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Maxwell equations + scalar and vector potentials

  1. Dec 5, 2008 #1
    Im doing some study on scalar and vector potentials in the area of electromagnetics, and the author of the book derived this equation

    [tex]\vec{E} = -j\omega\vec{A} - \nabla\phi[/tex]

    where [tex]\vec{A}[/tex] = vector potential and

    [tex]\phi[/tex] = scalar potential and

    [tex]\vec{E}[/tex] = time harmonic form of electric field

    The author goes on to make a statement saying this may be a familiar result, however Im not sure exactly what he is referring to ?? Can anyone shed some light ?
  2. jcsd
  3. Dec 6, 2008 #2


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    Looks like one of these.
    What is j, is it [itex]\sqrt{-1}[/itex]? Is a specific vector potential given (say, [tex]A \propto e^{-j \omega t}[/tex]?)
  4. Dec 6, 2008 #3


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    The author probably assumes you have read an intermediate level EM textbook.
  5. Dec 7, 2008 #4

    j = sqrt(-1). The textbook assumes a general vector potential (where at this stage only the curl of the vector potential has been defined)
  6. Dec 7, 2008 #5


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    Well, as I said, the Maxwell equations contain
    [tex]\vec E = \frac{\partial \vec A}{\partial t} - \vec\nabla\phi[/tex]
    so if A is something like [tex]\vec A = \vec A_0 e^{-j\omega t}[/tex] then you would get what you posted. That's all I can guess based on your information,
  7. Dec 8, 2008 #6
    Sorry, didn't notice your wikipedia link. Will look into it and get back to you !
  8. Jan 17, 2009 #7
    i'm not quite sure about what j and omega presents,but the formula seems to be written in the form that satisfy helmhotlz's theorem,hope it help...
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