A charged particle (charges = q, mass = m) is rotating in a circle of radius R with uniform speed V ratio of its magnetic moment `(mu)` to the angular momentum (L) is

Options

A. `(q)/(2m)`
B. `(q)/(m)`
C. `(q)/(4m)`
D. `(2q)/(m)`

Answer

A

Explanation

`L=mv R`
`n=1`
`i=(q)/(T)rArr T=(2 pi R)/(v)`
`rArr I =(q)/((2pi R)/(v))=(qv)//(2 pi R)`
`A= pi R^2`
`therefore mu =n I A= 1 xx(qv)/(2 pi R) xx pi R^2`
`= (qv R)/(2)`
`L =IW = MR^2xx(v)/( R) =MRv`
l= Moment of inertia
`(mu)/(L)=(n i A)/(mvr)=((qv R)/(2))/(m v R )=(q)/(2 m)` .