2019/08/17 by M. Creff, F. Faisant, J. M. Rubì +2 · 1 citation
Engineering · Physics and Astronomy · #Magnetic Field Sensors Techniques #Quantum and Classical Electrodynamics #Thermal Analysis in Power Transmission #cond-mat.mes-hall
paper · pdf · doi:10.1063/5.0013182
9 pages, 2 figures
arxiv created 2019/08/17 · openalex created_date 2019/08/22 · openalex publication_date 2020/08/06 · arxiv updated 2020/08/26 · openalex updated_date 2026/07/30
A variational approach is used in order to study the stationary states of Hall devices. Charge accumulation, electric potentials and electric currents are investigated on the basis of the Kirchhoff-Helmholtz principle of least heat dissipation. A simple expression for the state of minimum power dissipated -- that corresponds to zero transverse current and harmonic chemical potential -- is derived. It is shown that a longitudinal surface current proportional to the charge accumulation is flowing near the edges of the device. Charge accumulation and surface currents define a boundary layer over a distance of the order of the Debye-Fermi length.