弧微分等价代换定理的适用范围

The Scope of Arc Differential Equivalent Substitution Theorem

摘要: 把平面光滑曲线弧微分拓展到空间坐标系中，完成二维条件下的弧微分与空间坐标下弧微分的等价代换，确定了弧微分等价代换定理的适用范围。弧微分等价代换定理可以有效解决有圆形场源存在的电磁场解析解算法问题，可作为高等院校数学和物理电磁学课程教材及教学的补充内容。

Abstract: The arc differential of planar smooth curve is extended to the three-dimensional coordinate system. According to the equivalent substitution relation between arc differential in two-dimensional condition and arc differential in three-dimensional coordinate system, the applicable scope of arc differential equivalent substitution theorem is determined. The equivalent substitution theorem of arc differential can effectively solve the algorithm of electromagnetic field analytical solutions with circular field sources, Can be used as a supplementary content of teaching materials and teaching for mathematics and physics electromagnetism courses in colleges and universities.