On independence, completeness of Maxwell's equations and uniqueness theorems in electromagnetics

Abstract

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.