# Questions tagged [lienard-wiechert]

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### Do the Lienard Wiechert Potentials satisfy the wave equation?

The Lienard Wiechert potential (leaving out the vector potential for simplicity), $$\left.\phi(\vec{r},t)=\frac{e}{4\pi\epsilon_0R\,(1-\hat{n}\cdot\vec{\beta})} \right|_{t'=t_{\rm ret}},$$ where the ...
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### Gauge invariant Green's function for electrodynamics

Varying the electromagnetic action S=-m c \int d s\left(\dot{z}^{2}\right)^{\frac{1}{2}}-\frac{e}{c} \int d s A_{\mu} \dot{z}^{\mu}-\frac{1}{16 \pi c} \int d^{4} x F_{\mu \nu} F^{\mu \...
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### Is the Liénard-Wiechert electric field conservative?

I know that an accelerated charge should emit an e.m. field and loose energy. Therefore, the Liénard-Wiechert (L.W.) electric field of an accelerated charge should be non-conservative. But I checked ...
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### Falling charged objects: energy conservation paradox?

Imagine that we start with two oppositely charged objects on the ground, separated by a distance $d$, with charges $+q$, $-q$ and masses $m$. We raise them both up to a height $h$. In doing so we ...
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### Energy conservation in electrodynamic system

Consider two charged particles initially at rest in the configuration below. Let us assume the following: Starting at time $t=0$, we apply a constant force $f$ to the the bottom particle so that it ...