First slide

Magnetic Dipole moment

Question

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

Moderate

A

$ω and q$
B

$ω q and m$
C

q and m
D

$ω and m$

Solution

The effective current, $i = \frac{qω}{2 π} and A = {πr}^{2}$
Magnetic moment, $M = iA = \frac{1}{2} {qωr}^{2}$
Angular moment, $L = Iω = {mr}^{2} ω \Rightarrow \frac{M}{L} = \frac{q}{2 m}$

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