Are there sources for electromagnetic potential propagating wave solutions for $\phi$ and $\overrightarrow{A}$

for which the electromagnetic far-field $\,>\!\lambda\,$ in vacuum is zero $\overrightarrow{E}=\overrightarrow{B}=0\,$ globally in open space?

So that $$ 0=\overrightarrow{E}=-\nabla\phi-\partial_{t}\overrightarrow{A}$$ and $$0=\overrightarrow{B}=\nabla\times\overrightarrow{A}$$

  • $\begingroup$ My former question did lead somehow to this equation. $\endgroup$ – v217 Aug 5 at 13:59
  • $\begingroup$ Standing wave in an empty box made of perfectly conducting walls has zero field outside the box. Sources in that case are in the walls of the box. $\endgroup$ – Ján Lalinský Aug 5 at 14:05
  • $\begingroup$ @JánLalinský Thanks I have to update my question I mean propagating waves $\endgroup$ – v217 Aug 5 at 14:14
  • $\begingroup$ There can be propagating wave in the box as well, only it won't propagate indefinitely, it will reflect off the walls and bounce inside the box. $\endgroup$ – Ján Lalinský Aug 5 at 14:40

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