标题： 点电荷在无限导体圆柱体中的像 显示英文标题

标题： The image of a point charge in an infinite conducting cylinder

摘要： 点电荷靠近导电平面的静电学问题最好通过在相反侧放置一个镜像电荷来解决。 对于两个平行平面之间的电荷，可以通过在平面外以等距间隔放置镜像电荷并延伸到无限远来解决。 当点电荷位于圆柱体轴上时，对应的镜像会是什么？ 圆柱体内点电荷的电势是众所周知的，可以用涉及积分或贝塞尔函数级数的多种形式表示，但其中没有哪一个暗示了镜像的存在。 事实上，镜像是复杂的（在两种意义上），由一个盘上的无限多个环组成，具有某种表面电荷分布。 本文试图尽可能准确地描述该镜像，并在此过程中找到了电势的简单而精确的近似值。 显示英文摘要

摘要： The electrostatics problem of a point charge next to a conducting plane is best solved by placing an image charge placed on the opposite side. For a charge between two parallel planes this can be solved with image charges outside the planes at evenly spaced intervals moving out to infinity. What is the corresponding image of a point charge is when placed on the axis of a cylinder?. The potential of a point charge in a cylinder is well known and may expressed in many forms involving integrals or series of Bessel functions, but none of which elude to an image. In fact the image is complex (in both senses), consisting of infinitely many rings on a disk with some surface charge distribution. This manuscript attempts to describe the image as accurately as possible, and in doing so finds simple accurate approximations for the potential.