The Image Analytical Solution of the Magnetic Field for Ferromagnetic Sphere System in a Uniform External Magnetic Field

YAO Zhen-ning; LIU Da-ming; ZHOU Guo-hua; ZHU Xing-le

doi:10.3969/j.issn.0372-2112.2014.09.001

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The Image Analytical Solution of the Magnetic Field for Ferromagnetic Sphere System in a Uniform External Magnetic Field

更新时间：2025-07-16

- The Image Analytical Solution of the Magnetic Field for Ferromagnetic Sphere System in a Uniform External Magnetic Field
- Acta Electronica Sinica Vol. 42, Issue 9, Pages: 1665-1671(2014)
- 作者机构：
  
  海军工程大学电气工程学院,湖北,武汉,430033
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.51277176)
- DOI：10.3969/j.issn.0372-2112.2014.09.001
  CLC： TM153.1
- Published：2014
- 稿件说明：
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YAO Zhen-ning, LIU Da-ming, ZHOU Guo-hua, et al. The Image Analytical Solution of the Magnetic Field for Ferromagnetic Sphere System in a Uniform External Magnetic Field[J]. Acta Electronica Sinica, 2014, 42(9): 1665-1671.
DOI：

YAO Zhen-ning, LIU Da-ming, ZHOU Guo-hua, et al. The Image Analytical Solution of the Magnetic Field for Ferromagnetic Sphere System in a Uniform External Magnetic Field[J]. Acta Electronica Sinica, 2014, 42(9): 1665-1671. DOI： 10.3969/j.issn.0372-2112.2014.09.001.

摘要

均匀外磁场中铁质球体系统磁场的计算一般是比较困难的，这是因为铁质球体之间的相互磁化比较难处理.从点磁荷与磁介质球系统中的镜像法出发，对磁介质球中的镜像线磁荷进行简化等效，推导出铁质球体系统中镜像磁偶极子和镜像磁荷的表达式.然后计算铁质球体之间各阶相互磁化而产生的附加磁场，进而求出铁质球体系统磁场的镜像解析解，并分析讨论了镜像解析解最大阶数的选择.仿真实验结果表明，镜像解析解的误差非常小，且适用于各种相对磁导率下铁质球体系统磁场的计算.

Abstract

It is very difficult to calculate the magnetic field which a ferromagnetic sphere system produces in a uniform external magnetic field

as a result of the difficulty in handling the mutual magnetization between the ferromagnetic spheres.The expressions of image magnetic dipole and magnetic charge were derived from image method of the system that consists of the point magnetic charge and magnetic medium sphere on condition that the image linear magnetic charges were simplified.Additional magnetic field was calculated

which ferromagnetic spheres produce because of the mutual magnetization.The image analytical solution was obtained according to the basic expression for magnetic field of the ferromagnetic sphere system

and the choice of the maximum order is analyzed.The verified results of the simulation experiment show that the image analytical solution has a very small error

and applies to all ferromagnetic sphere systems.

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