The conductivity of thin wires in a magnetic field
- 7 August 1950
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences
- Vol. 202 (1070), 378-394
- https://doi.org/10.1098/rspa.1950.0107
Abstract
A thin film or wire of metal has a lower electrical conductivity than the bulk material if the thickness is comparable with or smaller than the electronic mean free path. Previous workers have obtained expressions for the magnitude of the effect by integrating the Boltzmann equation and imposing the appropriate boundary conditions. The problem is re-examined from a kinetic theory standpoint, and it is shown that the same expressions are obtained by this method, usually rather more simply, while the physical picture is considerably clarified. The method is applied to an evaluation of the conductivity of a thin wire with a magnetic field along the axis, and it is found that the resistivity should decrease as the magnetic field is increased; it should be possible to derive the mean free path and velocity of the conduction electrons by comparison of theory and experiment. The theory has been confirmed by experimental measurements on sodium; estimates of electronic velocity and mean free path are obtained which are in fair agreement with the values given by the free-electron theory.Keywords
This publication has 9 references indexed in Scilit:
- Anomalous Skin Effect in MetalsNature, 1950
- Influence of a Magnetic Field on the Conductivity of Thin Metallic FilmsNature, 1949
- Influence of a Magnetic Field on the Size-Variation of Electrical ConductivityNature, 1949
- Low-Level Atmospheric DuctsNature, 1949
- The Size-Variation of Resistivity for Mercury and TinProceedings of the Physical Society. Section A, 1949
- Elektrischer Widerstand, magnetische Widerstandsänderung und Hall-Effekt der AlkalimetalleAnnalen der Physik, 1948
- The conductivity of thin metallic films according to the electron theory of metalsMathematical Proceedings of the Cambridge Philosophical Society, 1938
- ZuschriftenThe Science of Nature, 1931
- Zur Elektrizitätsleitung und Struktur dünner Metallschichten I. Tatsachenbestand; allgemeiner Zusammenhang zwischen Elektrizitätsleitung und StrukturAnnalen der Physik, 1931