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Questions  

An insulating rod of length L carries a charge ‘q’ distributed uniformly on it. The rod is pivoted at its mid point and is rotated at a frequency f about a fixed axis perpendicular to the rod and passing through the pivot. The magnetic moment of the rod system is 

a
112πqfl2
b
πqfl2
c
16πqfl2
d
13πqfl2

detailed solution

Correct option is A

At a distance ‘x’ consider a small element of width ‘dx’ .As the element rotates, it can be considered as a current carrying loop.Magnetic moment of the small element is  dM=IA=dqTπx2=qldx fπx2⇒M=qfπl∫−l/2l/2x2dx=qπfl212 .

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