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

The angular momentum L of the particle is given by L=mr2w

where w=2πn.

∴ Frequency n = w/2π

Further i = q × n = wq/2π

Magnetic Moment, M = iA = wq/2π × πr2

∴ M = wqr2/2

So, M/L = wqr2/2mr2w = 2mq

Thus, the required ratio depends upon both q and m.