We examine the attractive interaction between an excess electron and the dipole moments of polar molecules forming a cluster or a liquid. This interaction determines the size dependence of the electron affinity of these clusters. We use the polarizable electropole model for the molecules and include interactions between the permanent and induced dipole moments. Thus, we obtain that the interaction between the excess electron and the molecules is strongly decreased by the induced polarization of the bound electrons, which is opposed to the permanent dipole moments and makes a dielectric screening. Note that previous calculations of the electron affinity of clusters of polar molecules resulted in much larger vertical detachment energies of the excess electron than observed in the experiment. This error is due to the use of an unphysical pair-potential approximation, which neglects the interaction between the permanent dipole moments and induced dipole moments. Thus the attractive interaction between the excess electron and the molecules and the resulting electronic binding energies have been overestimated. The results of our microscopic theory are identical with macroscopic continuum models and agree very well with experimental results. This theory also might be important for the study of solvent effects on oxidation-reduction reactions and on photosynthesis.