Insulator and conductor with electrostatic problems

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I was wondering, what is the distinction made with problems involving either conductors or insulators with electrostatic problems.

Is it that the electric field in an insulator doesn't have to be zero, whereas the electric field in a conductor is always 0?
 
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That's what experiments have shown and which were the basis for Gauss's law or the equivalent Coulomb's law.
 
A conductor is an object in which a current will flow for as long as an electric field is present inside the object. From which of course follows that if no current is flowing inside a conductor there can't be an electric field there.
However in practice every substance is at least slightly conductive. So where you draw the line between conductor and insulator is arbitrary and depends on what kind of voltage and current you are working with.