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Q.

A rod has total charge ‘Q’ uniformly distributed along it length ‘L’. If the rod rotates with angular velocity ‘ ω’ about one end, its magnetic moment is 

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a

3qω2L2

b

qωL26

c

qωL24

d

5qωL24

answer is D.

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Detailed Solution

For small length ‘dx’ at ‘x’ distance,dq=qLdx
Current, i=dqT=Q⋅dx/L2π/ω=qωdx2πL
dM= i. πx2=qω2Lx2⋅dx
Total M=∫0L dM=qω2L,x33
M=qωL26

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