基于麦克斯韦方程的交变电流长螺线管磁场

Analysis of solenoid magnetic field based on Maxwell equation

为了分析方波驱动长螺线管内磁场畸变机理,利用麦克斯韦方程研究了螺线管内外的磁场分布情况。首先,利用麦克斯韦方程,分别建立了正弦波驱动螺线管内外电场、磁场模型,并结合安培环路定律和电磁感应定律选取了合适的边界条件,得到了正弦波驱动长螺线管的磁场分布;其次,通过傅里叶变换将方波信号变换为多个正弦信号叠加的形式,从而得到了方波驱动长螺线管磁场分布;最后,通过仿真试验重点分析了方波驱动信号频率对磁场的影响,并得出结论:方波驱动长螺线管磁场波形会失真、畸变,驱动信号频率较低、距离螺线管轴线距离较近处,磁场的方波特性较好。

In order to analyze the distortion mechanism of the magnetic field inside a long solenoid driven by square wave,the magnetic field distribution inside and outside the solenoid was studied using Maxwell＇s equations. Internal and external electricfield, magnetic field model of long solenoid driven by sine wave was established respectively by using Maxwell ＇equations. Mag-netic field distribution of long solenoid driven by sine wave was obtained, selecting appropriate boundary conditions of ampere cir-cuit law and law of electromagnetic induction. Then square wave was transformed into the form of multiple sine signals by Fouriertransform, and an expression for the magnetic field of solenoid driven by square wave current was obtained. The driving signalsquare wave＇s frequency effect on magnetic field was emphatically analyzed through the simulation test at last. The conclusionsdemonstrate that there is distortion in the magnetic field of a solenoid driven by a square wave current. The lower the frequency isand the closer the distance from the axis is, the more square wave features the corresponding magnetic field can acquire.