Q. A model for quantized motion of an electron in a uniform magnetic field $B$ states that the flux passing through the orbit of the electron is $n(h/e)$ where $n$ is an integer, $h$ is Planck's constant and $e$ is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ($m$ is the mass of the electron)
A) $\frac{he}{\pi m}$
B) $\frac{he}{2\pi m}$
C) $\frac{heB}{\pi m}$
D) $\frac{heB}{2\pi m}$
Explanation
[Solution by Claude - not from source] Lowest state $n=1$: $B\pi r^2=h/e$. Orbit radius $r=\frac{mv}{eB}$. $\mu=\frac{evr}{2}=\frac{e}{2}\cdot\frac{eBr}{m}\cdot r=\frac{e^2Br^2}{2m}=\frac{e^2}{2m}\cdot\frac{h}{\pi e}=\frac{he}{2\pi m}$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.