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 1) ω and q 2) ω, q and m 3) q and m 4) ω and m

 The correct answer is 3) q and m

Solution

A magnetic moment is a quantity that represents the magnetic strength and orientation of a magnet or any other object that produces a magnetic field. More precisely, a magnetic moment refers to a magnetic dipole moment, the component of the magnetic moment that can be represented by a magnetic dipole.

We can generalize the magnetic moment for ‘N’ turns of the wire loop as

μ = NiA

Here

μ- magnetic moment

N-number of turns in the coil

i-current throughout the coil

A-area of the coil

The angular momentum L of the particle is given by 
L=mr2/w 

where w=2πn.
Also, we know that

Frequency n=w/2π;
the n

 i=q×n=wq/2π

Magnetic Moment, M=iA=wq / 2π×πr2

M= wqr2 / 2

M/L = wqr2 / 2mr2w = q/2m

Thus the ratio depends upon both q and m.

Hence option (3) is the correct answer