ON INDEPENDENCE, COMPLETENESS OF MAXWELL'S EQUATIONS AND UNIQUENESS THEOREMS IN ELECTROMAGNETICS

In this paper, the independence, completeness of Maxwell's equations and uniqueness theorems in electromagnetics are reviewed. It is shown that the four Maxwell's equations are independent and complete. A complete uniqueness theorem is proposed and proven for the first time by pointing out logic mistakes in the existing proof and presenting a truth table. Therefore, electrostatics and magnetostatics can be reduced from dynamical electromagnetics in all aspects including not only the equations as subsets of Maxwell's equations but also the corresponding uniqueness theorems. It is concluded that the axiomatic system of electromagnetic theory must consist of all four Maxwell's equations. In each discipline, we always try to identify the smallest, most compact set of laws or equations that could define the subject completely. This is the axiomatic system of the matter. The axiomatic laws are general physics laws that are not directly related to any particular cases such as specific material properties etc. The laws are independent when none of them can be deduced from others. The system is complete when no other laws are needed to describe the subject in any case other than the problem-related conditions. All other observations can be mathematically deduced, explained and solved based on those laws consistently and systematically. Although the laws in the axiomatic system must be abstracted from many observations (experiments in physics), they mean much more than any individual observation. They must be also compatible, not contradictory to each other. In mechanics, we have the great Newton's three laws. Correspondingly