Question

A line charge λ per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (Fig. 6.22). A uniform magnetic field extends over a circular region within the rim. It is given by,
B = − B₀ k (r ≤ a; a < R) 

= 0 (otherwise)
What is the angular velocity of the wheel after the field is suddenly switched off?

Answer 1

Line charge per unit length
Where,

r = Distance of the point within the wheel
Mass of the wheel = M
Radius of the wheel = R

At distance r, the magnetic force is balanced by the centripetal force i.e.,