Question

We are rotating a 2 m long metallic rod with an angular frequency of 200 rad/s with an axis normal to the rod passing through its one end. And on to the other end of the rod, it is connected with a circular metallic ring. There exist a uniform magnetic field of 1.5 T which is parallel to the axis everywhere. Find out the emf induced between the centre and the ring?

Answer 1

Length of the rod = 2m

\( Angular frequency,\\\omega =200rad/s \)

Magnetic field strength, B = 1.5 T

At one of the ends of the rod, it has zero liner velocity, while on to its other end it has a linear velocity of \( I \omega \)

\( Average\ linear\ velocity\ of\ the\ rod, v = \frac{I \omega + 0}{ 2 } \) =\( \frac{I \omega}{2} \)

Emf developed between the centre and ring.

\( E = Blv = Bl\left ( \frac{i \omega }{2} \right ) = \frac{B l^{2 } \omega}{2} \ \ = \frac{1.5 \times \left ( 2 \right )^{2} \times 200}{2} = 600 V \)

Hence, the emf developed between the centre and the ring is 600 V.

The emf developed between the centre and the ring is 600 V.