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.A uniform magnetic field extends over a circular region within the rim.It is given by, B= -B° k (r<=a; a

Line charge per unit length =λ=Total charg eLeng th=Q2πr
Where,
r, Distance of the point within the wheel
Mass of the wheel = M
Radius of the wheel = R
Magnetic field, B¯¯¯=−B0kˆ
At distance r,themagnetic force is balanced by the centripetal force i.e.,
BQv=Mv2r
Where,
v= linear velocity of the wheel
∴B2πrλ=Mvr
v=B2πλr2M
∴ Angular velocity , ω=vR=B2πλr2MR
For r≤ and a<R, we get
ω=−2B0a2λMRkˆ