亥姆霍兹线圈磁场的理论计算与实验讨论

首先,基于毕奥-萨尔定律分析了单个载流圆线圈在空间的磁场分布,得到了空间任意一点磁感应强度的积分表达式,并通过相应的计算得到了磁感应强度沿轴向和径向分量的解析结果;其次,将单个载流圆线圈在空间的磁场分布推广到亥姆霍兹线圈,获得了亥姆霍兹线圈在空间任一点磁感应强度的解析表达式,并利用Mathematica形象描绘了其磁感线分布;再次,通过数值计算分析了亥姆霍兹线圈的均匀磁场区;最后,结合"电磁感应法测量亥姆霍兹线圈磁场"实验作了相应的分析与讨论.

On Theoretical Calculation and Experimental Discussion of Magnetic Field Due to Helmholtz Coil

The magnetic field distribution of single current-carrying circular coil has been analyzed based on Biot-Savart law, and the integral expression of magnetic induction intensity at any point beenobtained, and the analytical results of the axial and radial components of magnetic induction intensity been obtained by corresponding calculation. Furthermore, the magnetic field distribution of a single current-carrying circular coil in space has beenextended to Helmholtz coil, and the analytical expression of magnetic induction intensity of Helmholtz coil at any point in space beenobtained and the distribution of magnetic induction line beendepicted visually by Mathematica. In addition, the uniform magnetic field of Helmholtz coilhas been analyzed by numerical calculation. Finally, the corresponding analysis and discussion have been made with the experiment of measuring magnetic field of Helmholtz coil by electromagnetic induction method.