Where do the electrons come from when energy is generated

[Ring]

@Chronos

Anything wrong with the old standby of 1/2(E[sup]2[/sup]+B[sup]2[/sup])? So far as I know, that works in every context in E&M, and also in GR, where the localization of energy actually means something.

Chronos you might find the following of interest, especially the part about GR.

u = energy density
S= energy flux

I’d be glad to post the complete section but I don’t think I’m suppose to do that.

Before we take up some applications of the Poynting formulas [Eqs. (27.14) and (27.15)], we would like to say that we have not really “proved” them. All we did was to find a possible “u” and a possible "S.” How do we know that by juggling the terms around some more we couldn’t find another formula for “u” and another formula for “S”?..

There are, in fact, an infinite number of different possibilities for u and S, and so far no one has thought of an experimental way to tell which one is right!..

but we must_say that we do not know for certain what is the actual location in-space of the electro¬magnetic field energy………….

It is sometimes claimed that this problem can be resolved by using the theory of gravitation in the following argument. In the theory of gravity, all energy is the source of gravitational attraction. There¬fore the energy density of electricity must be located properly if we are to know in which direction the gravity force acts. As yet, however, no one has done such a delicate experiment that the precise location of the gravitational influence of electromagnetic fields could be determined.

[David_Simmons]

@Ring

In electrodynamics there is no way to determine exactly where the energy is:

But in the case of an EM wave it’s pretty clear that the energy resides in the wave and not in the conductor since there is no conductor. So why not carry this given over to circuits, especially since the EM wave inside the conductor travels so much slower than the energy actually propagates. Granted that with DC there is no wave but there is a Poynting field.

Sure, all electrical problems can be done using field theory. However electricity becomes useful when charges are moving and by far the vast majority of charges are in conductors and all of the charges that go to our devices are in some sort of conductor. Circuit theory was developed precisely because of this fact and we use circuit theory in ordinary electrical work maybe 100 times as often as field theory so why not think in terms of it? To use field theory seems to me sorta like finding the area of a triangle each time by integrating.

Both methods are models. One of them is useful day in and day out. The other is vital when it is needed but most applications don’t need it.

[Chronos]

It is true that we’ve never observed a Riser-Nordstrom black hole, which would be the real test case for this, and given how weak gravity is, we probably haven’t ever measured the gravitational effect of electromagnetic fields at all. Offhand, I’d say the best bet would be the radio lobes of active galactic nuclei (which can contain millions of solar masses in magnetic field energy), but we’d need to know a lot more about dark matter before we could get any meaningful data out of them.

On the other hand, it is in principle to perform such an experiment, and u = 1/2(E[sup]2[/sup]+B[sup]2[/sup]) is consistent with the theory (I’m not certain this is true of all of the other hypothetical formulae for u mentioned in your quote). Incidentally, what’s the source of that quote? I don’t recall seeing it in Griffiths or Jackson, the two most likely suspects.

[Ring]

@Chronos

I don’t recall seeing it in Griffiths or Jackson, the two most likely suspects.

The same as above “The Feynman Lectures” II, 27-6.

BTW what’s the big deal about determining the radial distance when applying Coulomb’s law to a Reissner-Nordstrom Black Hole?

[Chronos]

BTW what’s the big deal about determining the radial distance when applying Coulomb’s law to a Reissner-Nordstrom Black Hole?

I’m not aware there is any big deal about it. Could you care to elaborate?

(aside: I had a hunch I was misspelling Reissner)

[Ring]

@Chronos

I’m not aware there is any big deal about it. Could you care to elaborate?

(aside: I had a hunch I was misspelling Reissner)

From sci.physics.research.

[Moderator’s note: The integral of the electric field’s radial component over a concentric sphere outside the black hole must be proportional to the total charge. In the spherically symmetric (Reissner-Nordstrom) case, this means that the exterior field must be inversely proportional to the area of the sphere, just as in Coulomb’s law. On the other hand, how the area of that sphere relates to radial distance depends on how you define radial distance, which is no longer a trivial issue. -MM]

Radial distance when dealing with any black hole isn’t exactly corn flakes, but from the tone of the above post I took it that there was something especially odd about it when dealing with a RN BH.