The use of image charges in the charge-simulation method: a parallel-plane dielectric plate covering a conductor

It is noted that, when applied to two dielectrics, the charge simulation method needs a number of additional charges with respect to the single dielectric case. This can strongly increase the time of computation. It is analytically shown that, if the geometry to be solved 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 insulation tests at high voltages: a conducting sphere in contact with a dielectric plate coating a plane conductor