The most difficult step in the analysis of the capacitance of arbitrarily shaped conducting plates is the determination of the electric center, or the expansion point of the charge density. This paper presents the generalized Huygens' principle, which indicates that the charge distribution on a conducting plate of convex shape has a tendency to be a circle before approaching the fringe. Therefore, the center of the largest extended circle can be taken as the electric center. The agreement with numerical methods is demonstrated.

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The electromagnetic properties of the moving media interface in a high frequency range is analysed and the dependence of generalized refraction on frequency is obtained based on special relativity.

A generalized refractive index in the form of optic eikonal is defined through comparing frame definitions of left-handed and right-handed sets and indicates the sign of the refractive index covered by the quadratic form of the eikonal equation. Fermat's principle is generalized, and the general refractive law is derived directly.Under this definition, the comparison between Fermat's principle and the least action principle is made through employing path integral and analogizing L. de Broglie's theory.

Based on Fermat's principle and the special relativity, the transmission of high-frequency electromagnetics is unified by variational formulation on the moving interface. Applying the theoretical model, we investigate the detailed practices of transmission of high-frequency electromagnetic under relativistic conditions. The deduced results illustrate that the effective estimation of the super high-speed effect on a moving interface supports the valuable frame of reference in controlling precision. The results also show that the theoretical model has potential applications in electromagnetically controlled precision in the quantum information, ray sensor, controllable environment, etc.