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## Homework Statement

Exercise 1:

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.

Exercise 2:

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

[tex]-\sigma/2\epsilon_0[/tex].

In my opinion, we should write two equations(from Guass's law in terms of E and D respectively):

[tex]\epsilon_0 E_1+\epsilon_0(1+\chi)E_2=0[/tex]

[tex]\epsilon_0(E_1+E_2)=\sigma[/tex]

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.

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