对载流圆线圈所激发磁场的新解法  

A new solution to the magnetic field excited by a current carrying circular coil

作　　者：王韵朗 张天一 游彪[2] 万建国[2] 王寅龙 WANG Yun-lang;ZHANG Tian-yi;YOU Biao;WAN Jian-guo;WANG Yin-long(College of Physics,Nanjing University,Nanjing 210093;National Experimental Teaching Demonstration Center of Physics,Nanjing University,Nanjing 210008)

机构地区：[1]南京大学物理学院,江苏南京210093 [2]南京大学物理国家级实验教学示范中心,江苏南京210008

出　　处：《大学物理》2023年第8期59-65,共7页College Physics

摘　　要：在大学物理的电磁学教学中,求解载流圆线圈激发的磁场是一个非常经典的问题.处理这类问题时,传统的方法是利用Biot-Savart定律进行矢量积分运算.该种方法得到的积分式无法用初等函数表示,仅在远场情形下能通过近似化为偶极子形式.本文提出了一种创新解法,在剔除了自由电流的空间中引入磁标势,求解拉普拉斯方程;并用轴线上的场强定解,避免了匹配边界条件的繁琐过程,成功得到了磁感应强度的级数解.通过数值计算,验证了此方法得到的解与矢量积分法得到的结果是吻合的,在电磁学教学中具有较大的启发意义.In the teaching of electromagnetics in college physics,it is a very classical problem to solve the magnetic field excited by a current carrying circular coil.When dealing with this kind of problem,the traditional method is to use Biot Savart's law for vector integration The integral formula obtained by this method can not be expressed by elementary functions,and can only be approximated to the dipole form in the far field case In this paper,an innovative solution is proposed,in which the magnetic scalar potential is introduced into the space without free current to solve the Laplace equation;By using the field strength on the axis to determine the solution,the tedious process of matching the boundary conditions is avoided,and the series solution of the magnetic induction is successfully obtained Through numerical calculation,it is verified that the solution obtained by this method is consistent with the result obtained by the vector integral method,which is of great significance in electromagnetics teaching.

关 键 词：磁标势 拉普拉斯方程 圆电流 数值仿真 

分 类 号：O4-4[理学—物理]