ON THE ELECTROSTATIC THEORY FOR QUADRUPOLAR MATERIALS

It is shown that to describe properly the electrostatic theory of quadrupolar materials, the electrostatic energy density of the medium has to contain a term quadratic in the spatial derivatives of the electrostatic field. In this manner well known results are recovered. Furthermore it is shown that due to the quadrupolar properties of the medium, an abrupt variation of the electric potential near the electrode is expected. This surface variation takes place over an intrinsic semi-microscopic length defined by the ratio between the phenomenological coefficient connected with the new electrostatic energy term, and the usual dielectric constant. However, the surface variation of the electric potential is independent of this new coefficient, but it depends only on the electric quadrupolar density and on the dielectric constant. This new result is also obtained in the frame of the usual theory.