Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How can I calculate dilectric constant from conductivity

  1. Jan 31, 2017 #1
    Hello,
    could you help me please about how can I calculate dielectric constant form electrical conductivity?
     
  2. jcsd
  3. Jan 31, 2017 #2

    Charles Link

    User Avatar
    Homework Helper

    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.
     
  4. Jan 31, 2017 #3

    Charles Link

    User Avatar
    Homework Helper

    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} ##.
     
  5. Jan 31, 2017 #4
    Thanks so much Charles,
     
  6. Feb 1, 2017 #5
    Why cant I see the equations, only what I presume to be the code for equations?
     
  7. Feb 1, 2017 #6

    NascentOxygen

    User Avatar

    Staff: Mentor

    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.
     
  8. Feb 1, 2017 #7

    f95toli

    User Avatar
    Science Advisor
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted