A point charge and two dielectricsThe method of image charges can also be applied to problems including dielectrics. In this problem, a charge in front of an interface between two dielectrics is considered. Find out how to solve it and what happens if the charge is put in between the dielectrics.

Two dielectrics and one point charge

Problem Statement

Let us assume two dielectric media with permittivities \(\varepsilon_1\) for \(z<0\) and \(\varepsilon_2\) for \(z>0\). In \(\mathbf{r}_q = \left(x_q,y_q,d\right)\) may be a charge \(q\). Calculate the electrostatic potential \(\phi\left(\mathbf{r}\right)\) for the whole space. Calculate \(\phi\) in the limit \(d\rightarrow 0\) and discuss your result. On the right is a schematic of the situation:



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