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(C) The magnetic moment $M$ of a particle of charge $q$ moving in a circular orbit is given by $M = IA$, where $I$ is the current and $A$ is the area

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$q$ and $m$

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(C) The magnetic moment $M$ of a particle of charge $q$ moving in a circular orbit is given by $M = IA$, where $I$ is the current and $A$ is the area of the orbit.The current $I = \frac{q}{T} = \frac{q\omega}{2\pi}$.The area $A = \pi r^2$.Thus, $M = \left(\frac{q\omega}{2\pi}\right)(\pi r^2) = \frac{q\omega r^2}{2}$.The angular momentum $L$ of the particle is $L = mvr = m(\omega r)r = m\omega r^2$.The ratio of the magnetic moment to the angular momentum is $\frac{M}{L} = \frac{q\omega r^2 / 2}{m\omega r^2} = \frac{q}{2m}$.This ratio is known as the gyromagnetic ratio and depends only on the charge '$q$' and mass '$m$' of the particle.

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

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