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

[kof9595995]

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

 

[Civilized]

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:

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

$$\mathbf{J}(x') = \int d\tau \mathbf{v}(\tau) \delta^4(x' - r(\tau))$$

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.
[tex]

 

[kof9595995]

Thanks.But I'm not quite familiar with the manipulation of those, I'll give a shot.
And are there any other derivations avaliable?

 

[ozymandias]

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.


-----
Assaf
http://www.physicallyincorrect.com"

 

[kof9595995]

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.


-----
Assaf
http://www.physicallyincorrect.com"

Thanks, I will have a look at it.