摘要
利用勒让德多项式的母函数公式将载流圆环的磁矢势展开为勒让德函数级数表达式,再用球函数加法公式,有效规避了传统方法中复杂的椭圆积分运算,能便捷高效地推导出磁矢势和磁感应强度的级数解析解。利用MATLAB软件将该磁场空间分布可视化时还发现,该解所得的磁场空间分布具有更高精度和可靠性,纠正了有关文献在近场区域磁感线分布的偏差。
The magnetic vector potential of a current-carrying circular loop was expanded into a series expression of Legendre functions by employing the generating function formula of Legendre polynomials.The complex elliptic integral operations inherent in conventional methods were effectively circumvented through the application of the addition theorem for spherical harmonics,enabling the series-form analytical solutions for both the magnetic vector potential and the magnetic induction intensity to be derived conveniently and efficiently.Furthermore,when the spatial distribution of the magnetic field was visualized using MATLAB software,it was found that the obtained solution exhibited higher accuracy and reliability.Deviations in the near-field magnetic flux line distributions reported in relevant literature were thereby corrected.
作者
李秀燕
伍志豪
周小方
LI Xiuyan;WU Zhihao;ZHOU Xiaofang(College of Physics and Information Engineering,Minnan Normal University,Zhangzhou,Fujian 363000,China;College of Physics and Electronic Engineering,Sichuan Normal University,Chengdu,Sichuan 610068,China)
出处
《闽南师范大学学报(自然科学版)》
2025年第4期54-61,共8页
Journal of Minnan Normal University:Natural Science
基金
福建省高校物理学学科联盟教学改革研究项目(FJPHYS022-B11)
闽南师范大学本科教育教学研究项目(JG202504)。
关键词
载流圆环
磁矢势
球函数加法公式
勒让德函数
磁感应强度
current-carrying circular loop
magnetic vector potential
addition theorem for spherical harmonics
Legendre functions
magnetic flux density
