导体球面电像变换函数及其应用

The application of conductor sphere electric image transform function

静电场的唯一性定理是电像法可行、可靠性的基础依据。而具体静电模型若采用电像法处理,必须面对像电荷的位置、电量和个数等问题,这也是电像法被称为"特殊方法"的原因,也正因此,电像法始终难以摆脱拼凑解的嫌疑。应用勒让德多项式与其母函数的关系证明了导体球面电像的合理性和唯一性。引进电像变换函数用以表达导体球外带电体的像格林函数,以实现任意带电体电场中存在导体球界面情形下数值计算的预处理,将边值问题转化为已知电荷分布下的电势计算问题。

The uniqueness of the solution of static electric field is the basic foundation to the feasibility and reliability of method of electric image.However,if the static electrical model needs to take method of electric image to process,it must face some problems such as the charge location,electricity consumption and the number,etc.That is also the reason why the method of electric image is called a 'special method'.Therefore,the method of electric image will not escape from the suspect of patchwork solutions.This paper proves the unique and uniqueness of conductor sphere by applying the relation between Legendre polynomials and its generating function.The introduction of electric image transform function to express the Green function outside the conductor sphere,in order to achieve the pre-processing under the circumstances of any conductor spheres in any charged bodies.The boundary value problem has changed in to a TV algorithm problem under given charge distributions.