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We've an isolated system inside which currents and charges reside.
If the Poynting vector on the surface of the system is non zero, then there is energy exchange between the system and the surroundings.

Then is it necessary that our system is radiating?

(To me it is because there is no other form in which energy can be exchanged)

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  • $\begingroup$ Can you give an example of a system with steady currents or static charges that illustrates what you mean? $\endgroup$ – Rob Jeffries Oct 21 at 18:46
  • $\begingroup$ Say a box filled with charges and currents outside of which is empty space. $\endgroup$ – Yasir Sadiq Oct 22 at 13:44
  • $\begingroup$ Please be specific. A box containing a single, stationary charge has a zero Poynting vector outside the box. Neither is there any Poynting vector outside an ideal wire carrying a current. $\endgroup$ – Rob Jeffries Oct 22 at 16:36
  • $\begingroup$ I didn't know that the detail did matter and I don't know how much detail is enough but let's say we have some stationary charges and some currents going on in ideal wires and some in non ideal wires. $\endgroup$ – Yasir Sadiq Oct 22 at 16:51
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I'm not really following your question well. It is well known that accelerating charges and non-stationary currents have a positive flux of Poynting vector over a closed surface around them. This is what we call electromagnetic radiation and it carries energy out of the system.

If you have static charges, they produce no magnetic field. So the Poynting vector is zero. If you have a steady current in an ideal wire, there is no electric field and the Poynting vector is zero.

If you consider an arbitrary box and the closed surface integral of the Poynting vector is positive, it means the electromagnetic fields are carrying energy out of the box. That does not necessarily make it "radiation".

For example if you look in the Wikipedia page on the Poynting vector you will see examples of influx and outflux of the Poynting vector in DC circuits (with resistance), which we wouldn't term radiation because the fields are stationary.

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  • $\begingroup$ Thank you Rob Jeffries, what I'm trying to say is that if we've a positive Poynting vector pointing out of our system and outside of our system is just vacuum. Then since we know that the system is giving away energy into the surroundings it remains to figure out the form of this energy flux. To me it has to be only radiation because what else way is there for the system to expel energy out of itself? $\endgroup$ – Yasir Sadiq Oct 23 at 0:29
  • $\begingroup$ @YasdirSadiq One way is to do work on charges. I still think you need to give a specific example of where you think this happens. $\endgroup$ – Rob Jeffries Oct 23 at 7:59

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