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

As we learnt in

Magnetic moment (M) -

M=NiA

- wherein

N-number of turns in the coil

i-current throughout the coil

A-area of the coil

Magnetic moment $=I.A.=\frac{q}{T}.A$

$=\frac{q\omega}{2\pi}. \pi r^2=\frac{1}{2}q\omega r^2$

angular momentum $=mr^{2}\omega$

$\therefore \frac{magnetic \ moment}{Angular \ momentum}=\frac{\frac{1}{2}q \omega r^{2}}{mr^{2}\omega}=\frac{q}{2m}$

Option 1)

ω and q

incorrect

Option 2)

ω, q and m

incorrect

Option 3)

q and m

correct

Option 4)

ω and m

incorrect

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