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1076 IEEE TRANSACTIONS ON MAG"ICS, VOL. 28, N0.2, MARCH 1992 The Use of Image Charges in the Charge-Simulation Method: a Parallel-Plane Dielectric Plate Covering a Conductor E. Poli University of Padova Department of Electrical Engineering IdY dielectric case: that can strongly increase the time of computation. In the present work it is analytically shown that, if the geometry to be salved is a dielectric medium facing a parallel plane dielectric plate covering a conductor, the problem can be again treated with the charge-simulation method in one dielectric only. In this way calculations of electric fields have been performed for a case relevant to the insulation tests at high voltages: a conducting sphere in contact with a dielectric plate coating a plane conductor. Abstract -- When applied to two dielectrics, the charge simulation method needs a number of additional charges with respect to the single % Ed INTRODUCTION The knowledge of the electric field distribution is essential for the proper design of any high voltage system. This is especially important at the contact point of a conductor with a dielectric, where the field strength can be high. This is the case of the basic arrangement of a dielectric plate placed between a sphere and a plane conductor, commonly used in high voltage dielectric-strength tests (fig. 1). Numerical computations of the electric fields in this geometry have been carried out by using the finite difference method [l] and the charge simulation method (CSM) in two dielectrics [2]. An analytical solution also exists [3], developed using the Bessel functions. The charge-simulation method is a simple and powerful tool for calculations of three-dimensional electric fields [4] : its extension to two dielectrics nevertheless exihibits some drawbacks. In this paper it will be first shown that, when the second dielectric is a plate coating a plane conductor, the CSM in one dielectric only can still be used: for that, the principle of images has to be taken into account; then, with the CSM so modified, numerical calculations of the electric fields at the contact point of a sphere with a dielectric plate covering a conductor will be performed. THE CHARGE-SIMULATION MEIXOD This method is based on a simulation of the actual field.with a field given by a finite number of fictitious charges [4]. Manuscript received July 7, 1991. Fig. 1 Section along the symmetry ax~s zsof a conducting sphere of radius r in contact with a parallel-plane dielectnc plate of width c covenng a plane conductor. 1 and 1' are contour points and charges, respectdy, for the simulation of the sphere. In b), the CSM in two dielectrics: 2 are contour points on the interface and 2' ,2" are the corresponding charges. In a sphere-plane configuration in a single dielectric
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This note was uploaded on 06/08/2011 for the course ELECTRICAL 124 taught by Professor Ghjk during the Spring '11 term at Institute of Technology.

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