Electromagnetic Induction

Suppose a conducting rod of length rotates with a constant angular speed about a point at one end.
A uniform magnetic field is directed perpendicular to the plane of rotation as shown in figure. Consider a segment of rod of length drat a distance r from O. This segment has a velocity

The induced emf in this segment is

Summing the emfs induced across all segments, which are in series, gives the total emf across the rod.


From right hand rule we can see that P is at higher potential than O.
Thus,

Power

Then
Percentage increase in power

Let ...(i)
and ...(ii)
By using Eqs. (i) and (ii)) we obtain
and

The induced emf

or
or