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Homework Help: Flux Integral

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the flux of [itex]\vec{F}=(x, y, z)[/itex] outward across the sphere [itex]x^2+y^2+z^2=a^2[/itex].

    I am able to get it to this point:
    [tex]\int\int_Cadxdy[/tex] and I then convert it to polar coordinates, and integrate rdr from 0 to a, and theta from zero to 2pi. However, this does not give me the correct result, as the answer is 4a^3*pi, and Im getting a^3*pi.
  2. jcsd
  3. Jan 30, 2012 #2


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    hi sandy.bridge! :smile:
    it's the surface of a sphere …

    what does r have to do with it? :confused:

    (and why are you integrating? surely you know the surface area of a sphere? :wink:)
  4. Jan 30, 2012 #3
    Okay, well I know that once I get it to this point, it's right:

    The projection of the sphere on the xy-plane is a circle, no? So why can I not use
  5. Jan 30, 2012 #4


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    projection? are you treating F as if it was a parallel field along one of the axes? :confused:

    in that case, yes, the projection perpendicular to the field would be a circle

    but the given F is radial ((x,y,z) = t), and constant in magnitude over the sphere,

    so you just need the amount of surface it cuts through, which is 4πa2
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