Question 7: Give formula for the flux linkages in terms of angular orientation.

ANSWER

Suppose a coil is placed in a uniform magnetic field of density B as shown. Let A is the area of the coil which makes an angle θ with the B. The magnetic flux linking the coil is thus

We know that the coil will rotate when a current is passed through it. The angle of rotation of the coil at any time instant t is

Put this value of θ and equation (i) becomes

Faraday’s law of electromagnetic induction states that if the magnetic flux linking a circuit is changed, an emf is induced in the circuit given by

Put the value of Ф from equation (iii)

If there are N turns in the coil then

This means the electromotive force thus induced is sinusoidal and will produce alternating current.