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单词 Method of inversion
释义

Method of inversion

中文百科

镜像法 Method of image charges

(重定向自Method of inversion)
延伸至两个点电荷的物理系统。

镜像法(又称镜像电荷法)是一种解析静电学问题的基本工具。对于静电学问题,镜像法将原本问题的某些元素改换为假想电荷,同时保证仍然满足定解问题原有的的边界条件(请参阅狄利克雷边界条件或诺伊曼边界条件)。

例如,给定一个由一片无限平面导体和一个点电荷构成的物理系统,这无限平面导体可以被视为一片镜子,在镜子里面的镜像电荷与镜子外面的点电荷,所形成的新系统,可以使得导体平面上的电场垂直于导体,与原本系统等价。借此方法,我们可以将问题简化,很容易地计算出导体外的电势、导体的表面感应电荷密度、总感应电荷等等。

镜像法的有效性是唯一性定理的必然结果,该定理指出如果指定了在体积 V 的整个区域内的电荷密度和 V 的所有边界上的电位值,区域 V 内的电位唯一确定。另外,应用此结果到高斯定理的微分形式就能表明,在由导体包围的包含电荷密度为 ρ 的体积 V 中,如果每个导体所带电荷已经给出,那幺电场是唯一确定的。拥有电势或电场的信息以及相应边界条件,只要在指定区域的电荷分布满足泊松方程并设定正确的边界值,我们就可以把我们考虑的电荷分布换为更容易分析的结构。

英语百科

Method of image charges 镜像法

(重定向自Method of inversion)
The field of a positive charge above a flat conducting surface, found by the method of images.
Method of images for an electric dipole moment in a conducting plane
Diagram illustrating the image method for Laplace's equation for a sphere of radius R. The green point is a charge q lying inside the sphere at a distance p from the origin, the red point is the image of that point, having charge -qR/p, lying outside the sphere at a distance of R2/p from the origin. The potential produced by the two charges is zero on the surface of the sphere.
Field lines outside a grounded sphere for a charge placed outside a sphere.

The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics. The name originates from the replacement of certain elements in the original layout with imaginary charges, which replicates the boundary conditions of the problem (see Dirichlet boundary conditions or Neumann boundary conditions).

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更新时间:2025/6/23 15:15:58