基于对称性分析的特殊容积导体中电流单极子磁场的理论研究
Theoretical study of magnetic field of current monopoles in special volume conductor using symmetry analysis.
作者信息
Durand D M, Lin J C
机构信息
Department of Biomedical Engineering Case Western Reserve University, Cleveland, OH 44106 USA.
出版信息
IEEE Trans Biomed Eng. 1997 Feb;44(2):177-87. doi: 10.1109/10.552247.
We derive a formula for the magnetic field outside volume conductors having axial symmetry with radial and axial symmetrically distributed source currents. The magnetic field is shown to have components only along the cylindrical polar angle direction and its magnitude to depend only on the topological structure of the volume conductor and the location of the source current. With this formula, the magnetic field generated by the volume current of a current monopole within and on the symmetrical axis of several volume conductors (such as semi-infinite volume, infinite slab, sphere, infinite cylinder, semi-infinite cylinder, finite cylinder, prolate spheroid, and oblate spheroid) is shown to be equivalent to the magnetic field generated by a line current calculated using the Biot-Savart's law. In the first three volume conductors, the monopole solution of the magnetic field allows the calculation of magnetic fields generated by arbitrarily distributed (and balanced for finite volume conductors) current monopoles.
我们推导了一个关于具有轴对称性且源电流呈径向和轴向对称分布的体积导体外部磁场的公式。结果表明，磁场仅具有沿柱面极角方向的分量，其大小仅取决于体积导体的拓扑结构和源电流的位置。利用该公式，证明了电流单极子在几个体积导体（如半无限体积、无限平板、球体、无限圆柱体、半无限圆柱体、有限圆柱体、长球体和扁球体）的对称轴上及内部产生的体积电流所产生的磁场，等同于使用毕奥 - 萨伐尔定律计算的线电流所产生的磁场。在前三种体积导体中，磁场的单极子解可用于计算由任意分布（对于有限体积导体为平衡分布）的电流单极子产生的磁场。
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