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How does one do the following Integral.

  1. Feb 10, 2009 #1
    1. The problem statement, all variables and given/known data

    The problem is really not bad; It's to find the flux due to a point charge at the center of Cube of side length d. I've gotten the answer I believe using Gauss's law (q/6epsilon)

    I tried doing a Flux integral, and the integral seems kind of a pain in the ***... I'm not sure how to do it. I will post where I'm at and hopefully someone can tell me how to integrate this.

    the exact question was

    "Find the flux through a face of a cube from a point charge at the cube's center"

    2. Relevant equations

    3. The attempt at a solution

    First I chose the face, assuming the charge is at the origin, such that da=dzdy(x), x = d/2, and y and z vary from -d/2 to d/2. I then changed Coulombs law to Cartesian coordinates and did some dot products, and substituted in d/2 for x.


    How can one integrate this?
    Last edited: Feb 10, 2009
  2. jcsd
  3. Feb 10, 2009 #2


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    Please write down the question exactly as it was given to you. An electric field can not have dimensions of q/epsilon (a flux can). And please be more clear in your working - write full equations instead of fragments. Right now, one can only guess what you are trying to calculate.
  4. Feb 10, 2009 #3
    Yeah, don't know why I typed Electric field, the problem is to find

    [tex]\int(E)\cdot da[/tex], the flux through the surface.
  5. Feb 10, 2009 #4


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    If you already figured out the flux using Gauss' law and symmetry, why do you need to do the painful integral?
  6. Feb 10, 2009 #5
    I mean, I just usually try to work problems multiple ways. If the integral isn't do-able then I suppose I won't, but often times I just don't think of the proper tricks to solve integrals and things, and doing problems that was as well keeps my bank of problem solving knowledge sharper.
  7. Feb 10, 2009 #6


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    I'm sure you probably can do it. But I think the lesson learned would be disproportionate to the effect involved. If it's easy both ways, do it both ways. If it MUCH easier one way stick with that one.
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