# Are there sources for potential wave solutions for which the electromagnetic far-field is zero?

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 $$0=\overrightarrow{B}=\nabla\times\overrightarrow{A}$$

• My former question did lead somehow to this equation. – v217 Aug 5 at 13:59
• 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. – Ján Lalinský Aug 5 at 14:05
• @JánLalinský Thanks I have to update my question I mean propagating waves – v217 Aug 5 at 14:14
• 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. – Ján Lalinský Aug 5 at 14:40