Understanding Electric Field Screening in Materials

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Can anyone explain in simple terms what the term screening means? My intuition is that a metal is a good screener because in the presence of an external electric field its free electrons will rearrange themselves such that the electric field is zero inside the metal.
But I am having a hard time coupling my intuition to something my teacher said the other day. He said that the screening properties are related to the permitivity of the material and that ε=∞ is a perfect screener. Can anyone help me draw the connection?
 
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Hey man I think you mean to say "shielding effect" !
Not screening
Or both might be same !
 
U might be knowing that a dielectric with relative permittivity e when kept in an electric field E develops an electric field E/e inside it
So for metals e = infinite
If not we should have electric currents flowing inside the metal ! But doesn't happen right ??!