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, what is the induced emf in the loop while the current is changing ?

Explanation

Here, because of magnetic field of solenoid, magnetic flux gets linked with the small loop, kept inside the solenoid, perpendicular to its axis. This flux is,
`phi=AB cos theta`
`phi=AB cos 0^@ " " (because vecA||vecB)`
`therefore phi=A(mu_0 nI)`...(1)
Now, emf induced in the loop is,
`epsilon=-(dphi)/(dt)`
`=-d/(dt)(Amu_0nI)`
`=-Amu_0n (dI)/(dt)`
`=-(2xx10^(-4))(4pixx10^(-7))(15/0.01)((4-2)/0.1)`
`epsilon=-7.536xx10^(-6)` V
`therefore |epsilon|=7.536xx10^(-6)` V
(Note: Above emf induced in the loop will send induced current in the clockwise direction, as seen from right to left).