We review the literature on what classical physics says about the Meissner effect and the London equations. We discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors and conclude that the theorem is based on invalid assumptions. We also point out results in the literature that show how magnetic flux expulsion from a sample cooled to superconductivity can be understood as an approach to the magnetostatic energy minimum. These results have been published several times but many textbooks on magnetism still claim that there is no classical diamagnetism, and virtually all books on superconductivity repeat Meissner’s 1933 statement that flux expulsion has no classical explanation.
REFERENCES
1.
N.
Bohr
, “Studies on the Electron Theory of Metals
,” in Niels Bohr Collected Works—Volume 1—Early Work (1905– 1911)
, edited by L.
Rosenfeld
and J.
Rud Nielsen
(North Holland
, Amsterdam
, 1972
), pp. 291
–395
. Translation of Ph. D. thesis, University of Copenhagen, 1911
.2.
H. J.
van Leeuwen
, “Problèms de la théorie électronique du magnétisme
,” J. Phys. Radium
2
, 361
–377
(1921
). Based on thesis from Leiden University (1919).3.
W.
Meissner
and R.
Ochsenfeld
, “Ein neuer Effekt bei eintritt der Supraleitfähigkeit
,” Naturwiss.
21
, 787
–788
(1933
).4.
J. H.
Van Vleck
, The Theory of Electric and Magnetic Susceptibilities
(Oxford at the Clarendon Press
, Oxford
, 1932
), pp. 94
–104
.5.
6.
7.
A.
Aharoni
, Introduction to the Theory of Ferromagnetism, 2nd ed.
(Oxford U.P.
, Oxford
, 2000
), pp. 6
–10
.8.
9.
S. L.
O’Dell
and R. K. P.
Zia
, “Classical and semiclassical diamagnetism: A critique of treatment in elementary texts
,” Am. J. Phys.
54
, 32
–35
(1986
).10.
Richard
P.
Feynman, Robert
B.
Leighton
, and M.
Sands
, The Feynman Lectures on Physics, Vol. II, Mainly Electromagnetism and Matter
, definitive ed. (Addison-Wesley, Reading
, MA
, 2006
).11.
C. G.
Darwin
, “The dynamical motions of charged particles
,” Phil. Mag. (ser. 6)
, 39
, 537
–551
(1920
).12.
We only consider magnetism from moving charged particles, not from dipole densities. We therefore need not distinguish between the B and the H-fields. Gaussian units are used.
13.
L. D.
Landau
and E. M.
Lifshitz
, The Classical Theory of Fields,
4th ed. (Pergamon
, Oxford
, 1975
).14.
E.
Breitenberger
, “Magnetic interactions between charged particles
,” Am. J. Phys.
36
, 505
–515
(1968
).15.
F. J.
Kennedy
, “Approximately relativistic interactions
,” Am. J. Phys.
40
, 63
–74
(1972
).16.
H.
Essén
, “Darwin magnetic interaction energy and its macroscopic consequences
,” Phys. Rev. E
53
, 5228
–5239
(1996
).17.
J.
Pfleiderer
, “Meissner effect in a classical electron gas
,” Nature (London)
210
, 614
–614
(1966
).18.
H.
Essén
, “Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas
,” EPL
94
, 47003
–1
(2011
).19.
H.
Essén
, “Magnetic fields, rotating atoms, and the origin of diamagnetism
,” Phys. Scr.
40
, 761
–767
(1989
).20.
H.
Essén
, “Electrodynamic model connecting superconductor response to magnetic field and to rotation
,” Eur. J. Phys.
26
, 279
–285
(2005
).21.
S. M.
Mahajan
, “Classical perfect diamagnetism, Expulsion of current from the plasma interior
,” Phys. Rev. Lett.
100
, 075001
–1
(2008
).22.
X.
Fu
and Z.
Fu
, “Realization of Maxwell’s hypothesis
,” e-print arXiv, physics/0311104v2 [physics.gen-ph]
.23.
Allister M.
Forrest
, “Meissner and Ochsenfeld revisited
,” Eur. J. Phys.
4
, 117
–120
(1983
). Contains a translation into English of the German original.24.
P. F.
Dahl
, Superconductivity—Its Historical Roots and Development From Mercury to the Ceramic Oxides
(AIP
, New York
, 1992
), pp. 102
–103
.25.
G.
Lippmann
, “Sur les propriétés des circuits électriques dénués des résistance
,” Compt. Rend.
168
, 73
–78
(1919
).26.
T.
Sauer
, “Einstein and the early theory of superconductivity, 1919–1922
,” Arch. Hist. Exact Sci.
61
, 159
–211
(2007
).27.
Friedrich W.
Hehl
and Yuri N.
Obukhov
, Foundations of Classical Electrodynamics
(Birkhäuser
, Boston
, 2003
), pp. 129
–141
.28.
L. D.
Landau
and E. M.
Lifshitz
, Electrodynamics of Continuous Media, 2nd
ed. (Butterworth-Heinemann
, Oxford
, 1984
).29.
M. C. N.
Fiolhais
, H.
Essén
, C.
Providencia
, and A. B.
Nordmark
, “Magnetic field and current are zero inside ideal conductors
,” Prog. Electromagn. Res. B
27
, 187
–212
(2011
).30.
H.
Essén
, “From least action in electrodynamics to magnetomechanical energy—a review
,” Eur. J. Phys.
30
, 515
–539
(2009
).31.
Kenneth K.
Mei
and G.-C.
Liang
, “Electromagnetics of superconductors
,” IEEE Trans. Microwave Theory Tech.
39
, 1545
–1552
(1991
).32.
H.
Alfvén
and C.-G.
Fälthammar
, Cosmical Electrodynamics, 2nd
ed. (Oxford U.P.
, Oxford
, 1963
).33.
Donald A.
Gurnett
and A.
Bhattacharjee
, Introductory to Plasma Physics
(Cambridge U.P., Cambridge
, United Kingdom
, 2005
), pp. 186
–191
.34.
A.
Badía-Majós
, “Understanding stable levitation of superconductors from intermediate electromagnetics
,” Am. J. Phys.
74
, 1136
–1142
(2006
).35.
W.
Farrell Edwards
, “Classical derivation of the London equations
,” Phys. Rev. Lett.
47
, 1863
–1866
(1981
).36.
Frank S.
Henyey
, “Distinction between a perfect conductor and a superconductor
,” Phys. Rev. Lett.
49
, 416
–416
(1982
).37.
B.
Segall
, L. L.
Foldy
, and R. W.
Brown
, “ “Comment on” classical derivation of the London equations
,” Phys. Rev. Lett.
49
, 417
–417
(1982
).38.
Paul G. N.
deVegvar
, “Comment on the applicability of Lagrangian methods to the London equations
,” Phys. Rev. Lett.
49
, 418
–418
(1982
).39.
J. B.
Taylor
, “A classical derivation of the Meissner effect?
” Nature (London)
299
, 681
–682
(1982
).40.
Richard L.
Moore
, “Derivation of the relation between the vector potential and the current in electromagnetic theory
,” Proc. IEEE
123
, 476
–476
(1976
).41.
P. G.
de Gennes
, Superconductivity of Metals and Alloys
(Perseus Books
, Reading, MA
, 1999
), pp. 4
–7
.42.
F.
London
, Superfluids, Volume 1, Macroscopic Theory of Superconductivity, 2nd ed.
(Dover
, New York
, 1961
), pp. 13
–15
.43.
44.
Neil W.
Ashcroft
and N.
David Mermin
, Solid State Physics
(Saunders College
, PA
, 1976
), p
–731
.45.
C. G.
Darwin
, “The inertia of electrons in metals
,” Proc. R. Soc. London A
154
, 61
–66
(1936
).46.
E. G.
Cullwick
, “Electromagnetic momentum and electron inertia in a current circuit
,” in Proc. IEE - Part C: Monographs
103
, 159
–170
(1956
).47.
J. A.
Stratton
, Electromagnetic Theory
(McGraw-Hill Book Company, Inc.
, New York
, 1941
), pp. 114
–116
.48.
E. G.
Cullwick
, “Magnetic energy and electron inertia in a superconducting sphere
,” in Proc. IEE - Part C: Monographs
103
, 441
–446
(1956
).49.
P. W.
Karlsson
, “Inductance inequalities for ideal conductors
,” Arch. f. Elektrotech.
67
, 29
–33
(1984
).50.
E. K.
Kudinov
, “Thermodynamics of current in superconductors and superfluids
,” Phys. Solid State
48
, 1447
–1454
(2006
). E. K.
Kudinov
, Original in Russian: Fiz. Tverd. Tela (St. Petersburg)
48
, 1366
–1373
(2006
).51.
V. L.
Ginzburg
and L. D.
Landau
, “On the theory of superconductivity
,” Zh. Eksp. Teor. Fiz.
20
, 1064
–1082
(1950
).V. L.
Ginzburg
and L. D.
Landau
, English translation in Collected Papers by L. D. Landau
edited by D.
Ter Haar
, (Pergamon
, Oxford
, 1965
), pp. 546
–568
.52.
J.
Bardeen, Leon
N.
Cooper
, and J. R.
Schrieffer
, “Theory of superconductivity
,” Phys. Rev.
108
, 1175
–1204
(1957
).53.
B. D.
Josephson
, “Coupled superconductors
,” Rev. Mod. Phys.
36
, 216
–220
(1964
).54.
W. A. B.
Evans
and G.
Rickayzen
, “On the equivalence of the phenomena of the Meissner effect and infinite conductivity in superconductors
,” Ann. Phys. (N.Y.)
33
, 275
–307
(1965
).© 2012 American Association of Physics Teachers.
2012
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.