Question

A metallic rod of
length 'L' is rotated at a constant angular speed of w normal to
the

uniform magnetic field B. What is the current induced in the rod if the resistance of rod

is R.?

Answer 1

Given that, a metallic rod of length 'L' is rotated at a constant angular speed of w normal to the uniform magnetic field B. 
We have to find the current induced in the rod, if the resistance of rod is R.
Solution:
Let 'x' be the distance and 'dx' be the small infinite length.
We know that,
E.M.F = v B L
Induced small  E.M.F = Bx dx
The  E.M.F between the ends of the rotating rod is 
 E.M.F = ∈ = ∫ d∈ 
∈ = ∫ (0,1) Bω.dx
∈ = 1/2 B ω l²
The Current with resistance 'R' is
I = ∈ / R 
I =  B ω l² / 2 R
Hopefully it helps. Thanks