# Dielectric constant or permittivity of metals

I'm wondering what the dielectric constant or permittivity of metals is --particularly copper. Do metals have an infinite permittivity?

• You can look this up on the internet. At low frequencies metals have large permittivity as shown here. However, since you mention COMSOL I wonder if you're working at higher frequencies, in which case I would suggest looking up real data. Jan 9 '16 at 19:42

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.

• Thanks. Since I have to specify the permittivity of copper in my COMSOL simulation with a constant number. Can I just use a big number? Is 1e10 large enough to express the permittivity of a metal? Jan 13 '14 at 22:45
• Yes definitely, the impurities only bring about minor deviations from idealistic behaviour, if it wasn't so electric shielding would not be realisitic and Faraday Cages would not be a real thing. :) Jan 13 '14 at 22:48
• Woah, what?! Metals do not have infinite permittivity when you are dealing with signals at nonzero frequency, and this definitely matters in applications. Jan 9 '16 at 19:39
• In fact, as DanielSank points out, the Drude model predicts a finite but negative (actually complex valued) permittivity when electron density is high enough. In plasmas, this crossover from positive to negative permittivity is called the “critical density”. When frequency is varied, the crossover is called the “plasma frequency”. In the limiting case of zero frequency, the skin depth does to go zero: skin depth = λ/(4π*Im{sqrt(ε)}). Dec 10 '19 at 20:03
• Agree with @DanielSank. This answer is wrong. You have to be very careful about the frequency at which your signals are being propagated. Sometimes, permittivity can be negative, sometimes positive, sometimes complex; depending on the frequency of the incident field and the plasma frequency. Nov 19 '20 at 12:52

Unlike dielectrics the electrons in conductors are not bound to atoms, therefore, metals can be modeled as electrons in free space. Permittivity of conductors is, therefore, equal to the permittivity of free space.

• Electrons are not vacuum. Free space IS vacuum. Oct 30 '17 at 9:50
• This whole discussion ismissleadg. Electrons in conductors are bound to atoms. In effect the molecules rotate due to the electric potential so that the effect of the potential travels down the wire causing the other end to be the opposite potential or at least less than the applied potential. The speed of this effect is less than the speed of light in free s[pace which is about 1 foot per nanosecond. In copper it is maybe 93-98% of that speed, de[pending on the ratio of the 1/2 wave length of the freq of the electric potential applied/by the diameter of the conductor which is usually copper. Jul 7 '19 at 16:57
• Electrons absolutely couple to EM radiation, this is in fact what causes electric permittivity to be different in materials from in vacuum. Dec 10 '19 at 19:57