Question

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.

Answer 1

Length of the rod, I = 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 l\(\omega\).
Average linear velocity of the rod, \(v\) = \(\frac{l\omega+0}{2}\)= \(\frac{l\omega}{2}\)
Emf developed between the centre and the ring,
e = Blv=\(Bl\bigg(\frac{l\omega}{2}\bigg)\) = \(\frac{Bl^2\omega}{2}\)
= \(\frac{0.5\times(1)^2\times400}{2}\) =100 V
Hence, the emf developed between the centre and the ring is 100 V.