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!

Finding the Electric Field of a non-uniform Semi-Infinite Slab of Charge

  1. Sep 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Non uniform slab of charge density [tex]\rhov = \rho_{0}cos(pi*x/(2d))[/tex]
    extends infinitely in the y and z planes is present between -d < x < d.
    Find the Electric Field everywhere.


    2. Relevant equations
    [tex]\int\epsilon_{0}{E^\rightarrow}\bullet{ds^\rightarrow}= \int\rho_{v}dv[/tex]


    3. The attempt at a solution
    So I have an understanding of how Gauss' Integral Law is supposed to function but this semi-infinite slab is confusing me.

    First I will attempt to solve the rhs of Gauss' integral law
    [tex]\int\rho_{v}dv = \int_{0}^{L}\int_{0}^{W}\int_{-d}^{d}\rho_{0}cos(\pi x/(2d))dxdydz = \int_{0}^{L}\int_{0}^{W}\frac{2d\rho_{0}sin(\pi x/(2d))}{\pi} |^{d}_{-d}dydz = \frac{4d\rho_{0}WL}{\pi} [/tex]

    Now I believe I did that correct the lhs has me much more confused.

    Since it is infinite about the y and z axis wouldn't it observe some of the same principles as a infinite sheet charge?

    I dont believe we can define ds as the surface area is infinite. So that forces the use of the integral. Which is where I believe I am going wrong. There is only charge at the +x and -x axis outside of d and -d. How do I set up the Lhs?
    [tex]\int_{0}^{L}\int_{0}^{W}\epsilon_{0}E a_{x}dydz = \epsilon_{0}EWL[/tex]
    This cannot be correct because when applying Gauss' Differential Law there is no way to get the surface charge density without a x variable in which to differentiate.

    Thats where I am stuck how is the LHS of Gauss' Integral Law to be implemented such that when applying Gauss' Differential Law I receive the surface charge density [tex]\rho_{0}cos(pi*x/(2d))[/tex]

    Thanks for the help
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Finding the Electric Field of a non-uniform Semi-Infinite Slab of Charge
Loading...