Halliday, Resnick & Walker — Maxwell's Equations; Magnetism of Matter: Problem 31

31 An electron with kinetic energy $K_e$ travels in a circular path that is perpendicular to a uniform magnetic field, which is in the positive direction of a $z$ axis. The electron’s motion is subject only to the force due to the field. (a) Show that the magnetic dipole moment of the electron due to its orbital motion has magnitude $\mu = K_e/B$ and that it is in the direction opposite that of $\vec{B}$. What are the (b) magnitude and (c) direction of the magnetic dipole moment of a positive ion with kinetic energy $K_i$ under the same circumstances? (d) An ionized gas consists of $3.1 \times 10^{21}$ electrons/m$^3$ and the same number density of ions. Take the average electron kinetic energy to be $6.2 \times 10^{-20}$ J and the average ion kinetic energy to be $7.6 \times 10^{-21}$ J. Calculate the magnetization of the gas when it is in a magnetic field of 1.2 T.