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Derivation of Lienard-Wiechart

  1. May 10, 2009 #1
    Can anyone point me to a derivation of the Lienard-Wiechart potential formulas? I assume that they can be derived from Maxwell's equations alone.

    Thanks.
     
  2. jcsd
  3. May 10, 2009 #2

    jtbell

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    Staff: Mentor

  4. May 11, 2009 #3
    That is very helpful, thank you.

    A follow-up question, if I may:

    What makes

    [tex]

    ( \frac {\phi }{c} , A^x , A^y , A^z )

    [/tex]

    a four-vector? That is, why is applying a Lorentz transformation to it vaild? Is the electric potential somehow the time-component of the magnetic potential? Is

    [tex]

    \vec B = \nabla \times \vec A

    [/tex]

    still valid if A is four dimensional? Is the curl of a four-dimensional vector field even defined?
     
  5. May 11, 2009 #4

    dx

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    The analog of that equation is Fαβ = ∂αAβ - ∂βAα. The thing on the right is the four dimensional curl. The thing on the left is the Farady tensor.
     
  6. May 11, 2009 #5

    clem

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    [tex](\phi,{\vec A})[/tex] is chosen to be a 4-vector in a LT so that the continuity equation
    [tex]\partial_\mu A^\mu=0[/tex] will hold in any LT so charge conservation will hold in any Loentz system.
    They are no longer called the electric and magnetic potential, but just the 4-vector potential.
     
  7. May 11, 2009 #6
    OK, good. Thanks.

    I'm sorry - could you re-word this? I'm not sure I get your meaning.
     
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