dielectric constant of metals is infinity why
Answers
The dielectric constant is related to the electronic susceptance in an isotropic material.
The susceptance is basically the ratio of polarization to applied electric field.
You can think about a conductor as having "bound" electrons in that they cannot leave the entire material, but are free to polarize across the entire length of a conductor.
When you apply an external electric field to a conductor, you polarize the entire conductor, such that the polarization causes the electric field inside the conductor to be zero (electrostatic equilibrium). In a normal dielectric, the bound electrons cannot move as far as in a conductor, they have a much smaller polarization.
The definition of a dipole moment is charge separation times separation distance.
In a conductor, the induced dipoles have distances of the magnitude of the size of the macroscopic object, which is much much larger than the dipole distances of a dielectric.
Hence, the polarization vectors in a conductor are nearly infinite compared to the polarization vectors of a dielectric (whose order of magnitude we are accustomed to dealing with). The susceptance is therefore near infinite, and so is the relative permittivity.