A rectangular coil is rotated with uniform angular speed inside a uniform magnetic field so that its plane makes an angle θ with the field at any instant. Answer the following questions based on this situation:
(i) Write the mathematical expression for the magnetic flux linked with the coil in terms of the magnetic field B, area of the coil A and the angle θ. State clearly the physical meaning of each symbol used.
(ii) Using the concept of electromagnetic induction, explain why the electromotive force (emf) induced in the coil varies sinusoidally with time.
(iii) Show that the average value of the induced emf over one complete revolution of the coil is zero.