大学物理 ›› 2018, Vol. 37 ›› Issue (1): 46-47.doi: 10.16854 /j.cnki.1000-0712.1706165

• 教学讨论 • 上一篇    下一篇

点电荷至接地导体球面的曳引时间的解析解及其渐近行为

李力,张银   

  1. 1.重庆清华中学,重庆400054;2.郑州轻工业学院数学与信息科学学院,河南郑州450002
  • 收稿日期:2017-04-05 修回日期:2017-08-07 出版日期:2018-01-20 发布日期:2018-01-20
  • 作者简介:李力( 1972—) ,男,重庆清华中学高级教师、特级教师,课余从事数学物理、理论物理以及相关高等数

An analytic solution and asymptotic behavior for traction time of point charge to grounded conducting sphere

LI Li1,ZHANG Yin2   

  1. 1.Chongqing Qinghua High School,Chongqing 400054,China; 2. College of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou,Henan 450002,China
  • Received:2017-04-05 Revised:2017-08-07 Online:2018-01-20 Published:2018-01-20

摘要: 在不计重力、空气阻力以及相对论效应的条件下,通过求解运动微分方程,计算出点电荷在其附近接地导体上的感 应电荷作用下,被曳引到导体表面所需的时间.结果为用第一、二类完全椭圆积分的线性组合表示的解析解,并考察当球面变 为平面时解析解的渐近行为,得出与已有文献一致的结果.

关键词: 曳引时间, 解析解, 渐近行为, 完全椭圆积分

Abstract: Under the conditions of irrespective gravity,air resistance and relativistic effect,this paper solves the relevant differential equation of motion directly,and obtains the analytic solution of traction time,which is expressed by the linear combination of Legendre complete elliptic integral of first and second kind. The asymptotic behavior is considered when sphere is changed into infinite plain,and then the same result with known literature is obtained.

Key words: traction time, analytic solution, asymptotic behavior, complete elliptic integral