Physics Cup – TalTech 2021 – Problem 4

by Jaan Kalda (TalTech).

Sparse electron gas is in a z-directional magnetic field of strength B\gg mk_BT/\hbar e, where T denotes the temperature; m and e stand for the mass and charge of the electrons, respectively. Walls that represent very high potential barriers confine the gas into the region 0<z<L; the pressure exerted by the electrons to these walls is initially equal to p_0. A shock wave in the form of a potential barrier of height U_0=100k_BT travels with speed u through this region. This means that while the potential energy of electrons at z>ut is zero, the potential energy at z<ut is U_0. Find the pressure exerted on the walls after the shock wave has traveled through the entire space of length L between the walls. Assume that u\ll \sqrt{k_BT/m}; neglect the electrostatic interaction of the electrons.

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