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.

Explanation

Length of rod l=1m
Angular frequency of rod `omega= 400 "rad/s"`
Magnetic field B = 0.5T
The linear velocity of fixed end =0
The linear velocity of other end `=lomega(therefore V=romega)`
Average linear velocity `V=(0_lomega)/(2)`
`V=(lomega)/(2)......(1)` By using the formula of motional emf,
`e=Bupsilonl=(Blomega)/(2).l"(from equation (i))", e=(0.5xx1xx400xx1)/(2),e=100`
Thus, the emf developed between the centre and ring is 100V.