I'm confused about what polarization of a dielectric does to its electrical properties. It is clear to me that polarization causes every little atom to get a tiny dipole moment. A measure of the polarization is therefore P = dipole moment per unit volume. However, what is really a dipole moment of an atom? Is it just the potential connected to the field of the polarized atom? If so I need some help: My book defines what is called the electric displacement, which is used for a new form of Gauss' law which holds for dielectrics. I wont bother to write that here, since you have probably seen that many times. Well, we can then ask the question: Is the path integral independent of your path in the presence of dielectrics. And the general answer to that is for some reason no, because the curl of P (the dipole moment per unit volume) is not always zero. Now I don't really understand why the path integral cannot be independent of the path. I wont pretend to understand why the curl of P is not zero since I'm not sure what P really is - is it a field or something else? Well in either way: No matter what we are dealing with electrostatics right? Because this is all stationary charges and so are the charges formed by the polarization. And since no magnetic forces are present we have: nabla x sum of all E fields = 0. So the curl of the total field, even counting the polarization must be zero musn't it? So what is it that makes a work integral still be dependent on the path? My teacher says it happens between two different materials, but I just don't see why the curl of the total field (or what ever this electric displacement) represents.