Question

A small generator produces 2.4 V of peak emf. If it contains a 0.050-T permanent magnet and 96 wire loops, each of which is roughly a 6.0-cm diameter circle, at what frequency does the generator rotate?

Answer 1

  

For the generator rotating with velocity v and length l, breadth b in a uniform magnetic field B, the motional emf induced is given by

This is the induced emf developed on one side. For both sides, the induced emf is given by,

  

In order to find the time dependence of emf, we assume the coil to be rotating with a constant angular velocity . The angle is related to angular velocity by,

So,

Now linear velocity v is related to angular velocity by v = b

From the figure,  

  

The area of the loop is given by A = and let N be the total number of loops

Hence this the emf induced in a generator. For maximum value of induced emf, the value of

  

therefore maximum emf (peak emf) is given by,

where,

where f is the frequency of rotation

  

Given,

emfmax = 2.4 V

n = 96 turns

B = 0.050 T

Diamere of coil, d = 6cm

Therefore radius of coil, r = 3c = 3x10-2 m

Therefore Area, A = (the coil is wound in circular form)

Therefore from the above

= 28.14 Hz (Ans.)