Abstract
A process to apply the method of images for a charge located in a three-layer medium is presented. The images are found according to the boundary conditions between the layers for the electric field. The characteristics of the electric potential are also considered, thus the number of unknown variables becomesa guide to set the image charges needed to solve the problem. The results are compared with finite element simulations through the use of the software FEMM 4.2, showing good agreement. The found limitations of the process are also noted, mainly in regards to the dependence of the images on the coordinates where the field is to be calculated. The model obtained was applied to different cases, where it was seen that it was not limited to three material media only. Finally, the null potential boundary condition was applied, showing how the method of images could be applied to this type of problems.
Highlights
Electrostatics is an important subject of Electromagnetic Theory that contributes to the understanding of complex phenomena and industrial applications such as high voltage breakdown (Abdel, 2018), aerosol particles (Kawada, 2002), or the analysis of molecular surfaces (Bulat, 2010)
The Finite Element Method (FEM) is the most used method in electromagnetics research as it may be seen in the number of publications found in the scientific community
If compared with the Finite Element Method, the Method of Images has the disadvantage of not being suitable to treat borders with fixed potential, which are known as Dirichlet border condition
Summary
Electrostatics is an important subject of Electromagnetic Theory that contributes to the understanding of complex phenomena and industrial applications such as high voltage breakdown (Abdel, 2018), aerosol particles (Kawada, 2002), or the analysis of molecular surfaces (Bulat, 2010). For this reason, some numerical techniques to solve electrostatics problems have been developed and are still under investigation. The Finite Element Method (FEM) is the most used method in electromagnetics research as it may be seen in the number of publications found in the scientific community It solves the Laplace equation, taken as a boundary-value problem (Jin, 2017). The model is simplified in order to apply a null potential boundary condition
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