亥姆霍兹定理在求解静电场边值问题中的应用

The Application of Helmholtz's Theorem to Solving the Boundary Value Problem of Electrostatic Field

将电位标量场视为矢量场的一种特例,从亥姆霍兹定理出发直接导出了静电场中电位边值问题的积分解表达式,这种方法的推导过程较采用格林定理的方法更为简单明了。根据边值问题的唯一性原理,由此积分解表达式给出了第一类和第二类边界条件的积分解表达式。

Starting from Helmholtz＇s theorem, the integral formulation of the boundary problem of electrostatic field is deduced based on the fact that scalar field can be regarded as a special example of vector field. The method is more concise than using Green＇s theorem. According to uniqueness theorem, the integral formulations of the first class boundary condition and the second class boundary condition are given form the above integral formulation.