环电流矢势的数值积分和数值旋度的计算和可视化  

Calculating Numerical Integration and Numerical Curl of the Magnetic Vector Potential for a Circular Current and Their Visualization

作　　者：周群益 莫云飞 侯兆阳 周丽丽[4] ZHOU Qun-yi;MO Yun-fei;HOU Zhao-yang;ZHOU Li-li(College of Tianhe,Guangdong Polytechnic Normal University,Guangzhou Guangdong 510540,China;School of Electronic and Communication Engineering,Changsha University,Changsha Hunan 410022,China;School of Science,Chang’an University,Xi’an Shaanxi 710064,China;Department of Information Engineering,Gannan Medical University,Ganzhou Jiangxi 341000,China)

机构地区：[1]广东技术师范大学天河学院,广东广州510540 [2]长沙学院电子信息与电气工程学院,湖南长沙410022 [3]长安大学理学院应用物理系,陕西西安710064 [4]赣南医学院信息工程学院,江西赣州341000

出　　处：《衡阳师范学院学报》2020年第3期58-61,共4页Journal of Hengyang Normal University

基　　金：湖南省自然科学基金(2018JJ3560);长沙市科技计划项目(kc1809022)。

摘　　要：根据柱坐标系中环电流在空间中产生矢势的积分公式,利用两类完全椭圆积分,推导了矢势的解析式。在直角坐标系中将积分公式和解析式无量纲化,对矢势的积分公式计算数值积分,绘制了曲面,同时绘制了解析式的曲面,两个曲面基本吻合,说明了解析式的正确性。根据柱坐标系中矢势的旋度求出环电流磁感应强度的偏导数公式,利用两类完全椭圆积分,推导了两个分量的解析式。同样在直角坐标系中将偏导数公式无量纲化,计算数值导数,绘制了磁感应强度的两个分量的曲面,同时绘制解析式的两个分量的曲面,分量的两个曲面基本重合,说明解析解的正确性。绘制了三维磁感应线,直观地显示了环电流磁场的分布规律。The integration formula of the magnetic vector potential for a circular current is derived,and its analytical solution is obtained by means of two types of complete elliptic integrals.The integration formula and analytical solution are nondimensionalized.The distribution surfaces of vector potential are drawn according to its integration formula and analytical solution,respectively.The figures drawing by the two methods are compared with each other.It is found that they are identical,suggesting the validity of analytical solution.Moreover,the magnetic field of the circular current is obtained according to the curl of its magnetic vector potential,and its analytical solution is obtained by means of two types of complete elliptic integrals.The distributions of the magnetic field are visualized according to the numerical derivative of magnetic vector potential,and the result is compared with its analytical solution.The magnetic induction lines are drawn,and their distribution feature is discussed.

关 键 词：环电流 矢势 数值积分 数值旋度 

分 类 号：O441[理学—电磁学]