An alternator consists of a coil of area a with n turns that rotates in a uniform field b around a diameter perpendicular to the field with a rotation frequency f.
a)find the fem in the coil
b)what is the amplitude of the alternating voltage if n= 100 turns, a = 10 ^ -2 m ^ 2, b = 0.1t, f = 2000 rev/min

(a): emf =

(b): Amplitude of alternating voltage = 20.942 Volts.

Explanation:

Given:

(a):

The magnetic flux through the coil is given by

where,

= area vector of the coil directed along the normal to the plane of the coil.

= angle between and .

Assuming, the direction of magnetic field is along the normal to the plane of the coil initially.

At any time t, the angle which magnetic field makes with the normal to the plane of the coil is

Therefore, the magnetic flux linked with the coil at any time t is given by

According to Faraday's law of electromagnetic induction, the emf induced in the coil is given by

(b):

The amplitude of the alternating voltage is the maximum value of the emf and emf is maximum when

Therefore, the amplitude of the alternating voltage is given by

We have,

Putting all these values,