0912.5041Dec 26, 200914 pages, See also the related paper [arXiv:0912.5044]: J. A. Heras, "Reply to comment on 'Can Maxwell's equations be obtained from the continuity equation?'" by E. Kapuscik, Am. J. Phys. 77, 755-756 (2009)
How to obtain the covariant form of Maxwell's equations from the continuity equation
Jose A. Heras
Abstract
The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.