矢量积分方法在电磁学中的应用

Application of Vector Integration Methods in Electromagnetism

本文分别通过矢量投影方法和矢量积分方法对电磁学问题进行求解,同时对比了两种方法在处理问题时的区别和联系,意在说明在处理电磁学问题上,矢量积分方法有直观简便的优点。为达到该目的,我们利用矢量积分方法数值地展示了均匀带电圆环的电场分布和圆形载流线圈的磁场分布,这是矢量投影方法所难以做到的。因此,我们的结果表明矢量积分法在处理矢量积分问题中更具一般性,在处理复杂问题中时具有巨大的优势。最后我们呼吁电磁学教学中应更加重视矢量积分方法的讲解和练习。

To illustrate that the vector integral approach has the advantages of intuition and simplicity in dealing with electromagnetic problems,this paper solves electromagnetic problems using the vector projection method and the vector integral methodrespectively,comparing their differences and connection.With this in mind,we adopt the vector integration approach to numerically demonstrate the electric field distribution of a uniformly charged circular ring and the magnetic field distribution of a circular current-carrying coil,which is difficult to achieve using the vector projection method.As a result,we show that the vector integration method is more universal in dealing with vector integration problems and provides significant benefits in complex scenarios.Finally,we advocate for a greater emphasis on the explanation and application of the vector integration approach in electromagnetic education.