Answer the following with reference to the emf generated by a coil rotating uniformly in a uniform magnetic field.
a. (i) Explain, without using any equations, why the induced emf in such a coil varies sinusoidally with time.
b. (ii) Give a reasoned argument to show why the effective (rms) value of a sinusoidally varying emf is equal to 21 times its maximum value.
c. (iii) A practical alternator for commercial power generation often has multiple magnetic poles. Explain how increasing the number of poles affects the output electrical frequency for a given mechanical rotational speed.