long solenoid with 15 turns per cm has a small loop of area `2.0 cm^2` placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, then what is the induced emf in the loop while the current is changing ?

Explanation

Given `n=(15 "turns")/(10^(-2)m)=1500 "turns " m^(-1)`
`A=2xx10^(-4)m^2`
di=4-2=2A
dt =0.1 s
`(di)/(dt)=2/(0.1)=20 As^(-1)`
w.k.t. `e=(dPhi)/(dt) where Phi=((mu_0Ni)/(l))A`
`e=-((mu_0NA)/(l))((di)/(dt))`
`e=-4xx3.142xx1500xx2xx10^(-4)xx20xx10^(-7)`
`e=-7.536xx10^(-6)V`.