二次等效法求三层媒质中静态电偶极子的场分布  

Electric field of a static electric dipole in three-layer medium model using secondary equivalent method

作　　者：陈聪[1] 李定国[1] 蒋治国[1] 刘华波[1] 

机构地区：[1]海军工程大学理学院,武汉430033

出　　处：《物理学报》2012年第24期199-205,共7页Acta Physica Sinica

基　　金：国家自然科学基金青年基金(批准号:51109215);国防预研究基金(批准号:51444070105JB11)资助的课题~~

摘　　要：在唯一性原理的基础上,提出采用二次等效的方法,求解三层平行媒质模型下,位于中间层的静态水平电偶极子在其他层媒质中产生的电场分布的解析表达式.也就是先经过一次等效求出场源同层时的场分布,然后利用二次等效将三层模型等效为两层模型,进而利用镜像法求出场分布.所得标量电位分布的表达式被证明是满足边界条件的,由此说明推导结果的有效性.并在实验室中模拟空气-海水-海床三层模型,对位于海水中的静态水平电偶极子在海水和海床中的标量电位进行了实测,并利用实验参数进行了仿真分析.实测结果和仿真分析相符合,表明推导结果的正确性.研究所得场分布表达式为以静态电偶极子为基本模拟体的电场分布的数学模拟、场分布特征分析等应用奠定了理论基础.In three-layer-parallel-medium mode, the method of secondary equivalent is proposed to derive the analytic expression of the electric field produced by a static electric dipole based on the uniqueness theorem when the source point is located in the middle layer but the field point is located in other layer. That is, the distribution of the electric field is solved when the source point and the field point are located in the same medium using the first equivalent method. Then the three-layer model is equivalent to two-layer model using the second equivalent method. Finally, the mirror image theory is used to obtain the field distribution. The expression of the scalar electric potential is proved to satisfy the boundary conditions, so the derivation results are proved to be effective. In order to prove the correctness of the expression of the scalar electric potential, a three-layer-parallel-medium mode, that is air-seawater-seabed, is simulated in laboratory, and the scalar electric potentials in the space of seawater and in the space of seabed are measured respectively. Some theoretical analyses are performed and the results of the analyses are in accordance with the experimental measurements, so the correctness of the solution is validated. The research results provide a theoretical base for the actual application such as modeling and characteristic analysis of electric field whose basic simulator is the static electric dipole.

关 键 词：二次等效 三层模型 静态电偶极子 镜像法 

分 类 号：O441[理学—电磁学]