Calculation of the Potential Distribution Around a Charge or a Current in the Presence of Three Dielectric Media Using the Image Method

The image method has been used to compute the potential distribution around electrostatic charges or electrical currents in the presence of conductors and dielectrics or magnetic materials. Only some particular cases of three media have been reported. This paper presents the general formula for calculating the potential generated by an electrostatic point charge or a point current (linear current density) in the presence of three arbitrary different dielectric media, i.e. two semi infinite media separated by a sheet. The potential expressions are deduced in each of the three media for the source charge placed outside or inside the sheet. The potential is expressed as an infinite series which is shown to be convergent. An evaluation of the trunkation error of the series has shown that the number N of terms required for a reasonable accuracy is usually less than 20, which is within the limits of a rapid calculation with a small computer. An equivalence between the point charge in the presence of three dielectrics and a point current ( linear current density) in the presence of three media with different resistivity is introduced.