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Electrix flux through a tetrahedron

  1. Oct 7, 2008 #1
    1. The problem statement, all variables and given/known data
    what is the outward flux through one of the 4 triangular faces of a tetrahedron centered at the origin if the charge density is q*(delta)^3(r)


    2. Relevant equations



    3. The attempt at a solution
    So, I figured that all I had to do was find the point charge q that the tetrahedron encloses....because I can find that by integrating over the charge density....
    my problems are...am I making this problem too hard? Is there a simpler way to solve this?
    and also, if I integrate over the charge density to, what are the limits of the integral, and how do you integrate the dirac delta?
    Please Help!!!!!!!!!!
     
  2. jcsd
  3. Oct 7, 2008 #2

    gabbagabbahey

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    Use the definition of the dirac delta:

    [tex]\int_{all space} f(\vec{r'}) \delta ^3 (\vec{r}) d^3r'=f(0)[/tex]

    So where does this mean the charge q is located? ;0)
     
  4. Oct 7, 2008 #3
    q would be located at the origin......right?

    but, don't I have to know what q is by the charge density?

    or is it simply the flux from a point charge at the origin? But if that's the case, where does the charge density come into play?
     
  5. Oct 7, 2008 #4

    gabbagabbahey

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    Yes, it is a point charge q, located at the origin. The charge density just tells you that the only charge is the point charge q at the origin, that's all the information that you need from it. Just calculate the Flux from a point charge at the origin through one face of the tetrahedron.
     
  6. Oct 7, 2008 #5
    so the flux from a point charge is q/e0

    So, since the flux is through a tetrahedron, then it would be q/4e0

    right????
     
  7. Oct 7, 2008 #6

    gabbagabbahey

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    Yes, but this is only true because the point charge is at the center of the tetrahedron, and so the flux through each face is equal.
     
  8. Oct 7, 2008 #7
    Thank you!
    Thank you!
    Thank you!

    I was over-thinking the problem.
     
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