带电细圆环与导体圆柱面系统静电问题的研究  

The study of electrostatic problems of the system consisting of charged rings and a conductor cylinder

作　　者：袁晓忠 刘世勇 YUAN Xiao-zhong;LIU Shi-yong(School of Physics and Astronomy,Shanghai Jiaotong University,Shanghai 200240,China)

机构地区：[1]上海交通大学物理与天文学院,上海200240

出　　处：《大学物理》2022年第8期30-34,共5页College Physics

摘　　要：研究了由两均匀带电全同细圆环与无限长接地导体圆柱面构成的静电系统,在柱坐标系下用δ函数表示线电荷的体分布函数,将带边界条件的泊松方程转化为拉普拉斯方程后精确求解.分析了系统中的电势分布,由电势得到圆柱内表面感应电荷面密度,计算了感应电荷在系统轴线上产生的电场,发现在适当条件下,由于感应电荷的影响,轴线上一对等量同号点电荷受到的静电力为吸引力.The electrostatic system consisting of two uniformly charged identical rings and an infinite grounded conductor circular cylinder is studied. δ function is used to express the volume density function of the line charges in cylindrical coordinates.The Poisson equation with boundary condition is changed into Laplace equation and solved exactly.The potential distribution of the system is analyzed.The induced surface charge density on the inner surface of the cylinder is obtained from the potential distribution.The electric field produced by the induced charge along the axis of the system is calculated.It is found that because of the influence of the induced charge, the electrostatic force on a pair of point charges with the equal magnitude and the same sign on the axis is attractive under proper conditions.

关 键 词：泊松方程 拉普拉斯方程 Δ函数 

分 类 号：O442[理学—电磁学]