# 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; 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 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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