等效源法求分层导电媒质中水平直流电偶极子的磁场

Research on the Magnetic Field of A Static Electric Dipole in Layered Conducting Media Using Equivalent Source Method

为获得水平直流电偶极子在平行分层导电媒质中产生的磁场分布的解析表达式,在镜像法求解其电场分布的基础上,提出等效源产生修正磁位的观点,进而提出磁场求解的等效源法,即场点的矢量磁位等于无限大导电媒质中源的矢量磁位加上等效源的修正磁位.采用该方法求解了3层导电媒质模型下,位于中间层的水平直流电偶极子在全空间的磁场分布,所得表达式被证明是满足场方程及边界条件的,由此说明磁场分布表达式的正确性及推导方法的有效性.该方法有效解决了场域分层且含导电媒质时电偶极子磁场分布不易求解的困难.研究结果为以水平直流电偶极子为基本模拟体的磁场分布的数学模拟、特征分析等应用奠定了理论基础.

Based on the solution of the electric field produced by a static horizontal electric dipole in layered conducting medium using mirror image method,the view that the equivalent sources will produce revised magnetic vector potential is introduced. Then an equivalent source method is put forward in order to obtain the analytic expression of the magnetic field distribution produced by a static horizontal electric dipole in layered conducting medium,that is the magnetic vector potential at the field point equals to the magnetic vector potential produced by the source in infinite conducting medium plus the revised magnetic vector potential produced by the equivalent sources. The equivalent source method is then used to derive the magnetic vector potential distribution in the three-layered conducting media produced by a static horizontal electric dipole located in the middle layer media. And the expressions are proved to be able to satisfy the field equations and the boundary conditions. So the correctness of the expressions and the effectiveness of the new derivation method are validated. The equivalent source method can settle the difficulties in deriving the magnetic field of electric dipole when the field area is layered and includes conducting medium. The research results provide a theoretical basis for the actual application,such as modeling and characteristic analyzing of magnetic field whose basic simulator is the static electric dipole.