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Two particles , each of mass m and char...

Two particles , each of mass ` m` and charge `q`, are attached to the two ends of a light rigid rod of length ` 2 R` . The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is

A

`q//2`

B

`q//m`

C

`2q//m`

D

`q//pim`

Text Solution

Verified by Experts

Let v be the speed of rotation of each charge in a circle of radius R. So the time period of revolution, `T=2piR//v`. Total current due to movement of charge, `I=2q//T=2qv//2pi`. `R=qv//piR`. So magnetic moment,
`M=IxxpiR^2=(qv//piR)xxpiR^2=qvR`.
Angular momentum of system `(L)=2mvR`
So `M//L=qvR//2 mvR=q//2m`
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