论文标题
传导椭圆和尖晶球体中的点电荷图像
Images of point charges in conducting ellipses and prolate spheroids
论文作者
论文摘要
这是对2D传导椭圆和3D pr酸球体中点电荷图像的确切形式的研究。对于具有外部点源的椭圆，我们将椭圆内部分析延续的两个先前表达式向下比较焦线，即图像电荷的位置。对于内部来源，我们发现了一系列外面的图像电荷。对于关闭球体表面的点源，在包含球体内反射电位延续的区域中电势差的串联解决方案。我们发现了一个图像系统，该系统在prale球体的轴上有一个点电荷，该轴是从焦点段延伸的，在轴上延伸了。对于离轴电荷，我们找到了新的近似图像充电。对于球体中心的点电荷，发现图像奇异性位于无限宽的平板上，孔周围有一个孔。对于位于球体内部任何地方的点电荷，我们找到了两个新的近似图像电荷解决方案，当源位于表面附近时适用的真实空间中的点电荷，或者在复杂空间中的点电荷，该点在旋转轴附近源时应用的真实空间中的环在真实空间中投射为环。当点电荷精确地位于焦点时，订单1/2的多极是理想的图像近似值。
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.
