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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.
Thanks.
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?
[tex](\phi,{\vec A})[/tex] is chosen to be a 4-vector in a LT so that the continuity equationThat is very helpful, thank you.
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 valid? Is the electric potential somehow the time-component of the magnetic potential?
The thing on the right is the four dimensional curl.
[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.