First slide

Magnetic Dipole moment

Question

A uniformly charged rod with charge Q and length L is rotating about one end with constant angular speed $ω$ . Find the magnetic dipole moment of the rod. Consider the mass of it is M.

Easy

A

$\frac{Q L^{2} ω}{2}$
B

$\frac{Q L^{2} ω}{3}$
C

$\frac{Q L^{2} ω}{12}$
D

$\frac{Q L^{2} ω}{6}$

Solution

We know that the magnetic dipole moment is given by
$μ = \frac{Q}{2 M} L = \frac{Q}{2 M} I ω \Rightarrow μ = \frac{Q}{2 M} (\frac{1}{3} M L^{2}) ω = \frac{Q L^{2} ω}{6}$

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