导电椭圆和长椭球中的点电荷象
Images of point charges in conducting ellipses and prolate spheroids
摘要：
本文研究了点电荷在二维导电椭圆和三维长椭球中象的精确形式。对于具有外部点源的椭圆，我们比较了两个以前的表达式，用于在椭圆内部解析延拓到焦线，即像电荷的位置。对于内部源，我们发现了一系列的图像电荷躺在外面。对于接近椭球表面的点源，电势的级数解在包含椭球内部反射电势的延续的奇点的区域中发散。我们揭示了一个图像系统的点电荷的轴上的一个长椭球体，从焦段有点进一步的轴延伸。对于离轴电荷，我们找到了一个新的近似像电荷。对于位于椭球中心的点电荷，发现其像奇异性位于无限宽的平板上，且椭球周围有一个孔。对于位于椭球内任意位置的点电荷，我们找到了两种新的近似镜像电荷解，一种是源位于椭球表面附近时的实空间点电荷，另一种是源位于椭球旋转轴附近时的复空间点电荷。当点电荷恰好位于焦点上时，1/2阶多极子是理想的像近似。
英文摘要：
This is an investigation into the exact forms of images of point charges in 2D conducting ellipses and 3D prolate spheroids. For an ellipse with exterior point source, we compare two previous expressions for the analytic continuation inside the ellipse down to the focal line, the location of the image charge. For an interior source, we discover a sequence of image charges lying outside. For a point source close the surface of a spheroid, series solutions for the potential diverge in a region that encompasses the singularities of the continuation of the reflected potential inside the spheroid. We uncover an image system for a point charge on the axis of a prolate spheroid that extends from the focal segment somewhat further up the axis. For an off axis charge we find a new approximate image charge. For a point charge at the center of the spheroid, the image singularity is found to lie on an infinitely wide, flat sheet with a hole around the spheroid. For a point charge located anywhere inside the spheroid, we find two new approximate image charge solutions, a point charge in real space which applies when source lies near the surface, or a point charge in complex space which projects as a ring in the real space which applies when the source lies near the rotation axis. When the point charge lies exactly on a focal point, a multipole of order 1/2 is an ideal image approximation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
