Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light, together with Galilean invariance of the Lorentz force, allows us to finalize Maxwell's equations and to introduce arbitrary electrodynamics units naturally.
REFERENCES
1.
Donald H.
Kobe
, “Derivation of Maxwell's equations from the local gauge invariance of quantum mechanics
,” Am J. Phys.
46
, 342
–348
(1978
).2.
Freeman J.
Dyson
, “Feynman's proof of the Maxwell equations
,” Am. J. Phys.
58
, 209
–211
(1990
).3.
José A.
Heras
, “Can Maxwell's equations be obtained from the continuity equation?
” Am. J. Phys.
75
, 652
–657
(2007
).4.
José A.
Heras
, “How to obtain the covariant form of Maxwell's equations from the continuity equation
,” Eur. J. Phys.
30
, 845
–854
(2009
).5.
Fritz
Emde
, “Polare und axiale Vektoren in der Physik
,” Z. Phys. A
12
, 258
–264
(1923
).6.
7.
J. W.
Norbury
, “The invariance of classical electromagnetism under charge conjugation, parity and time reversal (CPT) transformations
,” Eur. J. Phys.
11
, 99
–102
(1990
).8.
9.
The different nature of and is apparent also in the construction of the electromagnetic field tensor in the covariant formulation of electrodynamics.
10.
11.
The superposition principle for an inhomogeneous, partial differential equation with linear differential operator L states that with two solutions obeying and , the sum is also a solution for the inhomogeneity .
12.
Julian
Schwinger
, “A Magnetic Model of Matter
,” Science
165
, 757
–761
(1969
).13.
Frank S.
Crawford
, “Magnetic monopoles, Galilean invariance, and Maxwell's equations
,” Am. J. Phys.
60
, 109
–114
(1992
).14.
Max
Jammer
and John
Stachel
, “If Maxwell has worked between Ampère and Faraday: An historical fable with a pedagogical moral
,” Am. J. Phys.
48
, 5
–7
(1980
).15.
José A.
Heras
, “The Galilean limits of Maxwell's equations
,” Am. J. Phys.
78
, 1048
–1055
(2010
).16.
José A.
Heras
, “The c equivalence principle and the correct form of writing Maxwell's equations
,” Eur. J. Phys.
31
, 1177
–1185
(2010
).© 2013 American Association of Physics Teachers.
2013
American Association of Physics Teachers
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