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Laplacian Help

  1. Mar 27, 2007 #1
    I need to know the steps involved in solving this laplacian.

    Ex(r,z) = Eo*e^[-(r/ro)^2]*e^[-ibz]

    the laplacian \/^2*Eo = ?
    Eo is a vector
    \/ is laplacian symbol

    any help would be appreciated.

    Thanks in advance.
     
  2. jcsd
  3. Mar 27, 2007 #2

    quasar987

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    you probably meant \/^2*Ex, not \/^2*Eo.

    Well, the problem is that there are polar and cartesian coordinates mixed up in the expression of Ex. So either transform r in cartesian and use the cartesian laplacian or transform z in polar and use the polar laplacian.
     
  4. Mar 28, 2007 #3

    HallsofIvy

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    No, that's in "cylindrical coordinates" which is perfectly fine- just use polar coordinates with z appended.

    The Laplacian of Y in cylindrical coordinates is
    [tex]\frac{\partial^2 Y}{\partial r^2}+ \frac{1}{r}\frac{\partial Y}{\partial r}+ \frac{1}{r^2}\frac{\partial^2 Y}{\partial \theta^2}+ \frac{\partial^2 Y}{\partial z^2}[/tex]
     
    Last edited: Mar 28, 2007
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