1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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


    User Avatar
    Science Advisor

    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 by a moderator: Mar 28, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook