The current in a long solenoid of radius R and having n turns per unit length is given by `i= i_0 sin omega t`. A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid and the coil.

Explanation

`B = F1` Produced due to first coil
`= mu_(0)`
(a) `Emf.devel` `d = (dphi)/(dt) = d/(dt) (mu_(0) ni N pi R^(2))`
= (mu_(0) n Na piR^(2))`
`= mu_(0)n Na piR^(2) (di)/(dt)`
`= mu_(0)n N piR^(2) i_(0) omega cos omegat`.
(b) Flux `phi` linked witht he second
`mu_(0) ni xx NA = m_(0) ni N piR^(2)`.