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Curl of a Div of a Green's Function

  1. Mar 10, 2007 #1
    Okey Dokey, so I'm bored and decided to play around with some math. I've got a problem that I can't figure out now; I have the green's function for the laplacian

    [tex]G(\vec{x}, \vec{x'}) = - \frac{1}{4\pi |\vec{x} - \vec{x'}|}[/tex]

    There are no boundary conditions.

    Is there any lazy way to figure out the div of the curl of the green's function, or do I have to do some work on this one?

    [EDIT]: The lack of coffee is getting to me, it's the curl of a gradient of the green's function.
  2. jcsd
  3. Mar 11, 2007 #2
    div(curl(A))=0 for any vector A
  4. Mar 11, 2007 #3


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    The OP editted it to curl(grad f) but it easy to show that that is 0 also!

    [tex]\left|\begin{array}{ccc} \vec{i} & \vec{j} & \vec{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ f_x & f_y & f_z \end{array} \right|= \vec{0}[/tex]

    It doesn't matter whether the function is Green's function or not.
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