Question

The magnitude of induced emf in a coil of a generator is maximum when coil turns through an angle of

Answer 1

The magnetic flux as a function of time is

Φ(t)=B⋅A(t)=BAcos(ωt)Φ(t)=B⋅A(t)=BAcos⁡(ωt)

where BB is the magnetic field and A(t)A(t) is the area vector as a function of time and ωtωt is the angle between the field and the area vector as a function of time. Then the rate of change of the flux as a function of time is

Φ′(t)=−BAωsin(ωt)Φ′(t)=−BAωsin⁡(ωt)

Notice that if the angle between the area vector vector and the magnetic field is zero, then the flux is nonzero and equal to ABAB, its maximum, but the rate of change of the flux vanishes because sin(0)=0sin⁡(0)=0.