精确求解无限长通电螺线管周围磁场分布的两种新解法及仿真验证  

Two new methods for accurately solving magnetic field distribution around infinite solenoid and their simulation verification

作　　者：曹斌照 崔程 乔磊 CAO Binzhao;CUI Cheng;QIAO Lei(School of Physics and Optoelectronic Engineering,Taiyuan University of Technology,Taiyuan 030024.China)

机构地区：[1]太原理工大学物理与光电工程学院,山西太原030024

出　　处：《实验技术与管理》2021年第4期141-145,149,共6页Experimental Technology and Management

基　　金：教育部高等学校教学指导委员会教学研究项目(DDLX2018-06,DWJZW201705hb);太原理工大学2019年度精品资源共享课“电动力学”培育项目。

摘　　要：通电螺线管周围的磁场分布问题,尽管几乎在所有的"大学物理"或"电磁学"课程中作为典型例题进行了推导计算,但计算方法不具有普遍性。该文基于矢势法的基本原理通过求解拉普拉斯方程和用留数定理求解矢势积分,得出载流线圈的电流平面法线与轴线存在一定夹角时无限长通电螺线管内外矢势的精确解,进而求得磁感应强度的解析解。对有限长通电螺线管周围的磁场用MATLAB进行数值求解及COMSOL仿真,将数值解和仿真结果进行对比,并通过比较螺线管逐渐增长时磁场分布的变化趋势,验证了所提出的求解方法的正确性。该研究对于更好地理解通电螺线管周围磁场分布规律以及丰富电磁场问题的分析方法具有重要意义。Although the distribution of magnetic field around an electrified solenoid is derived and calculated as a typical example in almost all courses of "College physics" or "Electromagnetics", the calculation method is not universal. Based on the basic principle of vector potential method, by solving Laplace equation and using residue theorem to solve vector potential integral, this paper obtains the exact solution of inner and outer vector potential of an infinite solenoid when there is a certain angle between the current plane normal and the axis of current carrying coil, and then finds the analytical solution of magnetic induction intensity. The numerical solution by MATLAB and the COMSOL simulation of the magnetic field around the finite length solenoid are carried out. The numerical solution is compared with the simulation results, and the correctness of the solution is verified by comparing the change trend of the magnetic field distribution when the solenoid gradually grows. This research is of great significance for better understanding the distribution of magnetic field around the solenoid and enriching the analysis methods of electromagnetic field problems.

关 键 词：矢势法 螺线管 磁感应强度 仿真 

分 类 号：O411.1[理学—理论物理]