To answer my own question.
When I look at final situation (energy moved completely from the chosen volume), I should be more careful how I integrate the flux of ##E\times B## (gets smaller) over time (gets longer).
Now we are maybe getting somewhere, sorry I've wasted lots of your time on garbage before.
Lets look on the result.
Do I (with reduced speed) decrease the total flux that happens between ##(0,\infty)##, because I am reducing size of overall P. vector?
The rate of decrease of energy...
Energy of fields (in the area) from particle (which have been in place A) changed its value to 0, because particle moved to far away B, where the energy of fields risen to the value of energy of fields from this moved particle. Sorry I described it as leaving...Cleaning everything from the...
Neutral particle (with some other properties) requires some energy-momentum to get moving with certain speed.
Charged particle (with other properties unchanged) requires more energy-momentum to get moving with same speed as before.
We could just increase the mass of the particle and be...
And to prevent another possible misunderstanding.
P. vector of independent radiation which goes away is one thing.
P. vector of fields associated with moving point charge which has constant speed is another thing - the main contribution here I would say.
Ok, not precise formulation on my part. No arguing about separate freedom of EM fields (independent waves, implications of retarded potentials and so on).
I really should be more careful what I say. Could I say - P. vector caries the energy and momentum needed to "push" those originally static...
Ok, I have discussed this simultaneously on physics.stackexchange.com and it helped me to clear out the core of what I actually wanted to ask:
If it is as I just described, then everything fits and there is no problem - P. theorem just doesn't deal with the energy in static fields.
Indeed...
Thanks for trying to answer, but sadly it didn't help me much. If we take finite volume, it doesn't really matters whether we take an integral form or differential one, so let's stick with your "infinitesimal" volume.
Sure, if I just take the Poynting's theorem as a mantra, then all it's...
I was thinking the other day and it looks like I need feedback if I am being stupid or crazy.
My question is quite simple - does Poynting's theorem cover the situation of charged particles escaping through surface (just like radiation part does) of the volume over which we calculate?
I...
How would react ion of some gas (low energy anion or cation) in vicinity of a grounded metal surface or in vicinity of an insulator?
I guess a free electron and cation would automaticly recombine. But I don't know the probability nor mechanisms (just tunneling?) for the same thing happening...