I'm trying to derive the Lorentz-invariant field equations, using a point charge (well, a positron actually) centered in the coordinate system. I'm trying to find the electric & magnetic fields generated by it. I've tried using Dirac delta functionfor the charge density.(adsbygoogle = window.adsbygoogle || []).push({});

S' frame of reference is moving relative to S frame of reference with a velocity v along the x axis. At t=0, x'=x. At that moment, an observer in the S system (presumably me) is trying to calculate the electric & magnetic fields in his frame of reference.

Now, is S', positron is still, so

[tex]\vec{\nabla} \cdot \vec{E} = \frac{\rho}{\epsilon_0}[/tex]

and since it's standing still

[tex]\vec{B} = 0[/tex]

Then I tried switching the reference system with:

[tex]\frac{\partial E}{dx \sqrt{1-v^2/c^2}} + \frac{\partial E}{dy} + \frac{\partial E}{dz} = \frac{e \delta(\vec{r})}{\epsilon_0 \sqrt{1-v^2/c^2}}[/tex]

and... I simply don't where to go next? One possibility is I'm down-way wrong.

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# Derieving relativistic electrodynamics equations

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