What Is the Drude-Lorentz Model in Relation to Permittivity and Conductivity?

[thefireman]

I have an relation between permittivity and conductivity as follows:

$$\epsilon(\omega) = 1 + \frac{4\pi\iota\sigma(\omega)}{\omega}$$

Yet am unclear as to how it was derived. Does this relationship have a name and/or derivation to follow through somewhere? also, I believe it is cgs units, what is the SI equivalent?

Thanks

 

[tiny-tim]

I have an relation between permittivity and conductivity as follows:

$$\epsilon(\omega) = 1 + \frac{4\pi\iota\sigma(\omega)}{\omega}$$

Yet am unclear as to how it was derived. Does this relationship have a name and/or derivation to follow through somewhere? also, I believe it is cgs units, what is the SI equivalent?

Thanks

Hi thefireman!

(i think you just leave out the 4π … or is it 4πe₀ ? … to get SI units)

this looks a bit like like the "complex permittivity" definition …

$$\hat{\epsilon}(\omega)\ =\ \epsilon(\omega) + \frac{\iota\sigma(\omega)}{\omega}$$ is the "complex permittivity"

… see eg http://en.wikipedia.org/wiki/Permittivity#Lossy_medium

… but with a different notation

 

[sir-pinski]

for sharing this relationship between permittivity and conductivity. This relationship is known as the Drude-Lorentz model, which was developed by physicist Paul Drude and Hendrik Lorentz in the late 19th century. It is used to describe the behavior of electrons in a material and their interaction with an electromagnetic field.

The derivation of this relationship can be found in many textbooks on electromagnetism or solid state physics. It involves solving the equations of motion for electrons in a material under the influence of an external electric field. The result is a complex permittivity, which includes both the real part (related to the dielectric properties of the material) and the imaginary part (related to the conductivity of the material).

In SI units, the equivalent relationship is:

\epsilon(\omega) = \epsilon_0 + \frac{\sigma(\omega)}{\iota\omega}

where \epsilon_0 is the vacuum permittivity. This is just a matter of converting the units from cgs to SI.

I hope this helps clarify the relationship between permittivity and conductivity and its origins. It is a fundamental relationship that is used in many areas of physics and engineering, particularly in the study of electromagnetic waves and materials.