Engineering Electrodynamics

5 Magnetic Fields Near Iron Surfaces

5.1 Method of Mirror Images

5.1.1 Singular Images of Direct Current

The method of images is based on the analogy with optics. The analogy of electrostatic E = −grad V and magnetostatic H = −grad V_m fields gives us the possibility to consider them in the same way. Let us start with the magnetostatics, where B = μH. The method of mirror images, in the case of constant magnetic permeability μ_i of two adjacent media, consists of substitution of two media I and II (Figure 5.1a) by only one medium I (Figure 5.1b) or II (Figure 5.1c) and an auxiliary fictitious, image current i₁. The value of this fictitious current i₁ is determined by the rule of uniqueness of the field, specified by the boundary conditions (2.191) ...