A Second-Order Eigen Theory for Static Electromagnetic Fields (Report‪)‬

1. Introduction By the Maxwell's electromagnetic field equations, we know that the electric and magnetic field are independent each other under the condition of static fields. The classical electromagnetic field theory also believes that the static electric field can be described by a scalar potential function, and the magnetic field by a vector one. Furthermore, for the passive region, the magnetic field can also be described by a scalar potential function [1,2]. But it should be pointed out that these results can only be obtained in the condition of isotropy, and are also only suit for the isotropic media. However, with the development of material science, more and more anisotropic dielectric or magnetic materials are applied to various fields, such as electron devices, communications and sensors, even for the traditional geological structure, we also can see the electrically anisotropic media or magnetically anisotropic media. It is found by recent research works that the limitations of classical static electromagnetic field theory have become obvious for these anisotropic media. For example, the above results for isotropic media don't exist for anisotropic media, even we don't know the definite form of the electric field potential function or magnetic field potential function, which make a great difficulty in solving the problem of anisotropic static electric or magnetic fields [3-5]. Unlike the classical static electromagnetic field theory, which studies the Maxwell's equations under the geometric representation, in this paper, the Maxwell's equations are restudied under the physical representation. As the result of this, the modal equations of static electric or magnetic fields are deduced, which give the novel expressions for the potential functions of static electric or magnetic fields for anisotropic media, and bring to light the intrinsic laws of static electromagnetic field.