矩形截面有限长螺线管磁场的计算

摘要

如果将螺线管的表面电流看成是磁介质的磁化电流,那么螺线管的磁场就与介质的磁场完全相同.于是可以通过计算磁介质的磁场得到螺线管的磁场.根据公式B=μ0(H+M),磁介质的磁场或者磁感应强度可以分为两部分:一部分是磁化强度的贡献,另一部分是磁场强度.对于磁介质来说,由于没有传导电流,所以磁场强度的环路积分是零,而磁场强度对于闭合面的积分不是零.也就是说,这种情况下,磁场强度的方程与静电场电场强度的方程完全相同,因此可以用计算静电场电场强度的方法计算磁场强度,这就是处理磁场的等效的磁荷方法.利用等效的磁荷方法对矩形截面的有限长螺线管的磁场进行了讨论,给出了对称面上精确磁场的解析表达式,磁场的解析表达式中不包含积分和难以求和的级数,同时进行了数值分析.%If treating the conduction current of the solenoid as the magnetizing current of a magnetized object,the magnetic field of the solenoid will be the same as that of the magnetized object.Hence we can obtain the magnetic field of a solenoid by calculating that of the magnetized object.According to the formula B=μ0 (H+M),the magnetic field of the magnetized can be divided into two parts:one is the contribution from the magnetizing strength M and the other part is the magnetic strength H.For the magnetized object,there is no conducting current and the circulation of magnetic strength H is zero,but the flux through a closed surface is nonzero.That is to say,the equations of the magnetic strength are the same as that of the static magnetic strength.Therefore one can calculate the magnetic field by the same method to calculate the static electric field,which is the method of equivalent magnetic charge.Using such a method,the magnetic field of the finite solenoid with a rectangular cross section is studied.The exact analytical expression of the magnetic field on the symmetry plane is derived and there are no integrals and series in the analytical expression.Meanwhile,numerical analysis is given.