9303753286127016 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

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

Balkishan Agrawal

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s vision for the school is centered on providing a nurturing environment where every student can thrive, learn, and grow.

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