轴对称线圈磁场的精确计算方法研究

Study on The Precise Calculation Method of the Magnetic Field of the Axial Symmetrical Coil

全椭圆积分没有解析解,轴对称线圈磁场等对常遇到的此类计算问题多采用近似数值解算法,其计算精度无法得知.从求弧微分的思想出发,结合几何图形和极坐标下弧微分的计算方法,通过换元法把初始的弧微分及函数形式转化为优化形式,经积分求得圆环、圆螺旋管、空芯圆柱线圈空间任一点磁场的解析解,解决了轴对称线圈磁场精确值的计算问题.可作为高校电磁学课程教学补充教材,也可用于轴对称线圈磁场等高精度计算、设计和测量等领域.

The whole elliptic integral has no analytical solution.Such problems often occur in the use of approximate numerical solution algorithm to calculate the axisymmetric coil magnetic field,so the accuracy of calculation cannot be ensured.Following the thought of seeking differential arc,this paper uses the calculation method of arc differential based on geometric figure and polar coordinate,transforms the initial arc differential and function form into the form of optimization using the exchange element method.Through the analytical integral,the outside magnetic field solution is obtained to any point on the ring,circular spiral pipe,hollow cylindrical coil,and the problem of the accurate calculation of the magnetic field of the axial symmetry coil is therefore solved.This method can be as a supplement to university electromagnetic teaching materials,and can be used in high precision calculation,design and measurement of axial symmetry coil magnetic field.