Suppose a infinte plane z=0 divides the 3-dimensional space into two parts. The region below z=0 is filled with linear dielectric material of susceptibility [itex]\chi[/itex]. The bound charge density at z=0 is [itex]\sigma[/itex]. Find the electric field of the two regions.
The original problem in Griffith's book is to calculate the force on a point charge q situated a distance d above the the origion (x=0,y=0,z=d). The first step is to find the electric field [itex]E_z[/itex] just inside the dielectric at z=0, which is due in part to q and in part to the bound charge itself. And he states that the latter contribution is
In my opinion, we should write two equations(from Guass's law in terms of E and D respectively):
Then [itex]E_2[/itex] is my answer, which is quite different from the expression in Griffith's book [itex]-\sigma/2\epsilon_0[/itex].
I need a detailed solution to the electric field of this configuration.