The potential electric and vector potential of a moving charge

  • #1
LCSphysicist
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Homework Statement:
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Relevant Equations:
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Captura de tela de 2022-06-10 17-45-02.png

I could try to apply the Liénard-WIechert equations immediatally, but i am not sure if i understand it appropriately, so i tried to find by myself, and would like to know if you agree with me.

When the information arrives in ##P##, the particle will be at ##r##, such that this condition need to be satisfied:
$$\frac{(vt-r)^2}{v^2} = \frac{r^2+b^2}{c^2} (1)$$

So, we have $$\phi = \frac{kq}{s} = \frac{kq}{r}$$
Also, $$ \vec A = \frac{\mu}{4\pi} \int \frac{J' dV'}{|r-r'|} = \frac{\mu}{4\pi} \frac{q v}{|r|}$$

such that r satisfies ##(1)##.

Is it right? Do you agree with it? I am asking because i remember to read somewhere that the potential electric not necessarilly need to move at speed of light, but i think this is the case in Lorenz gauge. I haven't assumed any gauge here.
 

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  • #2
hutchphd
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