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

Explanation

Consider a rectangular coil in a uniform magnetic field B. Let A- Area of the coil
N- Number of turns of the coil
`theta`- Angle of rotation in time .t.
`omega = theta//t` angular velocity.
The magnetic flux through the coil is= Area `xx`(normal component of B) `xx N`
`phi_(B)= A (B cos theta)N`
`phi_(B)= NAB cos (omega t)`

From Faraday.s law
`epsi= - (d phi_(B))/(dt)= - (d(NAB cos omega t))/(dt)`
`epsi= - NAB omega (-sin omega t)`
`epsi= NAB omega sin omega t` .....(1)
When the plane of coil becomes normal to B then `theta= 90^(@) or 270^(@)`
`epsi_(0)= NBA omega rarr` maximum induced emf
Eqn (1) becomes
`epsi= epsi_(0) sin omega t`