用坐标变换方法求解倾斜圆环线圈时谐电磁场的解析解  

Analytical Solution to Time-Harmonic Electromagnetic Field of Tilted Circular Coil by the Coordinate Transformation Method

作　　者：雷银照[1] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《电工技术学报》2010年第4期15-18,共4页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金(50777002);国防基础科研(A2120080260)资助项目

摘　　要：求解了无限大真空中倾斜通电圆环线圈产生的时谐电磁场的解析解。基于麦克斯韦方程组,导出了无限大真空中修正磁矢位满足的泊松方程。根据修正磁矢位的泊松方程与无限大真空中稳恒磁场的矢量泊松方程的相似性,直接利用已知的平行于直角坐标平面的圆环线圈稳恒磁场的解析解,通过直角坐标系的旋转和平移,导出了倾斜圆环线圈的时谐电磁场的解析解。根据同一物理量在不同坐标系下保持不变的性质,验证了导出的解析式的正确性。本文分析方法初等,解析式简单,可用于求解复杂形状线圈的线性电磁场问题。The analytical solution to time-harmonic electromagnetic field of tilted circular coil in infinite vacuum is solved in this paper. A vector Poisson’s equation of modified magnetic vector potential in infinite vacuum is derived from Maxwell’s equations. According to the similarity of vector Poisson’s equation of the modified magnetic vector potential and that of the steady magnetic field in infinite vacuum, the analytical solution to the time-harmonic electromagnetic field produced by the tilted circular coil is derived from the known analytical solution to the steady magnetic field of the circular coil parallel to rectangular coordinate plane by rotation and translation of rectangular coordinate system. According to the invariable quality of the same physical quantity in different coordinate systems, the derived analytical solution is validated. The proposed method is primary and the presented analytical expression is simple, which can be used to solve the linear electromagnetic field problems of complex shape coils.

关 键 词：解析解 倾斜线圈 坐标变换 涡流 无损检测 电磁场 

分 类 号：O441.4[理学—电磁学]