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Flux 2

  1. Jul 30, 2008 #1
    1. The problem statement, all variables and given/known data

    I need to find the flux of this vector field (in the pic) that goes through this plan (in the pic) and z goes from 0 to 1.
    How am I suppose to do that?


    2. Relevant equations



    3. The attempt at a solution
     

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  3. Jul 30, 2008 #2

    HallsofIvy

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    The surface is [itex]z= \sqrt{x^2+ y^2}[/itex], the upper nappe of a cone. In cylindrical coordinates, that is z= r. So good parametic equations would be [itex]x= r cos(\theta)[/itex], [itex]y= r sin(\theta)[/itex], [itex]z= r[/itex] which means that the vector equation would be
    [itex]\vec{r}(r, \theta)= r cos(\theta)\vec{i}+ r sin(\theta)\vec{j}+ r \vec{k}[/itex]. Since z goes from 0 to 1, r goes from 0 to 1 and [itex]theta[/itex], of course, from 0 to [itex]2\pi[/itex].

    Does that help?
     
  4. Jul 30, 2008 #3
    Check this out, is that what you meant?
     

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  5. Jul 31, 2008 #4

    HallsofIvy

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    Once you have done the cross product, and the integral, yes, that should be correct. I would recommend you do the integrations with respect to [itex]\theta[/itex] first. Most of those trig functions, integrated from 0 to [itex]2\pi[/itex] will give 0.
     
  6. Jul 31, 2008 #5
    10x a lot.
     
  7. Jul 31, 2008 #6

    HallsofIvy

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    10-4 good buddy!
     
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