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On the basis of the exact relations the general formula for the staticdielectric permittivity for Coulomb system is found in the region of small wavevectors. The obtained formula describes the dielectric function of the Coulombsystem in both limits: in the "metallic" state and in the "dielectric" one. Onthis basis the determinations of the "apparent" dielectric and the "apparent"radius of screening are introduced. In the random phase approximation (RPA) theexact relations for the function dielectric function of the electron gas in thelong-wavelength region of the wave vectors are found for an arbitrarydegeneration of the particles.

On the Static Dielectric Permittivity for Coulomb System in the Long Wavelength Limit