Bound charges - are they real or mathematical?

[aaaa202]

In my chapter about electric fields in matter my book derives and expression for the potential due to the polarization of a dielectric material. For that you find that the polarization is equal to the potential of a collection of negative charges on the surface and positive charges inside the volume.
I want to know: Do these charges represent genuine, physical charges or are the expression merely a mathematical tool? My book (Griffiths) certainly seems to believe that bound charges are indeed something physical. On the other hand I keep seeing pictures like the one attached, which wants to explain why putting a dielectric between two conductors gives a different capacitance for the capacitor they make. AND... Here both plus and minus charges are smeared over the surface of the material.

 

[dipole]

In my chapter about electric fields in matter my book derives and expression for the potential due to the polarization of a dielectric material. For that you find that the polarization is equal to the potential of a collection of negative charges on the surface and positive charges inside the volume.
I want to know: Do these charges represent genuine, physical charges or are the expression merely a mathematical tool? My book (Griffiths) certainly seems to believe that bound charges are indeed something physical. On the other hand I keep seeing pictures like the one attached, which wants to explain why putting a dielectric between two conductors gives a different capacitance for the capacitor they make. AND... Here both plus and minus charges are smeared over the surface of the material.

Bound charges are very much real. They are the valence electrons and nuclei of atoms in a material. When an electric field is applied, the atoms tend to "elongate", and the charges separate somewhat, but they can only move slightly, hence being "bound".

The statement in bold is not accurate, you'd find one surface is more negatively charged, and the opposite surface more positively charged, where as in the bulk, assuming the material is uniform, there is zero charge density. Polarization of a uniform material creates a surface charge, not any volume charge.