A 1m long calculating rod rotates with an angular frequency of 400 rad `s^(-1)` an axis normal to the rod passing through its one one end. The other end of the rod is contact with a circular metallic ring. A constant magnetic field of 0.5 T parallel to the axis everywhere. Calculate the e.m.f. developed between the centre and the ring.

Explanation

Length of the rod, l = 1 m
Angular frequency,`omega = 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 `Iomega`
Average linear velocity of the rod, `v=(lomega+0)/(2)=(lomega)/(2)`
Emf developed between the centre and the ring,
`e=Blv=Bl((lomega)/(2))=(Bl^(2)omega)/(2)`
`=(0.5xx(1)^(2)xx400)/(2)=100 V`
Hence, the emf developed between the centre and the ring is 100 V.