Q. 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) $\pi ver^{2}$
B) $\frac{\pi vr^{2}}{e}$
C) $\frac{\pi ve}{r}$
D) $\frac{\pi er^{2}}{v}$
Explanation
(a) Magnetic moment or magnetic dipole moment is given by
$M = iA\ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
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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
$M = ev.\pi r^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.