Abstract
In this chapter we show first that the magnetic field B arises naturally from a Lorentz transformation of the electric force in Coulomb’s law and so we can investigate the electric and magnetic fields of rapidly moving charges. Then by introducing a vector potential A subject to the Lorentz gauge condition we find a remarkable similarity between the equations of electrostatics, expressed in terms of the scalars Ø (potential) and ρ, and the equations of magnetostatics in terms of the vectors A and j. Finally we show, using a four-dimensional notation, that it is possible to reduce Maxwell’s four equations to just one equation which expresses directly the invariance of electromagnetism under the Lorentz transformation.
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© 1993 E. R. Dobbs
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Dobbs, E.R. (1993). Electromagnetism and relativity. In: Basic Electromagnetism. Physics and Its Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2112-5_8
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DOI: https://doi.org/10.1007/978-94-011-2112-5_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-412-55570-1
Online ISBN: 978-94-011-2112-5
eBook Packages: Springer Book Archive