A copper rod of length l is rotating about midpoint of rod, perpendicular to the magnetic field B with constant angular velocity omega. The induced emf between the two ends is

Given: A rod of length L rotating in magnetic field B with angular velocity ω.

Solution: We will take mid point as the reference as the rod is rotating about the mid point. So, consider the differential length of the rod dx from its center.
Therefore, in a magnetic field B, the angular velocity of the differential area will be,
ω×x 
So, emf induced in the coil is given by, 
E=Blv
E=Bωxdx
Integrating within the limits we have,
E=∫2−L​2L​​Bωxdx

E=Bω∫2−L​2L​​xdx

E=Bω[2x2​]2−L​2L​​

On solving, we get 
E=0