DOI: 10.1098/rspa.1950.0107. The conductivity of thin wires in a magnetic field

The conductivity of thin wires in a magnetic field

10.1098/rspa.1950.0107

Crossref journal-article

The Royal Society

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (175)

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.

Bibliography

The conductivity of thin wires in a magnetic field. (1950). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 202(1070), 378â394.

Authors 0

None

References 22 Referenced 222

10.1088/0370-1298/62/2/301
Chambers R. G. 1950 Nature 165 239. (10.1038/165239b0)
{'key': 'p_3', 'first-page': '545', 'article-title': 'Proc. Roy', 'volume': '201', 'author': 'Dingle R. B.', 'year': '1950', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Dingle R. B. (1950)
Eucken A. & Forster F. 1934 Nach. Ges. Wiss. Gottingen N.S. 1- 2 43 129. See also Ann. Phys. Lpz. 28 603 (1937b 33 733 (1938) (Riedel); 30 494 (1937) (Reuter); 40 121 (1941) (Moser).
10.1017/S0305004100019952
Gruneisen E. 1945 Ergebn.
{'key': 'p_7', 'first-page': '101', 'article-title': 'Proc. Roy', 'volume': '144', 'author': 'Jones H.', 'year': '1934', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Jones H. (1934)
10.1002/andp.19484380127
{'key': 'p_9', 'first-page': '311', 'article-title': 'Proc. Roy', 'volume': '157', 'author': 'Lovell A. C. B.', 'year': '1936', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Lovell A. C. B. (1936)
{'key': 'p_10', 'first-page': '270', 'article-title': 'Proc. Roy', 'volume': '166', 'author': 'Lovell A. C. B.', 'year': '1938', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Lovell A. C. B. (1938)
{'key': 'p_11', 'first-page': '718', 'article-title': 'Proc. Roy', 'volume': '158', 'author': 'Lovell A. C. B.', 'year': '1937', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Lovell A. C. B. (1937)
MacDonald D. K. C. 1949 Nature 163 639. (10.1038/163639a0)
MacDonald D. K. C. & Sarginson K. 1949 Nature 164 921. (10.1038/164921a0)
Nordheim L. 1934 Act. Sci. et Ind. no. 131. Paris: Hermann. See also Planck W. 1914 Phy 8. Z. 15 569
Tisza L. 1931 Naturwissenschaften 19 8 6 (10.1007/BF01516774)
Nordheim L. 1931 Ann. Phy 8. Lpz. 9 607. 394 Peierls R. 1931 Ann.Phys. L pz. 10 97.
{'key': 'p_15', 'first-page': '385', 'article-title': 'Proo. Boy', 'volume': '191', 'author': 'Pippard A. B.', 'year': '1947', 'journal-title': 'Soc. A'} / Soc. A / Proo. Boy by Pippard A. B. (1947)
10.1002/andp.19314020602
{'key': 'p_17', 'first-page': '336', 'article-title': 'Nature, 161, 394; Proc. Roy', 'volume': '195', 'author': 'Reuter G. E. H.', 'year': '1948', 'journal-title': 'Soc. A'} / Soc. A / Nature, 161, 394; Proc. Roy by Reuter G. E. H. (1948)
Sondheimer E. H . 1949 Nature 164 920. (10.1038/164920a0)
{'key': 'p_19', 'first-page': '120', 'article-title': 'Proc', 'volume': '11', 'author': 'Thomson J. J .', 'year': '1901', 'journal-title': 'Camb. Phil. Soc.'} / Camb. Phil. Soc. / Proc by Thomson J. J . (1901)
Wilson A. H . 1936 Theory of metals. Cambridge University Press.

Dates

Type	When
Created	18 years, 8 months ago (Dec. 18, 2006, 5:49 p.m.)
Deposited	4 years, 6 months ago (Feb. 19, 2021, 8:10 a.m.)
Indexed	1 year ago (Aug. 13, 2024, 9:54 a.m.)
Issued	75 years ago (Aug. 7, 1950)
Published	75 years ago (Aug. 7, 1950)
Published Online	28 years, 7 months ago (Jan. 1, 1997)
Published Print	75 years ago (Aug. 7, 1950)

Funders 0

None

BibTeX

@article{1950, volume={202}, ISSN={2053-9169}, url={http://dx.doi.org/10.1098/rspa.1950.0107}, DOI={10.1098/rspa.1950.0107}, number={1070}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1950}, month=aug, pages={378–394} }

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