8.2 Orbital Magnetic Dipole Moment of the Electron

A hydrogen atom is placed in a magnetic field. Which of the following quantities are affected? (a) total energy; (b) angular momentum; (c) z-component of angular momentum; (d) polar angle.

Find the magnitude of the orbital magnetic dipole moment of the electron in in the 3p state. (Express your answer in terms of $\mu_{\text{B}} .$)

Estimate the ratio of the electron magnetic moment to the muon magnetic moment for the same state of orbital angular momentum. (Hint: $m_{\mu} = 105.7 \text{MeV} / c^{2} \left.\right)$

For a 3d electron in an external magnetic field of $2.50 \times 10^{− 3} \text{T}$, find (a) the current associated with the orbital angular momentum, and (b) the maximum torque.

Find the minimum torque magnitude $\left|\right. \overset{\rightarrow}{\tau}$ | that acts on the orbital magnetic dipole of a 3p electron in an external magnetic field of $2.50 \times 10^{- 3} \text{T}$.

Show that $U = − \overset{\rightarrow}{\mu} \cdot \overset{\rightarrow}{B}$.

(Hint: An infinitesimal amount of work is done to align the magnetic moment with the external field. This work rotates the magnetic moment vector through an angle $- d \theta$ (toward the positive z-direction), where $d \theta$ is a positive angle change.)