# Relation between conductivity and permittivity

1. Oct 20, 2008

### Repetit

Hey. Is the conductivity of a material related to the dielectric constant (permittivity) in some way? And what about the electrical susceptibility?

Thanks

2. Oct 23, 2008

### olgranpappy

Yes. It depends on the system of electrostatic unit you choose. But, in general the (angular frequency dependent) conductivity is proportional to the imaginary part of the dielectric function times the angular frequency
$$\sigma(\omega)\sim\omega{\rm Im}(\epsilon(\omega))\;.$$

Again with the susceptibility the relation depends on the units, but should look something like
$$\epsilon(\omega)\sim1+4\pi\chi(\omega)\;.$$

Cheers.