论文标题
无限传导缸中点电荷的图像
The image of a point charge in an infinite conducting cylinder
论文作者
论文摘要
通过将图像电荷放置在相对侧，可以解决导电平面旁边的点电荷的静电问题。对于两个平行平面之间的电荷，可以用平面外部的图像电荷以均匀间隔的间隔移出到无穷大。当放置在圆柱体的轴上时，点电荷的相应图像是什么？圆柱体中的点电荷的潜力是众所周知的，并且可能以许多形式表达，涉及积分或一系列贝塞尔函数，但没有任何形式的图像。实际上，图像是复杂的（在两种感觉上），由磁盘上的无限多环组成，具有一定的表面电荷分布。该手稿试图尽可能准确地描述图像，并在此过程中找到了对电势的简单准确近似值。
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.
