Why is the emf maximum when the plane of the armature is parallel to the magnetic filed in an ac generator ?

The emf of a generator is given by the rate of change of magnetic flux passing through the coil. Now when the rate of change of magnetic flux be maximum, there the emf too will be maximum. Let us see mathematically,

Φ = BAcosωt

By Faraday’s law

e = -dΦ/dt

=> E  = BωAsinωt

=> E = E₀sinωt

θ = ωt

=> E = E₀sinθ

Now E will be maximum if θ = π/2 rad.

This means E will be maximum if normal to the plane of coil is perpendicular to the magnetic field. Thus, plane of the coil must lie along the magnetic field.