论电磁场媒质分界面衔接条件

Discussion of the Electromagnetic Interface Conditions

电磁场媒质分界面衔接条件是电磁场基本原理的重要组成部分,是电磁场基本方程组微分形式的补充。电磁场原理的应用充分说明了媒质分界面衔接条件的正确性。但长期以来,一直被引用的分界面衔接条件论证过程,需要在论证中引入附加条件。论证切向分量衔接条件时,在包围分界面上一点的矩形回路中,假设垂直于分界面的边比平行于分界面的边以更快的速度趋于零;论证法向分量衔接条件时,在包围分界面上一点的圆柱闭合面中,假设与分界面垂直的侧面以更快的速度趋于零。本文提出了一种不需要上述假设的论证方法,在泰勒级数展开的基础上,只需令矩形和正六面体的各维尺寸同时趋近于零,即可证明分界面衔接条件;以更自然的方式,揭示了分界面上场矢量切向和法向分量突变的本质。

Interface conditions are important parts of the electromagnetic theory. They supplement the differential equations of electromagnetic field. It is clear that they are correct. But the proof of them had defect until now. The existing proof was based on basic supposition. To prove the interface conditions for the tangential components, scholars constructed a small closed path in a plane normal to the interface. They assumed that the edges perpendicular to the interface approached to zero more quickly than the parallel ones. To prove the interface conditions for the normal components, scholars constructed a small cylindrical or hexahedral gaussian surface at the interface. They assumed that the height of side approached to zero more quickly. In this paper we proved the interface conditions without the supposition. Based on the Taylor series expansion, the interface conditions are proved on condition that each dimension approached to zero at same speed in the closed path and hexahedral gaussian surface. It reveais the intrinsic properties of the change of tangential and normal components at the interface between two different media.