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Allowed EM waveforms

  1. Apr 18, 2017 #1
    1. The problem statement, all variables and given/known data
    which of the following proposed space-time dependent electric fields in vacuum is/are allowed by the equations of EM theory?
    a) $$E_x=E_1\sin(kz-wt),E_y=E_2\sin(kz-wt),E_z=0$$
    b) $$E_x=E_1\sin(kz-wt),E_y=2E_1\cos(kz-wt),E_z=0$$
    c) $$E_x=E_1\sin(kz-wt),E_y=0,E_z=E_2\sin(kz-wt)$$

    2. Relevant equations
    $$E = E_0\sin(kz-wt)$$

    3. The attempt at a solution
    I think all the three equations are allowed according to the normal waveform. However I do not know what exactly to look for in such case that does not make it an allowed waveform. I would appreciate if someone could show an example that is not a waveform if my answer turns out to be correct.
     
  2. jcsd
  3. Apr 18, 2017 #2

    BvU

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    Hello Rahulrj, :welcome:

    What are
    ?

    I'm afraid your relevant equation doesn't mean much in the context of this problem. Anyway: what are all those symbols referring to ? You write vectors and scalars the same way ?
     
  4. Apr 18, 2017 #3
    I do not know how to identify the allowed wave form and 'the equations of EM theory' idea doesn't help me much since I do not know what I require to distinguish an allowed waveform. $$E_x E_y $$and$$E_z$$ are electric field components,that's how the question itself is given.
     
  5. Apr 18, 2017 #4

    BvU

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    The equations of EM theory are called the Maxwell equations, as I suspect you are supposed to know (from the fact you are given this exercise)...
     
  6. Apr 18, 2017 #5
    I do know Maxwell equations but I am not sure how to make use of them to know the allowed waveform which is why I said that it doesn't help me much.
     
  7. Apr 18, 2017 #6

    BvU

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    Do you now how to transform the maxwell equations into a wave equation ? Then you can check if the given ##\vec E## can satisfy such equations...
     
  8. Apr 18, 2017 #7
    I don't think I understand that could please provide an example?
    $$\nabla.D = \rho$$
    How do i transform this?
     
  9. Apr 19, 2017 #8

    BvU

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    In vacuum ##\rho = 0##...
     
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