How can I calculate dilectric constant from conductivity

In summary, the linear response equations for a dielectric medium are connected to the polarization current and the continuity equation. By taking Fourier transforms, these equations can be solved for the dielectric constant in terms of the conductivity. However, in practice, it is difficult to calculate the dielectric constant accurately from electrical conductivity data. It is usually more accurate to measure the dielectric constant directly using capacitance or a resonator.
  • #1
Aseel5
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Hello,
could you help me please about how can I calculate dielectric constant form electrical conductivity?
 
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  • #2
There is a connection between the linear response equations for a dielectric medium:
## P(x,t)=\int \chi(x-x',t-t') E(x',t') \, d^3 x' \, dt' ## and ## J_p(x,t)=\int \sigma(x-x',t-t') E(x', t') \, d^3x' dt' ##. Taking Fourier transforms these become: ## \tilde{P}(k,\omega)=\tilde{\chi}(k,\omega) \tilde{E}(k,\omega) ## and ## \tilde{J}_p(k,\omega)=\tilde{\sigma}(k,\omega) \tilde{E}(k,\omega) ##. The equation ## J_p=\dot{P} ## (for the polarization current=it follows also from the continuity equation) and its Fourier transform ## \tilde{J}_p(k,\omega)=-i \omega \tilde{P}(k,\omega) ## tie these together, along with ## D(x,t)=\int \epsilon(x-x',t-t') E(x',t') \, d^3 x' \, dt' ## and its Fourier transform, ## \tilde{D}(k, \omega)=\tilde{\epsilon}(k,\omega) \tilde{E}(k,\omega) ## so that ## \tilde{\epsilon}(k,\omega)=1+4 \pi \tilde{\chi}(k,\omega) ##. ## \tilde{\sigma}(k,\omega) ## is the conductivity, and ## \tilde{\epsilon}(k,\omega) ## is the dielectric constant. I used cgs units so that ## D=E+4 \pi P ##, but conversion to any other units can be readily done. Hopefully this was helpful. (With a little algebra, you can solve for ## \tilde{\sigma}(k,\omega) ## in terms of ## \tilde{\epsilon}(k,\omega) ##). For a reference, Ichimaru's Plasma Physics book has much of this in the first couple of chapters.
 
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  • #3
Note: The continuity equation is ## \nabla \cdot J_p+\frac{\partial \rho_p}{\partial t}=0 ##. Since ## \rho_p=-\nabla \cdot P ##, this gives ## \nabla \cdot (J_p-\dot{P})=0 ## which gives the result that the polarization charge current density ## J_p=\dot{P} ##.
 
  • #4
Thanks so much Charles,
 
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Why can't I see the equations, only what I presume to be the code for equations?
 
  • #6
Phellippe Marques said:
Why can't I see the equations, only what I presume to be the code for equations?
I think the app does not run whatever is needed to interpret MathJax. So users of the PF app will not see the rendered equations.
 
  • #7
Aseel5 said:
Hello,
could you help me please about how can I calculate dielectric constant form electrical conductivity?

You have to be more specific? Do you mean in theory (see Charles response)? Or in practice (i.e. you have some data for the conductivity of a dielectric) ?
If it the latter the answer is that you can't, at least not in the general case. I can think of a few situations where it might work, but you would need data which -as far as I am aware- tends to be quite difficult to measure. It usually makes more sense to measure the dielectric constant directly by measuring the capacitance or -even better- putting the material in a resonator.
 
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FAQ: How can I calculate dilectric constant from conductivity

What is the formula for calculating the dielectric constant from conductivity?

The formula for calculating the dielectric constant (ε) from conductivity (σ) is ε = 1/(σ * ε0), where ε0 is the permittivity of free space (8.85 x 10-12 F/m).

How do I measure the conductivity of a material?

The conductivity of a material can be measured using a variety of techniques, such as using a conductivity meter, performing a four-point probe measurement, or using a dielectric constant analyzer. The specific method will depend on the type of material and its properties.

Can I calculate the dielectric constant from the conductivity of any material?

No, the relationship between dielectric constant and conductivity is not universal for all materials. It depends on the properties and composition of the material. Additionally, the formula used to calculate the dielectric constant may vary for different materials.

How does the dielectric constant relate to the electrical properties of a material?

The dielectric constant is a measure of a material's ability to store electrical energy. It is directly related to the material's capacitance and determines how easily an electric field can penetrate the material. Materials with higher dielectric constants are better insulators and have lower conductivity.

Is the dielectric constant a constant value for a material?

No, the dielectric constant can vary depending on factors such as temperature, frequency of the applied electric field, and the presence of impurities or defects in the material. In some cases, it may also vary within a material depending on its structure or composition.

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