The Galilean limits of Maxwell's equations

Details The Galilean limits of Maxwell's equations The Galilean limits of Maxwell's equations

2010-12-06

arxiv.org/abs/1012.1068v1

Am. J. Phys. 78, 1048-1055 (2010)

Physics

Classical Physics

Scientific paper

10.1119/1.3442798

We show that if Maxwell's equations are expressed in a form independent of specific units, at least three Galilean limits can be extracted. The electric and magnetic limits can be regarded as nonrelativistic limits because they are obtained using the condition $|\bf{v}| \ll c$ and restrictions on the magnitudes of the sources and fields. The third limit is called the instantaneous limit and is introduced by letting $c\to \infty$. The electric and instantaneous limits have the same form, but their interpretation is different because the instantaneous limit cannot be considered as a nonrelativistic limit. We emphasize the double role that the speed of light $c$ plays in Maxwell's equations.

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