Dielectric constant is the ratio of permittivity of a medium to the permittivity of free space. How to find dielectric constant of a conductor?
Answer
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.
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