Microscopic fields in liquid dielectrics

We present the results of an analytical theory and numerical simulations of microscopic fields in dipolar liquids. Fields within empty spherical cavities (cavity field) and within cavities with a probe dipole (directing field) and the field induced by a probe dipole in the surrounding liquid (reaction field) are considered. Instead of demanding the field produced by a liquid dielectric in a large-scale cavity to coincide with the field of Maxwell's dielectric, we continuously increase the cavity size to reach the limit of a mesoscopic dimension and establish the continuum limit from the bottom up. Both simulations and analytical theory suggest that the commonly applied Onsager formula for the reaction field is approached from below, with increasing cavity size, by the microscopic solution. On the contrary, the cavity and directing fields do not converge to the limit of Maxwell's dielectric. The origin of the disagreement between the standard electrostatics and the results obtained from microscopic models is traced back to the failure of the former to account properly for the transverse correlations between dipoles in molecular liquids. A new continuum equation is derived for the cavity field and supported by numerical simulations. Experimental tests of the theoretical results are suggested.