Abstract
We give a new proof that the constitutive relation of macroscopic electrostatics holds in a dipolar fluid with a sample's shape independent dielectric constant. Our approach is based on BGY-like hierarchy equations which allow us to calculate the canonical one-body density function up to linear order in the electric field, in the thermodynamic limit. The dielectric constant comes out as an integral over a 3-point correlation function of the infinite (unpolarized) system, from which one can recover the well known formula for e in terms of the direct correlation function.
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