分层导电媒质中水平直流电偶极子磁场分布的积分法求解

An integral solution to magnetic field of horizontal static electric dipole in layered conductive media

首先,提出了采用积分法求解分层导电媒质中水平直流电偶极子的磁场,即在获得其电场分布的条件下,借助欧姆定律先求得全空间中的电流分布;然后,通过空间分割,将全空间电流分割成无数电流元,并利用毕奥-萨伐尔定律,求出其元磁场;最后,将全部元磁场叠加即得到水平直流电偶极子产生的磁场。在此基础上,利用所提出的方法,编程计算了半无限大导电媒质中的水平直流电偶极子的磁场分布,并与理论值进行比较分析。结果表明:该方法是有效的。此外,还对影响求解精度的几个问题进行了探讨。

An integral solution is proposed to work out the magnetic field of horizontal static electric dipole in layered conductive media.That is to say,when the electric field distribution of horizontal static electric dipole is given,the distribution of electric current in whole space can be obtained through Ohm′s law.Then the whole space current is divided into millions of current elementary whose elementary magnetic field can be acquired through Biot-Savart law.At last,the magnetic field is obtained by superimposing the elementary magnetic fields.Through MATALAB programming,the magnetic field of a horizontal static electric dipole in half infinite conductive media is calculated.In order to show the method is effective,the results are compared with the theoretical calculation value of the magnetic field.Several aspects that affect the precision of algorithm are also discussed.