First slide

Magnetic dipole - Moving charges and magnetism

Question

An electron is revolving in a circular orbit of radius r in a hydrogen atom. The angular momentum of the electron is L. The dipole moment associated with it is

Moderate

A

$(\frac{2 e}{m}) L$
B

$(\frac{e}{2 m}) L$
C

$(\frac{e}{m}) L$
D

$(\frac{2 m}{e}) L$

Solution

Magnetic moment of revolving electron, $M = i A = (\frac{e}{\frac{2 π r}{V}}) \times (π r^{2}) = \frac{e V r}{2}$ …………….(1)
But, Angular Momentum = L = mVr …………….(2)
Dividing (1) and (2)
$\begin{array}{l} \Rightarrow \frac{M}{L} = \frac{e V}{2} (\frac{r}{m V r}) = (\frac{e}{2 m}) \\ \Rightarrow M = (\frac{e}{2 m}) L \end{array}$

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