多层密绕圆线圈空间磁场分布的计算与分析

Calculation and Analysis of Spatial Magnetic Field Distribution of Multi-layer Tightly Wound Circular Coil

根据毕奥-萨伐尔定律和磁场叠加原理,对于多层密绕的方形和圆形截面圆线圈及其组成的亥姆霍兹线圈,推导出空间磁场分布的积分表达式。分别计算圆线圈和亥姆霍兹线圈轴线上的磁场分布,分析线圈截面积对轴线磁场分布的影响:在圆线圈平均半径R保持不变的情况下,当截面积为0.01R 2时,轴线上的磁场分布曲线与按线电流计算的分布曲线几乎重合,中心磁场的相对误差只有0.02%,可不用考虑线圈绕组的几何尺寸对磁场分布的影响;当截面积增大到0.25R 2时,圆线圈和亥姆霍兹线圈中心磁场与按线电流计算的磁场相对误差达到1.2%和0.4%,在计算精度要求高的情况下需要考虑线圈绕组几何尺寸对磁场分布的影响。通过比较单组和双组亥姆霍兹线圈中心磁场均匀区,为设计高精度等级的磁场定标线圈提供理论参考。

According to Biot-Savart law and superposition principle of magnetic field,the integral expression of spatial magnetic field distribution is deduced from multi-layer tightly wound circular coil with square and circular cross sections as well as Helmholtz coil.The magnetic field distribution on the axis of circular coil and Helmholtz coil are calculated separately,and the influence of the coil cross-sectional area on the magnetic field distribution on the axis is analyzed:under the condition that the average radius of the circular coil is kept unchanged,when the cross-sectional area is 0.01 R 2,the curve of magnetic field distribution on the axis is almost coincident with the line cur-rent′s,and the relative error of the central magnetic field is only 0.02%.It is unnecessary to consider the influence of the geometric size of the coil winding on the magnetic field distribution;When the cross-sectional area of circle coil and Helmholtz coil increases to 0.25 R 2,the relative errors of the two methods are 1.2%and 0.4%.It is necessary to consider the influence of coil winding geometry on magnetic field distribution in the case of high calculation accuracy.The uniform magnetic field region in the center of single and double Helmholtz coil is compared to provide theoretical reference for designing high precision magnetic field calibration coil.