Title: A derivation of generalized Maxwell's equations for electromagnetism that permit net charge creation
Abstract: Maxwell's four differential equations that describe electromagnetism are amongst the most famous equations in science. Feynman said they provide four of the seven fundamental laws of classical Physics. However, Coulomb's law of electrostatics and the Biot-Savart law of magnetostatics are used to justify two of the equations, an ad hoc addition of Maxwell's displacement current density term is used to complete the third equation, and the fourth is a description of Faraday's experimental data. This mixed approach has provided the standard pedagogical introduction to these equations for more than a century. It leaves uncertain whether Maxwell's equations should be considered axioms. Here we show that all four of Maxwell's equations (including Faraday's Law) can be derived by simultaneously solving Coulomb's law, the Biot-Savart law and the conservation of charge. We also derive generalised Maxwell's equations that in contrast to the standard forms, allow the creation of net charge. We argue that Coulomb's law, and the Biot-Savart law rather than Maxwell's equations are a better choice of axioms for classical Physics and speculate about the types of experiment that may provide evidence for the break-down of Maxwell's equations in their standard form.
Publication Year: 2015
Publication Date: 2015-10-07
Language: en
Type: preprint
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