1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear isotropic dielectric mixture two materials

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider an x1:x2 mix of two linear isotropic dielectrics (by volume). x1+x2=1. On large length scales the mixture is homogenous and can be characterized with a dielectric constant ε_mix but on short length scales the material is granular so the dielectric constant is either ε_1 or ε_2. Neglecting spatial variations completely we have ε_mix = x1*ε_1 + x2*ε_2. Calculate the first correction to this result, if spatial variations δε = ε_2 - ε_1 are small (that is |δε| << ε_1,2.

    2. Relevant equations

    Are you kidding? it's a dielectrics problem even if it wasn't 4:30 AM I probably wouldn't write them all. Basically equations for linear isotropic dielectrics and maybe Claussius-Mossotti.

    3. The attempt at a solution

    I couldn't tell what form to assume for ρ the charge density, so unable to directly calculate the average dipole moment. So I tried to algebraically solve for ε_mix in terms of the dielectric constants and volume ratios...to no avail (probably).

    Then I re-read an email, the Prof. seemed to be implying that he wanted us to derive (in general) the displacement when the media is a dielectric mixture.

    However he does not specify we must use certain methods to solve a problem, so I think I can do it by directly calculating the average dipole moment. So I need to know a reasonable assumption to make for the charge density. Can you advise? Or point me to a reference?

    Or can you point me to a reference with the general derivation done?

    It's due tomorrow. Yes I'd like to start on hw early. The reality is, it's nearly impossible.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?