Question

Question 6.5: 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.

Class 12 - Physics - Electromagnetic Induction Electromagnetic Induction Page-230

Answer 1

given,
length of the rod , l = 1 m
angular frequency , $\omega$ = 400rad/s
magnetic field strength,B = 0.5T
one end of the rod has zero linear velocity while other end of rod has a linear velocity of $l\omega$.
average linear velocity of the end, $v=\frac{l\omega+0}{2}=\frac{l\omega}{2}$
emf developed between the centre and ring,
$e=Blv =Bl\frac{l\omega}{2}$

now, e = 0.5 × 1 × 1 × 400/2 = 100V
hence, emf developed between the centre and the ring is 100V