Since in any material the nucleus is surrounded by electrons some of the electron's electric field does interact with the other electrons from the same atom and with the electrons from the surrounding atoms. Even on the surface of an uncharged body there are a lot of electrons.
Adding electrons we observe an electric field. Is it possible to define a density of electrons on the surface shell and to calculate the increase of the electric field's strength when the body becomes charged (as electrons are added)? Has this been calculated and does the electron's electric field strength differ when bound to a nucleus from the strength in a free state?
Answer
What you're talking about is a part of the free electron theory in solid state physics. I believe you have to consult a solid state physics book, like Kittel's or Aschcroft's.
A good start can be in Wikipedia at the Screening effect.
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