求任意形状截面无限长直载流螺线管磁场的一种方法

ONE WAY TO DERIVE THE MAGNETIC FIELD OF THE STRAIGHTLY INFINITE LONG SOLENOID WITH AN ARBITRARY CROSS SECTION

在电磁学中,无限长直载流螺线管的磁场是一个基本与核心的问题,为了得到这一系统的磁场,通常的做法是:先就圆截面情况计算,然后把截面为任意形状无限长直螺线管看成是由无数大大小小的圆截面螺线管叠加而成,由此得到螺线管内的磁场均匀而管外磁场为零的一般结论.这里给出了一种推导截面为任意形状无限长直螺线管内外磁场的直接方法.先计算螺线管表面一窄条的磁场,再算总磁场.这种方法物理图像清楚,数学过程简单,可以在教学中加以应用.

In electromagnetism,the magnetic field of the straightly infinite long solenoid is a basic and core problem.To obtain the magnetic field of this system,the usual way is to calculate the magnetic field of the solenoid with a round cross section firstly,and then treat the solenoid with arbitrary cross section as superposition of infinite many solenoids with round cross sections,finally conclude that the magnetic is uniform within the solenoid and zero outside the solenoid is obtained.Here,one direct way to calculate the magnetic field inside and outside the straightly infinite long solenoid with an arbitrary cross section is given.This method is to derive the magnetic field corresponding to a strip on the surface of the solenoid first and then calculate the total magnetic field.The method has a clear physical picture.The mathematical derivations are simple and can be used in teaching activity.