教学讨论

电场线方程的数值求解及可视化

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  • 陆军军事交通学院 基础部,天津300161
贾小文(1983—),男,陕西神木人,陆军军事交通学院基础部副教授,博士,主要从事大学物理实验教学和实验数据分析处理研究工作. E-mail:2002jiaxiaowen@163.com

收稿日期: 2024-11-14

  修回日期: 2024-12-02

  网络出版日期: 2025-09-16

Numerical solution and visualization of electric field line equations

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  • Army Military Transportation University, Basic Education Department,Tianjin 300161, China

Received date: 2024-11-14

  Revised date: 2024-12-02

  Online published: 2025-09-16

摘要

提出了一种基于数值计算的电场线微分方程求解的通用方法,讨论了求解过程中的奇异性问题,简化了微分方程的求解过程,利用Igor Pro对孤立点电荷、一对同号电荷、一对异号电荷、一对同号长直导线、一对异号长直导线、复杂电场的电场线方程进行了数值求解和可视化,比较了基于泰勒展开的网格法逐点求解与数值微分方程求解的求解精度.

本文引用格式

贾小文, 范海英 . 电场线方程的数值求解及可视化[J]. 大学物理, 2025 , 44(7) : 25 . DOI: 10.16854/j.cnki.1000-0712.240525

Abstract

A general method for solving the differential equations of electric field lines based on numerical computation is proposed. The singularity issues in the solving process are discussed, and the procedure for solving the differential equations is simplified. Using Igor Pro, numerical solutions and visualizations are performed for the electric field line equations of an isolated point charge, a pair of like charges, a pair of opposite charges, a pair of like long straight wires, a pair of opposite long straight wires, and complex electric fields. The accuracy of the point-by-point solution based on the Taylor expansion grid method is compared with that of the numerical differential equation solution.

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