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Maxwell's electromagnetic wave equation confusion

  1. Jan 9, 2010 #1
    I'm not understanding something here. Maxwell's wave equation is:

    Laplacian of E = (1/c^2) * second partial of E
    (sorry, I don't know how to write symbols)

    But the second partial derivative is the Laplacian. So how can you scale the laplacian of E by a number and get the laplacian of E as a result? Is there some fundamental rule of EM that allows this? What is physically happening? Thanks in advance.
     
  2. jcsd
  3. Jan 9, 2010 #2

    vela

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    Partial with respect to what variable on the right-hand side?
     
  4. Jan 9, 2010 #3
    time

    Laplacian of E = (1/c^2)* second partial of E with respect to t.
     
  5. Jan 9, 2010 #4

    vela

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    Does that answer your question?
     
  6. Jan 9, 2010 #5
    No. Should it?
     
  7. Jan 9, 2010 #6

    vela

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    Well, perhaps I don't understand your question, but there's no Laplacian on the right-hand side.
     
  8. Jan 9, 2010 #7
    Since the laplacian is the second partial derivative, you can write the expression as:

    Laplacian of E = (1/c^2)*Laplacian of E

    I don't see how you can multiply by a scalar and still get the Laplacian of E back or why it is written as a second derivative instead of the Laplacian. That is what my question is.
     
  9. Jan 9, 2010 #8

    jtbell

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    For an introduction,

    https://www.physicsforums.com/showthread.php?t=8997

    For your specific equation:

    [tex]\nabla^2 \vec E = \frac{1}{c^2} \frac {\partial^2 \vec E}{\partial t^2}[/tex]

    Click on the equation and you get a popup window that shows the code.
     
  10. Jan 9, 2010 #9
    I just realized what my problem was. The RHS is JUST with respect to time, not x or y or anything. That's not the laplacian...

    Lets just imagine this thread never happened, haha! Thanks for your help.
     
  11. Oct 14, 2011 #10
    there is a simble in physics that is due to the special relativity that u can show the second derivative of time combined with the laplacian of x,y and z.

    u can find it in the "electromagnetic theory" book that is written by,milford,rits and cristy.(i'm not sure at all,about the spelling of the writers and the name of the book.)
    u can search in the last chapters and find it.
     
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