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Homework Help: Help find the flux through the surface

  1. Sep 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Given a vector field [itex]A=(2x,-z^2,3xy)[/itex], find the flux of A through a surface defined by [itex] ρ
    =2, 0<\phi<\pi/2, 0<z<1[/itex]

    2. Relevant equations


    3. The attempt at a solution

    Can I use divergence method here?
    This is a closed surface correct? A cylindrical wedge?
    Also do I need to convert the vector field to cylindrical form? Or the defined surface to rectangle form?

    If I used divergence do I divide my answer by 4 since the wedge is a 1/4 of the cylinder?

  2. jcsd
  3. Sep 18, 2012 #2
    The surface is not closed.
  4. Sep 18, 2012 #3


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    I agree. I read the problem as asking for the flux through the round surface of the wedge and not the other four faces.
  5. Sep 18, 2012 #4
    Thanks for the replies.

    This makes a lot more sense now. So knowing this I would integrate over the surfaces separately.

    So it appears it would be easier to integrate in cylindrical form correct? So I would want to change the vector field from rectangular to cylindrical?
  6. Sep 18, 2012 #5


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    You should only need to integrate over the one surface that is defined by the equalities & inequalities given.

    Yes, that would probably be the easiest way to do it since the surface normal and differential area, and limits of integration will all be much simpler in cylindrical coordinates than in Cartesian coordinates.
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