What is the dielectric constant of a pure conductor? Dielectric constant is the ratio of permittivity of a medium to the permittivity of free space. How to find dielectric constant of a conductor?
 A: Inside a metal, there is no formation of dipoles, hence there is no polarization as such. We have free electrons in metals not bound like that of a dielectric. Hence we can argue its electric susceptibility $\chi$ = 0. We know $\epsilon_r = 1 + \chi$, so it can be said that its relative permittivity($\epsilon_r$) is 1, considering electrostatics problems. For time varying fields, i.e. electrodynamics, we define complex permittivity as $\hat{\epsilon}=\epsilon \times (1+\sigma/i\omega\epsilon)$, where for metals we can have the imaginary part $\sigma/\omega\epsilon >> 1$. Thus for metals $\hat{\epsilon}=i\sigma/\omega)$, which is a large imaginary value considering high conductivity of metals.
Though, not a source for this answer,the basic idea was gained by observing the value of $\epsilon = \epsilon_0$ being used in Introduction to Electrodynamics by David Griffiths, in problems (see Chapter 9, Problem 20,bit (b)).
A: The permittivity of a conductor is infinite. 
Let the value of an external electric field in free space (relative permittivity = 1) be $E$.  
If this is applied to a material of relative permittivity $\epsilon_r$ then the electric field in the material is $\dfrac {E}{\epsilon_r}$
Inside a conductor the electric field is zero hence its relative permittivity is infinite.
A: Value $k$ gives an idea of how it isolates the charges. Insulators are used for this purpose so the conductors do less in this regard.
A: Dielectric constant is proportional to the ratio of polarization density (P) and electric field (E) which means dielectric constant is inversely proportional to  electric field.
The Electric field (E) inside a conductor is always zero under the static situation so the dielectric constant for conductor is infinite.
A: If permittivity is infinite inside conductor, then won't it mean that for a given time varying electric field (say E(t)=250sin wt), the displacement current density is very high inside conductor? Theoretically, it should be zero though.
And electric field is zero inside conductor, because of the effect of induced electric field inside the conductor, in direction opposite to external field. Induced field adds vectorially to external field and cancels its effect. 
A: The net or resultant electric field inside in a conductor is zero
therefore dividing electric field by zero we get infinity
A: The more in the value of dielectric constant the more is the nonconducting property. If dielectric constant of a conductor is infinite, it will be a perfect insulator. Electric field inside a conductor in electrostatic condition is because of induced electric filed of induced charges, opposing external electric field and it is not due to infinite value of dielectric constant or permittivity of the conductor. And the displacement current inside a conductor with time varying electric field like a.c voltage across a conductor, is zero because pemitivity of the conductor is zero.
A: Drude formula is not so bad for real metals:
$\varepsilon(\lambda) = 1 - \frac{1}{\frac{\lambda_p}{\lambda}(\frac{\lambda_p}{\lambda} + i \gamma)}$, where $\lambda$ is the wavelength in the vacuum.
For gold in the infrared region, $\lambda_p$ is about 190 nm, and $\gamma$ is about 0.005.
Bit what is a "pure" conductor? If you want to remove the losses, put $\gamma = 0$. $\lambda_p$ term is instrinsic to the mass and density of electrons.
For a perfect conductor, $\frac{1}{\varepsilon} = 0$. For a real good conductor, $\frac{1}{\varepsilon}$ is a small negative number in the optical domain and a small imaginary number in RF or DC domain.
A: A pure conductor which is placed between potential difference it strats conducting. So dielectric constant is zero
