大学物理 ›› 2019, Vol. 38 ›› Issue (6): 48-.doi: 10.16854 /j.cnki.1000-0712.180581

• 大学生园地 • 上一篇    下一篇

密立根油滴实验中的布朗运动

关舒月,张明,张师平,吴平   

  1. 北京科技大学数理学院,北京100083
  • 收稿日期:2018-10-19 修回日期:2018-12-21 出版日期:2019-06-20 发布日期:2019-07-02
  • 通讯作者: 张师平,E-mail: zhangshiping@ ustb.edu.cn.
  • 作者简介:关舒月( 1998—) ,女,满族,辽宁抚顺人,北京科技大学应用物理学专业2016 级本科生.

Brownian motion of Millikan's oil-drop experiment

GUAN Shu-yue,ZHANG Ming,ZHANG Shi-ping,WU Ping   

  1. School of Mathematics and Physics,University of Science and Technology,Beijing 100083,China
  • Received:2018-10-19 Revised:2018-12-21 Online:2019-06-20 Published:2019-07-02

摘要: 在进行密立根油滴实验时,如果选择的油滴过小,油滴会有明显的布朗运动,造成测得的下落时间与理想下落时间存在偏差.本文对密立根油滴实验中油滴的下落问题进行了实验观察和理论研究,并基于朗之万理论,求解了描述油滴运动的随机微分方程. 通过引入单次下落时间偏差和多次下落时间偏差分别考察了油滴布朗运动的剧烈程度以及布朗运动对油滴下落时间的影响.结果表明,实验中由于实验次数有限,当油滴比较小时油滴的布朗运动对于实验的影响仍然需要考虑.

关键词: 布朗运动, 油滴实验, 朗之万方程, 运动轨迹

Abstract: In Millikan's oil-drop experiment,if the oil drop is chosen too small,it shows obvious Brownian motion,which causes the measured dropping time to deviate from the ideal dropping time. In this article,through practical experiment and theoretical study,the stochastic differential equation of the movement of the oil drop is established by solving the Langevin equation. By introducing single and multiple time deviation,both the Brownian motion and the time deviation are quantitatively analyzed. As being indicated by the result,when the oil drop is relatively small,the influence of Brownian motion should be taken into account because of the limit of experiment times.

Key words: Millikan's oil-drop experiment, Brownian motion, Langevin equation, moving trail