Electrostatic field of cube electrodes

Abstract

Electric field and potential distribution in the surroundings of cube electrodes are numerically determined using Equivalent Electrodes Method

Approximate Calculation of Capacitance of Lines with Multilayer Medium

“…The basic idea of the method [3,4] is that an arbitrarily shaped electrode can be replaced by a finite system of the equivalent electrodes (EE) located on the body surface. The radius of EE is equal to the equivalent radius of electrode part which it substitutes.…”

“…When designing lines and cables with multilayer medium of different geometry, one should often be well acquainted with most accurate values of the capacitance per unit length. Calculation of the capacitance per unit length of lines with multilayer medium can be performed using various analytical and numerical methods such us the Charge Simulation Method (CSM), Finite Element Method (FEM), Equivalent Electrode Method (EEM) [1][2][3][4][5][6][7], etc. All these methods, offering different degrees of precision, give results with satisfying accuracy, but also require extensive mathematical work.…”

The electric field of a uniformly charged cubic shell

“…So we have another situation that is confusing to student who are learning We note that the calculation of the surface charge density on a charged cubic conductor is a difficult calculation that is not discussed even in graduate textbooks on electricity and magnetism like Jackson 14 . The authors only know of numerical calculations using specialized computer codes that have been carried out mainly by electrical engineers who have been interested in the capacitance of a cube-shaped capacitor [16][17][18] . Nevertheless, the fact that the surface charge density on a conducting cubic surface in electrostatic equilibrium is not uniform is easily understood by undergraduates and they should be familiar with at least one quantitative example like the one discussed in this paper.…”

An approximate expression for the calculation of the electric field in vicinity of the cube electrode with rounded wedges

“…Wedges are rounded having radius of curvature r. With point P the center of the rounded vertex is denoted, where we can expect greatest value of the electric field and which is the most critical from the stand point of possible electric field breakdown. First the calculation of electric field in the center of the rounded vertex is done using specific Equivalent Source Method (ESM) [2], which can be considered a combination of methods shown in [7,8]. By applying this method, the unknown electrode surface charges are simulated by equivalent sources whose positions and types are chosen to achieve high accuracy of electric field calculations in all regions in vicinity of rounded cube including wedges and vertices.…”