I'm wondering what the dielectric constant or permittivity of metals is --particularly copper. Do metals have an infinite permittivity?
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium.
Yes, metals have infinite permittivity as they completely negate the electric field inside their bulk. I.e. infinite resistance to setting up of field and hence infinite permittivity. But this case is more valid for perfect conductors as realistic conductors would have defects and impurities.