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.