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How to derive Lienard-Wiechert potential from Maxwell's equation?

  1. Jun 28, 2009 #1
    I've seen one derivation on Feynman Lectures on Physics, but the derivation is not really rigorous(he took a very special case for the derivation),I googled about the topic and couldn't find a satisfactory one. So can anybody give me a rigorous one?
    Thanks in advance
  2. jcsd
  3. Jun 28, 2009 #2
    Jackson derives it in 6 equations at the start of chapter 14, but you need to be familiar with the relativistic formalism (current and potential as four-vectors) and retarded Green's functions. If you are familiar with these, than the LW potentials follow from:

    [tex]\mathbf{A} = \frac{4\pi}{c} \int d^4x' G(x-x') \mathbf{J}(x') [/tex]

    [tex]\mathbf{J}(x') = \int d\tau \mathbf{v}(\tau) \delta^4(x' - r(\tau))[/tex]

    where r is the trajectory (four-vector), and v is the four-velocity. All you do is sub the second eq into the first and crank it out to derive the LW potentials.
  4. Jun 29, 2009 #3
    Thanks.But I'm not quite familiar with the manipulation of those, I'll give a shot.
    And are there any other derivations avaliable?
  5. Jun 29, 2009 #4
    I'm not a big fan of Griffiths, but his "Electrodynamics" text has a pretty good derivation of it in chapter 10 - self contained and quite intuitive.

    http://www.physicallyincorrect.com" [Broken]
    Last edited by a moderator: May 4, 2017
  6. Jun 30, 2009 #5
    Thanks, I will have a look at it.
    Last edited by a moderator: May 4, 2017
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