Chapter 8: Problem 16
Assume that an electron is describing a circular orbit of radius \(a\) about a positively charged nucleus. (a) By selecting an appropriate current and area, show that the equivalent orbital dipole moment is \(e a^{2} \omega / 2\), where \(\omega\) is the electron's angular velocity. \((b)\) Show that the torque produced by a magnetic field parallel to the plane of the orbit is \(e a^{2} \omega B / 2 .(c)\) By equating the Coulomb and centrifugal forces, show that \(\omega\) is \(\left(4 \pi \epsilon_{0} m_{e} a^{3} / e^{2}\right)^{-1 / 2}\), where \(m_{e}\) is the electron mass. \((d)\) Find values for the angular velocity, torque, and the orbital magnetic moment for a hydrogen atom, where \(a\) is about \(6 \times 10^{-11} \mathrm{~m} ;\) let \(B=0.5 \mathrm{~T}\).
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.