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EM Waves

  1. Feb 27, 2005 #1
    Hi, I have the following question on my problem sheet, and I just want to check that my answer to it is correct as I need to use the result in a later problem. If someone could confirm it is correct, or point out mistakes/erros that would be great.

    Q. Derive the wave equation for E in empty space (Form the curl of Maxwell II and use a vector identity.). Find the condition that the plane wave E = eyEycos(wt - kx) is a solution (k=2pi/lamda). Use Maxwell II to find the B field associated with this electric field.

    A. I've done the derivation fine to get:

    Laplacian E = epsilon-0.mu-0. d^2E/dt^2 [these are partial derivatives]

    this is the same as d^2E/dx^2 = (1/c^2).(d^2E/dt^2) which can be solved using separation of variables to get E = eyEycos(wt - kx).

    To find the associated B field, we used Maxwell II, ie. curlE = -dB/dt.

    CurlE = -keyEysin(wt - kx)

    B = integral - [curl E] dt

    B = k/w. eyEycos(wt - kx)


  2. jcsd
  3. Feb 27, 2005 #2


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    [tex] \vec{B}=-\int dt \nabla\times\vec{E} [/tex]

    What is the curl of [itex] \vec{E} [/itex]...?And then evaluate the integral correctly.

  4. Feb 27, 2005 #3
    Isn't the curl of E in this case, just the value of E calculated earlier, integrated wrt x?
  5. Feb 27, 2005 #4


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    That curl is a vector and should have 2 components,namely on [itex] Ox_{1}[/itex] and [itex] Ox_{3} [/itex] axis of coordinates...

    So it's incorrect what you have written.Please do the calculations again.

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