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Question
Answer the following question regarding an a.c. generator.
Why is the e.m.f. produced by the generator zero at a certain instant and maximum at some other instant when the coil is rotating at a constant speed?
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Solution
The e.m.f. induced in the rotating coil depends on the rate of change of magnetic flux linked with the coil, not on the total flux itself. When the coil plane is perpendicular to the magnetic field at 0° and 180°, the magnetic flux linked with the coil is maximum but momentarily not changing, so the rate of change of flux is zero. Hence, the induced e.m.f. is zero at these instants. When the plane of the coil is parallel to the magnetic field at 90° and 270°, the magnetic flux linked with the coil is minimum, but its rate of change is maximum, so the induced e.m.f. is maximum. For a coil of N turns and area A rotating with constant angular speed ω in a magnetic field B, the induced e.m.f. is given by e = NBAω sinθ, where θ is the angle between the normal to the coil and the magnetic field. At θ = 0° and 180°, sinθ = 0, so e = 0. At θ = 90° and 270°, sinθ = ±1, so e is maximum.
