Consider a system of charged particles (not dipoles), obeying classical mechanics and classical statistics. Show that the magnetic susceptibility of this system is identically zero (Bohr-van Leeuwen theorem).

[Note that the Hamiltonian of this system in the presence of a magnetic field \(\boldsymbol{H}(=abla \times \boldsymbol{A})\) will be a function of the quantities \(\boldsymbol{p}_{j}+\left(e_{j} / \boldsymbol{c}ight) \boldsymbol{A}\left(\boldsymbol{r}_{j}ight)\), and not of the \(\boldsymbol{p}_{j}\) as such. One has now to show that the partition function of the system is independent of the applied field.]