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 Ï. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

Moderate

A

$Ï and q$
B

$Ï q and m$
C

q and m
D

$Ï and m$

Solution

The magnetic moment of a charged particle moving in circular orbit is given by
$p_{m} = iA = \frac{q}{T} Ã {Ïr}^{2} = \frac{q Ã {Ïr}^{2}}{(2 Ï / Ï)}$
or $p_{m} = \frac{q Ã {Ïr}^{2} Ã Ï}{2 Ï} = \frac{{qÏr}^{2}}{2}$ â¦(1)
The angular momentum L is given by
$L = IÏ = {mr}^{2} Ï$ â¦.(2)
Dividing eq. (t) by eq. (2), we get
$\frac{p_{m}}{L} = \frac{q}{2 m}$
So, the ratio of magnetic moment to angular momentum depends on q and m.

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