几种特殊形状柱面导体边界镜像法的静电场问题分析ANALYSIS OF ELECTROSTATIC FIELD PROBLEMS BY IMAGE METHOD OF CYLINDRICAL CONDUCTORS OF SEVERAL SPECIAL SHAPES
徐振然,邓博韦,曹斌照
摘要(Abstract):
导体柱面在实际生活和工程实践中并不少见,无限长直导线就是最典型的例子,因此对其相关问题如何处理的研究十分必要。目前对导体圆柱面镜像法的研究已经有了准确的结果,本文提出了不一样的求解思路,更多地借助了几何特征,而且不同于常规的利用场强和电势的微分关系求解电场分布,采取矢量叠加的方法,将电场的大小和方向分开研究。此外,本文将柱面镜像法适用的场景进行了拓展,将上述思路运用到几种特殊形状柱面导体的边值问题,拓宽了柱面镜像法的适用范围。
关键词(KeyWords): 镜像法;导体柱面;静电场定解问题;矢量叠加
基金项目(Foundation): 山西省高等学校教学改革创新项目(J20240208)
作者(Author): 徐振然,邓博韦,曹斌照
参考文献(References):
- [1] 梅中磊,曹斌照,李月娥,等.电磁场与电磁波[M].北京:清华大学出版社,2018.MEI Z L,CAO B Z,LI Y E,et al.Electromagnetic fields and electromagnetic waves[M].Beijing:Tsinghua University Press,2018.(in Chinese)
- [2] 曹斌照,马宁.电动力学[M].北京:清华大学出版社,2019.CAO B Z,MA N.Electrodynamics[M].Beijing:Tsinghua University Press,2019.(in Chinese)
- [3] 梁灿彬,秦光戎,梁竹健.普通物理学教程电磁学[M].4版.北京:高等教育出版社,2018.LIANG C B,QIN G R,LIANG Z J.General Physics Tutorial Electromagnetics[M].4th ed.Beijing:Higher Education Press,2018.(in Chinese)
- [4] 殷勇,王福谦.线电荷与带有垂直低脊的接地导体薄圆筒所形成的电场及其数值模拟(下)[J].实验室研究与探索,2020,39(10):110-112,145.YING Y,WANG F Q.Electric field formed by a line charge and a thin cylinder of grounded conductor with a vertical low ridge and its numerical simulation (Part Ⅱ)[J].Laboratory Research and Exploration,2020,39(10):110-112,145.(in Chinese)
- [5] 张拴柱.双极坐标系下的柱面镜像法(电轴法)[J].物理与工程,2017,27(3):82-83,90.ZHANG S Z.Cylindrical image method in bipolar coordinate system (electric axis method)[J].Physics and Engineering,2017,27(3):82-83,90.(in Chinese)
- [6] 同济大学数学系.高等数学[M].7版.北京:高等教育出版社,2014.Department of Mathematics.Tongji University.Higher Mathematics[M].7th ed.Beijing:Higher Education Press,2014.(in Chinese)