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.
Length of the rod, l = 1 m
Angular frequency,ω = 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 lω.
Average linear velocity of the rod, $v=\frac{l \omega+0}{2}=\frac{l \omega}{2}$
Emf developed between the centre and the ring,
$e=B l v=B l\left(\frac{l \omega}{2}\right)=\frac{B l^{2} \omega}{2}$
$=\frac{0.5 \times(1)^{2} \times 400}{2}=100 \mathrm{~V}$
Hence, the emf developed between the centre and the ring is 100 V.