An electron with kinetic energy Ke 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 μ = Ke/B and that it is in the direction opposite that of 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 5.3 x 1021 electrons/m3 and the same number density of ions. Take the average electron kinetic energy to be 6.2 x 10-20 J and the average ion kinetic energy to be 7.6 x 10-21 J. Calculate the magnetization of the gas when it is in a magnetic field of 1.2 T.