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Q.

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

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a

112πqfl2

b

πqfl2

c

16πqfl2

d

13πqfl2

answer is A.

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Detailed Solution

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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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