Derive an Expression for instantaneous induced emf in an A.C generator

Explanation

Let the coil having N turns be rotated with constant angular speed `omega`,the angle `theta` between the magnetic field `barB` and the area vector `vecA` of the coul at any intant of time t is `theta=omegat`
The magnetic flux at any time t is
`Theta_(B)=barB.barA=BAcostheta=BA cos omegat`
From Faraday.s law ,the induced emf in the rotating coil of N turns
`epsi=-N((dTheta_(B))/(dt))` Thus ,the instantaneous value of the emf `epsi=epsi_(0)` sin `omegat`
where `epsi_(0)=NBA_(omega)` is the amplitude (peak/maximum value)of the emf.