The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the Liénard-Wiechert potentials. The derivation uses arguments based on Lorentz invariance and a physically transparent expression originally due to Thomson for the field of a charge that experiences an impulsive acceleration.

Topics
Electromagnetism, Covariant formulation, Four-velocity, Relativistic four vector, Fundamental constants, Maxwell equations, Electrodynamics, Special relativity, Partial differential equations, Educational aids
1.
See, for example,
L. D.
 
Landau
 and
E. M.
 
Lifshitz
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The Classical Theory of Fields
(
Butterworth-Heinemann
,
Oxford
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2.
Hamsa
 
Padmanabhan
, unpublished.
3.
J. J.
 
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Electricity and Matter
(
Archibald Constable
,
London
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1907
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4.
T.
 
Padmanabhan
,
Theoretical Astrophysics: Astrophysical Processes
(
Cambridge U. P.
,
Cambridge
,
2000
), Vol.
1
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Crossref
Search ADS
 
5.
E. M.
 
Purcell
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Electricity and Magnetism
,
The Berkeley Physics Course
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Mc-Graw-Hill
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See also
F. S.
 
Crawford
,
Waves
,
The Berkeley Physics Course
(
Mc-Graw-Hill
,
New York
,
1968
), Chap. 7.
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6.
J. D.
 
Jackson
,
Classical Electrodynamics
, 3rd ed. (
Wiley
,
New York
,
1999
), Chap. 14.
Google Scholar
 
© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
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