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.
Given:
Length of the metallic rod = 1.0 m
Angular frequency = 400 rads - 1
Strength of magnetic field B= 0.5 T
Since it is clear that one end of the metallic rod has zero linear velocity whereas the other end of the rod has linear velocity of lω
∴ The average linear velocity of the metallic rod can be calculated as follows:
v = (lω + 0)/2
⇒ v = lω /2
The e.m.f. developed between the centre and the ring can be calculated as follows:
e = Blv ...(1)
where B is the magnetic field
l is the length of the loop and,
v is the velocity of the rectangular loop
⇒ Substituting the value of v in above equation, we get
e = B × l × (lω/2)
e = (Bl2ω)/2
e = (0.5 T × 1m2 × 400 rads - 1)/2
On calculating, we get
e = 100 V
Hence, the emf developed across the ring is 100 V.