亥姆霍兹定理重要性分析

The Analysis on the Importance of Helmholtz Theorem

为了将"电磁场与波"课程中的亥姆霍兹(Helmholtz)定理主线化隐为显,从矢量场定解的角度出发,对于各种电场和磁场由散度方程和旋度方程联立产生2阶偏微分方程的方式方法进行了详细的分析、归纳和总结。在强调Helmholtz定理重要性的同时更突出其应用指导意义。这有利于学生在学习过程中清晰构建电磁场理论体系架构,从而有效降低学习难度。

In order to transfer Helmholtz theorem, which is main line in the course of electromagnetic field, from implicit into explicit, the methods to establish the second-order partial differential equation by simultaneous divergence and curl equations for all kinds of electric and magnetic field are analyzed in detail from the viewpoint of the definite solution of vector fields. Emphasis on its application guidance as well as its importance of the Helmholtz theorem will help students to build a clear theoretic architecture of electromagnetic fields and thus effectively reduce the difficulty of learning.