Q. 174.1( 14 Votes )

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 :

Line charge per unit length is given by the following relation:

Total charge/ length = Q/2π r


Where r is the distance of the point within the wheel


Let m and R are mass and radius of the wheel


Magnetic field is given by the following relation:



The magnetic force at balanced by the centripetal force at a distance of r


i.e. BQv = mv2/r


v is the linear velocity of the wheel and is equal to v= 2π rλ


B × 2π rλ = mv/r


Or


As we know that angular velocity is given as: ω = v/r


w =


When R> a and r ≤ a


ω =


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