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

Abstract

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.