How Does Polarization Affect Capacitor Charge and Potential Difference?

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Say you have two conductors and there is a dielectric material between them (a capacitor with a dielectric). The field will the polarize the atoms in the dielectric in such away that the potential difference between the two conductors is weakened. Thus a capacitor with a dielectric between it's conducting surfaces can practically store more charge at a given potential. This is, as I understand it, what the effect of polarization is.

1) Is that correct?

2) To polarize a material you do work, as you are pulling the electrons away from the nucleus. This extra work must go into the potential difference between - and + - i.e. it must be associated with how difficult it is to pull electrons from + to -. Does all the above mentioned, which implies that separating charges gets easier with polarization, account for this "extra" work?
 
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1) yes

2)

To polarize a material you do work, as you are pulling the electrons away from the nucleus. This extra work must go into the potential difference between - and + - i.e. it must be associated with how difficult it is to pull electrons from + to -. Does all the above mentioned, which implies that separating charges gets easier with polarization, account for this "extra" work?

The energy lost by the source (battery) goes into separation of the charges at the capacitor plates (potential eletrostatic energy) and also to polarization of the dielectric (also potential energy, but of the charges in the dielectric).
 
Yes exactly, so doesn't the polarization itself require extra energy from the source? And thus, is thoroughly correct to just say that the potential difference decreases, when the material gets polarized? - evidently we see that more energy is required to charge up the capacitor per unit charge, because of the extra charges.