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!

Derivation of induced charge on a dielectric

  1. Dec 4, 2015 #1

    Titan97

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Show the the induced charge density on a dielectric placed inside a capacitor is given by $$\frac{k-1}{k}\sigma$$ where ##\sigma## is the charge density of the capacitor plates and ##k## is the dielectric constant.

    2. Relevant equations
    $$E=\frac{E_0}{k}$$

    3. The attempt at a solution
    IMG_20151204_150222_024.JPG

    Using the above image, let ##E_0## be the electric field before inserting the dielectric and ##E_i## be the induced electric field.

    Total electric field between the plates $$E=E_0-E_i$$
    $$\frac{E_0}{k}=E_0-E_i$$
    $$E_i=\frac{k-1}{k}E_0$$

    Now, ##E_0## is the total electric field due to the plates of the capacitor which is equal to ##\frac{\sigma}{k\epsilon_0}##. The factor of ##k## is because the medium is not vacuum anymore. (Clarification needed because in my book, K does not come in both the expressions for ##E_0## and ##E_i##).
    Similarly, ##E_i=\frac{\sigma'}{k\epsilon_0}##

    Hence, ##\sigma'=\frac{K-1}{K}\sigma##.

    Although I got the answer, in my book, its given ##E_0=\frac{\sigma}{\epsilon_0}## and ##E_I=\frac{\sigma'}{k}##. The K term is missing. Is it a printing error or am I wrong?
     
  2. jcsd
  3. Dec 4, 2015 #2

    cnh1995

    User Avatar
    Homework Helper

    Your answer looks correct to me.
    εo is missing in E1 and k is missing in E0. I believe that's a printing mistake as you said.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Derivation of induced charge on a dielectric
  1. Dielectric Charges (Replies: 1)

Loading...