The Contradictions in Poynting Theorem and Classical Electromagnetic Field Theory

When studying the energy principle of N current elements, the author found that the Poynting’s theorem of N current elements is very similar to the principle of mutual energy, except that the subscript of the summation symbol is different. Because the mutual energy principle of N current elements and Poynting’s law of N current elements are all energy conservation laws, the author considers that they should be the same. Due to this consideration, the author found that the self-energy flow should not transfer energy. Self-energy flow is the energy flow corresponding to the Poynting vector of a current element, but this energy flow is not zero for any antenna. The author believes that this is a loophole in classical electromagnetic theory. The author’s previous solution was to add a time-reversal wave to Maxwell’s theory. This paper studies this problem through the electromagnetic field of plane-sheet current. It is found that the magnetic field calculated by Maxwell’s equations is still the magnetic field generated by the current itself, but the electric field calculated by Maxwell’s equation is actually the advanced wave generated by the environment of the current.