Question

An electron of charge e moves in a circular orbit of radius r around the nucleus at a frequency v. The magnetic moment associated with the orbital motion of the electron is

• A. $ \pi ve{{r}^{2}} $
• B. $ \frac{\pi v{{r}^{2}}}{e} $
• C. $ \frac{\pi v\,e}{r} $
• D. $ \frac{\pi v{{r}^{2}}}{v} $

Answer 1

Answer: (A)

Magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. It is given by
$ \mu =IA $ .. (i) where $ I $ is current and $ A $ the area. The effective current $ (I) $ is $ I=\frac{e}{T} $ where $ e $ is electron charge and $ T $ the time period. Also, $ v=\frac{1}{T}= $ frequency and area $ A=\pi {{r}^{2}} $ , where $ r $ is radius of circular path. Putting these values in Eq. (i), we get $ \mu =ev.\pi {{r}^{2}} $ Note: Magnetic moment can also expressed terms of angular momentum
$ (L) $ $ \mu =IA=-\frac{2}{2{{M}_{e}}}L $ . where $ {{M}_{e}} $ is mass of electron.