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Curl and Surface Integral

  1. Apr 10, 2004 #1
    Curl and Surface Integral (help!)

    Hello people!
    I've been working on this problem, but I can't find how differentials of V on the left side of the equation appear.

    Show, by expansion of the surface integral, that (see attached image).
    Hint: choose the volume to be a differential volume, dx dy dz .

    Here d(sigma) is a vector surface element, V is a vector field, and d(tau) is a infinitesimal volume element.
    Well, from the right side of the equation is clear that derivatives of V will appear, but I can't do the same on the left side, where I only get components of the vector field multiplied by infinitesimal area elements.
    Using the lower part of the fraction, some of these elements "disappear", but no hint of the derivatives of V appear to me. Any ideas?

    By the way, is there any way to put images inside the message?

    Attached Files:

    Last edited: Apr 10, 2004
  2. jcsd
  3. Apr 10, 2004 #2

    matt grime

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    Here's the tex version (faq in general physics forum)

    [tex]\lim_{\int d\tau \to 0} \frac{\int_S d\sigma\wedge V}{\int d\tau} = \nabla\wedge V[/tex]

    I'm not sure that you really want the limit as the integral of d\tau goes to zero since the integral of d\tau is just the volume (though you've not said what you're integrating d\tau over so I'm guessing here)

    Click on the image to see the code for it
    Last edited: Apr 10, 2004
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