圆电流和亥姆霍兹线圈磁场的数值模拟

根据毕奥-萨伐尔定律和磁场叠加原理,导出圆电流和亥姆霍兹线圈的磁场分布含积分的表达式。利用Mathematica软件进行数值计算,得到磁场分布的数值解,由此绘出圆电流和亥姆霍兹线圈的磁场分布图像,并对两者的磁场均匀区进行分析比较：在垂直于中心轴线平面上亥姆霍兹线圈磁场均匀区的面积是圆电流的10.4倍;在轴平面上前者是后者的5.4倍。最后对亥姆霍兹线圈磁场均匀区（±1%）作对比分析,数值计算的结果与相关实验测量十分吻合。

Numerical Simulation on the Magnetic Field of Circular Current and Helmholtz Coil

Based on the Biot-Savart law and superposition principle of magnetic field,the magnetic field distribution with integral expressions were derived for circular current and the Helmholtz coil.By using Mathematica software to numerical calculation,the numerical solution of magnetic field distribution was obtained and the distributional images of the magnetic field of circular current and Helmholtz coil were drawn,at the same time the both of uniform magnetic field were made analysis and comparison.In the perpendicular to the central axis plane,the uniform magnetic field of Helmholtz coil was 10.4times size of the circular current;in the axial plane the former was 5.4times size of the latter.At last by comparatively analysis the uniform magnetic field（±1%）of the Helmholtz coil,the result of numerical calculation was in good agreement with the relevant experimental measurement.