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.

#### Solution

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" = ("l"omega + 0)/2 = ("l"omega)/2`

Emf developed between the centre and the ring,

e = Blv = `"Bl"(("l"omega)/2) = ("Bl"^2omega)/2`

= `(0.5 xx (1)^2 xx 400)/2`

= 100 V

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