Comments on Maxwell's equations

It is desirable from the viewpoint of the teaching of relativity, to emphasize both the four‐tensor and the Maxwell formulations of the equations of the electromagnetic field in curved space‐time. Both formulations are also equally useful in research. With probably only one notable exception, the Maxwell formulation in curved space‐time is not given in the literature. Furthermore, we find that in some particular cases discussed in the literature, the charge‐ and current‐containing electromagnetic field equations expressed in terms of the electromagnetic spatial vectors, have a form which is distinctly unlike Maxwell's equations. We clearly state the reasons why this form of the equations is incorrect. The aim of this paper is not to focus attention on an error in the literature so much as to state the case for the Maxwell formulation in the teaching of relativity to mathematics and physics students. We briefly outline the connection between the four‐tensor form and Maxwell's form of the equations, and seek to clarify some misconceptions and misleading statements in the literature.