Question

The energy E of a magnetic moment ~µ in a magnetic field B~ is E = −~µ · B~ . Consider an isolated particle with magnetic moment ~µ. The projection of ~µ along z can only take two values: (~µ)z = ±µB, where µB is a constant called the Bohr magneton. i) What are the particle energies E± corresponding to the two projections when the particle is subject to a magnetic field B~ ≡ (0, 0, Bz) along the z-axis ? The systems (i.e. the particle) is now in equilibrium with a heat bath of temperature T. ii) For T → ∞, what are the values of the particle’s average energy hEi and entropy S? iii) Plot schematically the behavior of the relative energy fluctuations (∆E) 2 as function of T. Hints. Knowing the actual value of µB is not relevant.

Answer 1