A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s⁻¹ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.

Length of the rod, l = 1 m

Angular frequency, ω = 400 rad/s

Magnetic field strength, B = 0.5 T

One end of the rod has zero linear velocity, while the other end has a linear velocity of lω

Average linear velocity of the rod, V = (lω + 0 )/2 = lω/2

Emf developed between the centre and the ring,

e = Blv = Bl (lω/2) = Bl²ω/2

= (0.5 x (l)² x400 )/2 =100V

Hence, the emf developed between the centre and the ring is 100 V.