Q. An electron is moving in an orbit of radius $R$ with a time period $T$ as shown in the figure. The magnetic moment produced may be given by |$e$| represents the magnitude of the electron charge.
A) $\mathbf{M} = \frac{2\pi|e|\mathbf{A}}{T}$
B) $\mathbf{M} = - \frac{2\pi|e|\mathbf{A}}{T}$
C) $\mathbf{M} = \frac{|e|\mathbf{A}}{T}$
D) $\mathbf{M} = - \frac{|e|\mathbf{A}}{T}$
Explanation
(b) Magnitude of the magnetic moment
$M = I\ A\ \begin{bmatrix}
where & I & is\ the\ current \\
and\ & A & is\ the\ area
\end{bmatrix}\ $
The current produced in one revolution
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ I = ev = e\frac{2\pi}{T}$
$\therefore$ Magnetic moment $= \frac{2\pi}{T}\ |e|A$
As the electron is flowing in the anticlockwise direction. The current is flowing in the clockwise direction.
$\therefore M = - \frac{2\pi}{T}\ |e|A$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.