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Homework Help: Surface integrals (without real integration)

  1. Mar 9, 2006 #1
    Given F= [tex](ix+jy) Ln(x^2+y^2)[/tex]

    and given S, which is a cylinder of radius r, and height h(in the z axis) evaluate [tex] \int\int_s F.n \,ds[/tex]. It says that you shouldn't need to do any work if you think about it enough. I figured I could find the area of the main part to be [tex]2 \pi r h[/tex] then multiply that by [tex]Ln(r^2)=2Ln(r)[/tex] to get the answer but I am off by a factor of r in my answer. I don't think the caps to the cylinder contribute to this as the normal is orthogonal to F.

    One more question, what exactly does a surface integral return? I feel stupid but I can't seem to find out exactly what the physical meaning of the result of a surface integral is. Thanks for the help.
     
    Last edited: Mar 9, 2006
  2. jcsd
  3. Mar 9, 2006 #2
    A surface integral is the integral of a function over a surface, as opposed to a line, etc. Unit-wise you are gaining an extra meter^2. As far as a physical meaning, it depends on what you are integrating.

    What's happening in this integration would be easier to understand if you switch everything to polar coordinates.

    -Dan
     
  4. Mar 9, 2006 #3
    I think i'm just confusing myself more :uhh: If I integrate that vector function around a cylinder than it will be 0. I can imagine that we would have constant vectors of magnitude [tex]Ln[r^2][/tex] all in the radial direction around the cylinder for any z value. I guess I still don't have a good enough understanding of what a surface integral really is to be able to find an easy way to express this. I think its time to re-read some div,grad,curl.
     
    Last edited: Mar 9, 2006
  5. Mar 9, 2006 #4

    siddharth

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    As topsquark said, switch over to polar.

    In fact, I suggest you work this out the hard way and then look back.
     
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