Question

A 2 m long metallic rod rotates with an angular frequency of $200rad{s}^{-1}$ 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 magnetic field of 0.5 T parallel to the axis exists everywhere. The emf developed between the centre and the ring is then

• A. 100 V
• B. 200 V
• C. 300 V
• D. 400 V

Answer 1

Answer: (B)

200 V

Given,

Length of the rod, $l=2m$

Angular frequency ,$\omega =200rad/s$

Magnetic field strength $B=0.5T$

One end of the rod has zero linear velocity while another end of the rod has a linear velocity of $l\omega$

Therefore, Average linear velocity of the end, $v=\frac{l\omega }{2}$

E.M.F developed between the center and ring,

$\epsilon =Blv=B\omega \frac{l^2}{2}$

$=\frac{0.5\times 200\times 2^2}{2}=200V$

Hence option $\left(B\right)$ is correct.