On Equivalence of Maxwell's Equations in Differential and Integral Forms


Polat B.

2nd International Conference on Electrical, Communication and Computer Engineering, ICECCE 2020, İstanbul, Turkey, 12 - 13 June 2020 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • Doi Number: 10.1109/icecce49384.2020.9179294
  • City: İstanbul
  • Country: Turkey
  • Yıldız Technical University Affiliated: Yes

Abstract

© 2020 IEEE.The analytical tools required to legitimize derivations of electromagnetic boundary conditions on an interface of singularity by using Divergence and Stokes's Theorems are presented in the Space of Schwartz-Sobolev Distributions in two steps. First, the differential and integral forms of Maxwell's Equations are demonstrated to be equally informative. By equal information it is implied that the integral/differential form of field equations can be derived when they are given in differential/integral form. Next, Divergence and Stokes's Theorems of Vector Calculus are shown to be valid in the sense of Schwartz-Sobolev distributions. This reveals that the distributional investigations of differential and integral forms of Maxwell's Equations reveal the same set of boundary conditions.