电流元观点下均匀磁化球体内部磁场问题的等效求解

An equivalent solution to the internal magnetic field of a uniformly magnetized sphere from the point of view of current element

与磁介质相关的一个典型问题是计算均匀磁化球体内部的磁场分布,即求解空间中半径为R、均匀磁化强度为M的球体内部的磁感应强度B的分布.若取球体表面或球体体积作为微元,对球内一点的磁场与积分上下限的表达式将难以解析求解;而传统的磁荷观点求解方法往往缺失了对磁荷等价性的严格论证,因此目前尚无在普通物理的知识背景下简洁严谨的求解方案.因此,本文在符合物理本质的电流元观点下,利用割补和等效替代的思想,用简明的推导给出了该问题的等效解法,对电磁学中的相关教学研究有较好的启发作用和参考价值.

A typical problem related to magnetic medium is to calculate the magnetic field distribution in a uniformly magnetized sphere,that is,to solve the distribution of magnetic induction B in a sphere with radius R and uniform magnetization M in the space.If the surface or volume of the sphere is taken as a microelement,it will be difficult to analytically solve the expression of the magnetic field and the upper and lower limit of the integral at a point in the sphere,but the traditional method for solving the magnetic charge often lacks a strict demonstration of the equivalence of the magnetic charge.Therefore,in this paper,under the viewpoint of current element in accordance with the essence of physics,an equivalent solution to this problem is proposed by using the idea of cut-complement and equivalent substitution,which has a good enlightening effect and reference value for the relevant teaching and research of electromagnetics.