Using the Method of Contradiction to Prove that the Definition of Magnetic Field in Maxwell’s Theory is Incorrect

Abstract

Shuang-Ren Zhao

The author discovers an error in the definition of the magnetic field in Maxwell’s classical electromagnetic theory. This paper employs a proof by contradiction to demonstrate that the error occurs during the transition from quasi-static electromagnetic fields to radiating electromagnetic fields. Initially assuming the correctness of Maxwell’s electromagnetic theory, the paper derives Poynting’s theorem and subsequently derives the theorem of mutual energy flow. Following the principles of the latter theorem, the magnetic field is defined, and methods for measuring it are established. It is further demonstrated that the magnetic field obtained using this method is consistent with classical electromagnetic theory under quasi-static conditions. However, in the transition to radiating electromagnetic fields, the newly defined or measured magnetic field conflicts with classical electromagnetic theory. This indicates a flaw in Maxwell’s classical electromagnetic theory. The author identifies this flaw as stemming from Maxwell defining the magnetic field as the curl of the magnetic vector potential, a definition valid only under quasi-static conditions. This definition undergoes a change in radiating electromagnetic fields, a change is overlooked by Maxwell and subsequent researchers. The author proposes a corrective solution to this error in Maxwell’s electromagnetic theory.

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