Question

A $1.0m$ long metallic rod is rotated with an angular frequency of $400rad{s}^{-1}$ 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 $0.5T$ parallel to the axis exists everywhere. Calculate the EMF developed between the center and the ring.

Answer 1

Step 1: Given Data

Length of the rod $L=1.0m$

Angular frequency $\omega =400rad{s}^{-1}$

A constant and uniform magnetic field $B=0.5T$

Step 2: Estimate the velocity

Velocity at the end of the rod is given as

$v=L\omega$

The length at the center of the rod is $\frac{L}{2}$.

Therefore, the velocity at the center of the rod is given as,

$v_C=\frac{L\omega }{2}$

Step 3: Calculate the EMF

So, emf given at the center of the rod is,

$\epsilon =BL{v}_C$

$=\frac{B{L}^2\omega }{2}$

Hence, the EMF developed between the center and the ring is

$\epsilon =\frac{0.5\times 1^2\times 400}{2}$

$=100V$

Hence, the EMF developed between the center and the ring is $100V$.