Mathematical Physics

Gauss’s Flux Theorem in Differential Form Has no Definite Physical Significance

Authors: Hongyuan Ye
Comments: 13 Pages.

In classical electromagnetism, Gauss’s flux theorem in integral form states that the electric flux through a closed surface is proportional to the charge enclosed by that surface. Recent research points out that Gauss’s flux theorem in integral form applies to static electric fields but not to time-varying electric fields. This paper reveals that when Gauss’s flux, characterized by three-dimensional space, is compressed to a single point, the divergence of a field no longer retains its original meaning of the flux. Based on the divergence of the electric field at a point in space, Gauss's flux theorem in differential form contradicts Coulomb's law and violates the superposition principle of the electric fields. Therefore, the differential and integral forms of Gauss’s flux theorem are not equivalent. In conclusion，Gauss’s flux theorem in differential form does not hold in both static and time-varying electric fields, and has no definite mathematical and physical significance. Theoretical physics and mathematics will undergo a revolutionary scientific transformation.
Category: Mathematical Physics