1. Limited time only! Sign up for a free 30min personal 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!

Capacitor filled with 2 different dielectrics

  1. May 19, 2010 #1

    _k_

    User Avatar

    1. The problem statement, all variables and given/known data
    Hi there, I got a little problem with this one:
    plate capacitor is filled with 2 different dielectrics with permittivities [tex]\epsilon_1, \epsilon_2[/tex] (surrounding environment is [tex] \epsilon_0 [/tex]) and their respective thicknesses are [tex] d_1 [/tex] and [tex] d_2 [/tex]. The layers are parallel to the plates of the capacitor. The voltage between the electrodes is U and their surface is S. What are the forces acting upon plates ?


    2. Relevant equations
    gauss' law for electric displacement field; F = qE; U=d E (d = distance between plates)

    3. The attempt at a solution
    I tried this:
    electric displacement field is the same in whole capacitor [tex] D = \sigma [/tex] where [tex] \sigma [/tex] is surface density of charge on plates.
    The voltage is then [tex] U = \frac{D}{\epsilon_1}d_1 + \frac{D}{\epsilon_2}d_2 [/tex].

    From the last equation, using the 1st one, the charge density is:
    [tex] \sigma = U \frac{\epsilon_1 \epsilon_2}{d_1 \epsilon_2 + d_2 \epsilon_1} [/tex].

    And the force on plate at dielectric 1: [tex] F = S \sigma E_0 = \frac{S}{\epsilon_0} \sigma^2 = \frac{S}{\epsilon_0}U^2 (\frac{\epsilon_1 \epsilon_2}{d_1 \epsilon_2 + d_2 \epsilon_1})^2 [/tex]
    [tex]E_0[/tex] is the field outside the dielectrics, since the plate is not in the dielectric.

    Which, according to the book, is wrong. The correct answer should be
    [tex] F = \frac{\epsilon_0^2}{2 \epsilon_1} (\frac{U}{d_1 + d_2})^2 S [/tex].

    I'm completely lost. The book gives no detailed explanation, and after 2 hours of scratching my head I need help. Thanks in advance for any suggestions.

    [edit: wrong names for electric field and electric displacement field... sorry for my english ;)]
     
    Last edited: May 19, 2010
  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?
Draft saved Draft deleted