A particle of charge q and mass m moves in a circular orbit or radius r with angular speed `omega`. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

Explanation

Current associated with the moving charge is given by:
`I = q/T`
Where q is the charge and T is the time period of revolution.
` rArr I = qf`
where ` f = 1/T ` = Frequency of revolution
Given, angular velocity = `omega`
Also, ` f = (omega)/(2pi)`
` therefore I = (q omega)/(2pi)`
Angular momentum of charged particle is
`L = m omega r^2`
Magnetic moment associated with the charge will be:
M =IA ` [A = pi r^2]`
` = I pi r^2 = (q omega pi r^2)/(2pi) = (q omega r^2)/(2)`
`M/L = ( (q omega r^2)/(2))/(m omega r^2) = (q)/(2m)`