On the Electrostatic Interaction between Point Charges due to Dielectrical Shielding

How will the electrostatic interaction between two point charges change if they are shielded from other by a dielectrical slab? While physical setting of this electromagnetic problem is relatively simple, it easy to be wronged and correct solution surprisingly complicated. Here we show general answer using method images, in which electrical field not found solving Poisson's equation but superposing an infinite number image recurrently satisfy all interfaces' boundary conditions. We also obtain analytical algebraic results some special cases.