A concept issue about EM field energy

[kof9595995]

About whether energy is stored in the charge or the field, in Griffiths EM textbook, i found this:
"...(for electrostatics) it is unnecessary to worry about where the energy is located. In the context of radiation theory it is useful(and in General Relativity it is essential) to regard the energy as being stored in the field..."
I agree that in electrostatics there's no difference between these two opinions, but I always thought "field energy" should be essential in radiation, because a radiation source can pass its own energy to a test charge far away, since energy must be conserved locally, the energy has to be carried by something all the way to the test charge, but there's nothing but EM field between the source and test charge, so I concluded the energy must be stored in the EM field and transferred to the test charge.
However, according to Griffiths, even for radiation the "field energy" concept is just useful, not essential, and I can't figure out why he said that.

 

[Dale]

I agree with you. If you don't consider the field to carry energy then I don't see how energy is conserved.

 

[Meir Achuz]

The EM energy is an integral over all space, not a local quantity.

 

[kof9595995]

The EM energy is an integral over all space, not a local quantity.

Yes, but how do you explain the energy transfer of radiation if you take the point of view that "energy is stored in charges"?

 

[sophiecentaur]

Is this to do with the fact that a static field doesn't change? (By definition, of course)

 

[kof9595995]

Is this to do with the fact that a static field doesn't change? (By definition, of course)

What are you referring to?

 

[sophiecentaur]

The energy transfer vs the energy 'storage' concept - was what I was thinking about.

 

[kof9595995]

The energy transfer vs the energy 'storage' concept - was what I was thinking about.

When i talked about energy transfer it's certainly not static, because the presence of radiation

 

[GRDixon]

I always thought "field energy" should be essential in radiation, because a radiation source can pass its own energy to a test charge far away, since energy must be conserved locally, the energy has to be carried by something all the way to the test charge, but there's nothing but EM field between the source and test charge, so I concluded the energy must be stored in the EM field and transferred to the test charge.
However, according to Griffiths, even for radiation the "field energy" concept is just useful, not essential, and I can't figure out why he said that.

Griffiths may have been referring to the apparent fact that radiant energy can be thought of as being transferred from a source to a sink via photons, which are arguably particles. In this world view I believe that the square of the electric field, like the square of the quantum wave function, would specify the probability of a photon/matter interaction taking place at a given point in space-time. Indeed, the concept of the electric field is overkill. As to why he says the electric field is essential in GRT, I'm out of my depth.

 

[kof9595995]

Griffiths may have been referring to the apparent fact that radiant energy can be thought of as being transferred from a source to a sink via photons, which are arguably particles. In this world view I believe that the square of the electric field, like the square of the quantum wave function, would specify the probability of a photon/matter interaction taking place at a given point in space-time. Indeed, the concept of the electric field is overkill. As to why he says the electric field is essential in GRT, I'm out of my depth.

Photons are arguable particles? I never heard of that. Besides, I'd rather believe Griffiths meant the "field energy" concept is not essential for radiation within the frame work of classical EM, from the way he wrote.

 

[Antiphon]

In GRT it's essential because the spatial location of the energy is a source term of the gravitation.

In radiation theory it's useful (Poynting's theorem) to determine which parts of the field are propagating and which parts are not.

For electrostatics it doesn't matter because the results of energy functionals give the same results whether you consider fields or charges. Example: working out the force on a dielectric in a non-uniform electric field.

 

[maverick280857]

Photons are arguable particles? I never heard of that. Besides, I'd rather believe Griffiths meant the "field energy" concept is not essential for radiation within the frame work of classical EM, from the way he wrote.

In electrostatics, when defining potential energies, it is implicit that charges are brought in with zero acceleration. More precisely, they are moved in quasistatically from infinity to set up a charge distribution. At any point then, the energy of the configuration consists only of mutual (interaction) energies.

Note that at this point, radiation due to a moving charge obviously does not enter the picture. So, it does not matter whether you regard the energy as being stored in the field or in the charge as far as this kind of energetics is concerned. But when you consider acceleration and radiation (and more generally relativistic effects), the viewpoint of the field carrying energy, momentum and angular momentum becomes important. For a discussion, have a look at the Feynman Lectures vol 2, section 17.4.

Griffiths is trying to address (quite early) the following natural question which might arise in the minds of readers: where is this energy stored?

As for photons, yes, they are particles. In fact they are the mediators (or force carriers) of the electromagnetic force. Classically, this may affect you little but EM information is 'communicated' from one charge to another due to the exchange of photons between the charges. This is the viewpoint of quantum field theory, and more precisely, of quantum electrodynamics -- the quantum generalization of electromagnetic field theory. This need not worry you right now, but this is what was being alluded to.

 

[sophiecentaur]

...
As for photons, yes, they are particles. . . . .

Meaning 'little bullets'? How big? How little?
I really have a problem with the idea of being sprayed with corpuscles - particularly at Long Wave or 50Hz. Why should a quantisation of Energy imply a localisation in space and time?

Can we really be saying what something 'really is' at this level of thought? When do they actually behave exclusively as particles?

The word "mediate" was introduced and that seems fine to me to describe how effects / forces are transferred between things and the idea of packetisation of the Energy is demonstrably true. Photons don't exhibit mass so why do we say they are particles? It seems to me that it's just not necessary and simply adds confusion as there are some very fundamental differences in the natures of particles with mass and photons (and gravitons, even).

 

[GRDixon]

Photons are arguable particles?

To my admittedly limited knowledge, the only thing we know from the Photoelectric Effect, the Compton Effect, etc., is that radiation interacts with matter in quantized exchanges of energy and momentum, at points in space-time. It is only when radiation interacts with matter that it seems to be corpuscular. Aside from the obvious semantics, there are perhaps more compelling reasons to believe that material particles (neutrons, etc.) are particulate not only when they interact with other material particles or with radiation, but also while they are "in flight." For example, Rutherford and Marsden seem to have been envisioning such corpuscles (alpha particles) when they discovered the small cross section of atomic nuclei.

 

[Antiphon]

Photons are not particles in the sense of being a small bit of stuff. Their spatial extent can be Angstoms or light years.

 

[sophiecentaur]

... Which, to my mind, makes the word "particle" singularly inappropriate and, worse still, misleading to the beginner in these matters. Semantics count.

 

[kof9595995]

Em, thank you guys, but despite all your efforts, I still don't understand my original question: if you take the view that energy is not stored in the field, how can you explain the fact that radiation can transport energy to another charge?

 

[maverick280857]

... Which, to my mind, makes the word "particle" singularly inappropriate and, worse still, misleading to the beginner in these matters. Semantics count.

Absolutely. Unfortunately, for a "more rigorous" definition of particle, one needs to get into QFT. The take home message for a beginner could just be that a particle is an oscillation mode of that field. But that is WHOLE different ball game, and absolutely nontrivial to come to terms with intuitively. The problem is that coming fresh from classical physics, we want a storage place for that energy to be well delineated...not that intuitive in a radiative/quantum regime.

Ok, with no intention to confuse the OP, here is what my answer to his original post is: we advocate the viewpoint that energy is stored in the (charged particle + field) configuration. In non-accelerated electrostatics, it is possible to write the energy cleanly as KE + PE where KE belongs to the charge and PE belongs to the field. But you have to be more careful when formulating a relativistic version of the problem. So personally, I would use a more conservative term such as "configuration" and ascribe the energy to it. That makes the transition to radiation easier.

See:

1. http://www.its.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html
2. Ed Purcell's Berkeley Series on Electricity and Magnetism

 

[kof9595995]

In electrostatics, when defining potential energies, it is implicit that charges are brought in with zero acceleration. More precisely, they are moved in quasistatically from infinity to set up a charge distribution. At any point then, the energy of the configuration consists only of mutual (interaction) energies.

Note that at this point, radiation due to a moving charge obviously does not enter the picture. So, it does not matter whether you regard the energy as being stored in the field or in the charge as far as this kind of energetics is concerned. But when you consider acceleration and radiation (and more generally relativistic effects), the viewpoint of the field carrying energy, momentum and angular momentum becomes important. For a discussion, have a look at the Feynman Lectures vol 2, section 17.4.

Ok, with no intention to confuse the OP, here is what my answer to his original post is: we advocate the viewpoint that energy is stored in the (charged particle + field) configuration. In non-accelerated electrostatics, it is possible to write the energy cleanly as KE + PE where KE belongs to the charge and PE belongs to the field. But you have to be more careful when formulating a relativistic version of the problem. So personally, I would use a more conservative term such as "configuration" and ascribe the energy to it. That makes the transition to radiation easier.

I think I'm a bit confused, so are you saying that the "field energy" concept is essential?

 

[reckon]

Em, thank you guys, but despite all your efforts, I still don't understand my original question: if you take the view that energy is not stored in the field, how can you explain the fact that radiation can transport energy to another charge?

radiation is the way charges interact with each other from far, far away. If you calculate interaction energy between these charges, you should get the same result as you calculated using radiation method.

*haven't prove what I said. That's my understanding of what I've read from books.

 

[elect_eng]

Em, thank you guys, but despite all your efforts, I still don't understand my original question: if you take the view that energy is not stored in the field, how can you explain the fact that radiation can transport energy to another charge?

It's not clear to me why you interpreted Griffith's statement to mean that energy is not stored in the field. It IS stored in the field. Or, at least there is potential energy available when there is a static field. In electrostatics or magnetostatics, the stored energy is not really important because that stored energy doesn't do anything. It is stored and it stays stored. However any static case is an abstraction. In reality, that state was obtained via a transient event. During that event, the energy was built up from zero to the steady state value.

 

[kof9595995]

radiation is the way charges interact with each other from far, far away. If you calculate interaction energy between these charges, you should get the same result as you calculated using radiation method.

*haven't prove what I said. That's my understanding of what I've read from books.

Em..What's the definition of "interaction energy" and how to calculate it?

 

[kof9595995]

It's not clear to me why you interpreted Griffith's statement to mean that energy is not stored in the field. It IS stored in the field. Or, at least there is potential energy available when there is a static field. In electrostatics or magnetostatics, the stored energy is not really important because that stored energy doesn't do anything. It is stored and it stays stored. However any static case is an abstraction. In reality, that state was obtained via a transient event. During that event, the energy was built up from zero to the steady state value.

That was my opinion, but Griffiths wrote "and in general relativity it's essential" immediately after "in the context of radiation theory it's useful ", I think clearly he indicated that for radiation it's not essential.

 

[elect_eng]

That was my opinion, but Griffiths wrote "and in general relativity it's essential" immediately after "in the context of radiation theory it's useful ", I think clearly he indicated that for radiation it's not essential.

I agree that the wording given is confusing, but I wouldn't assign too much meaning to the exact phrasing. No doubt there is a particular meaning intended, and it probably makes sense; but, if it is causing confusion, it's better to just ignore it for now.

Basically, GR is the more general theory. Both EM and GR are classical field theories which merge together seamlessly. Clearly electromagnetic energy is essential to GR, at least in principle. The main reason is that this energy is included in the energy-momentum density tensor, which is the source of gravitational fields in GR. Also, gravitational fields will affect the propagation of EM waves and change the direction of energy flow, which then changes the energy-momentum density tensor (and gravitational field). However, typically this EM energy is insignificant compared to the mass-energy in practical GR problems, so you could even question the word "essential" here too.

Anyway, the energy is real in GR, so it is real in any classical sense, including in the context of EM theory without gravity (i.e. special relativity). If it is real, then it should be considered essential to a theory. I think you are seeing the problems that crop up if the energy is not real and essential. The "usefulness" is another issue and you may get different answers from different people about this. If you use it then it is useful. If you don't use it, then it is not quite as useful, but for the fact that you know it could be used someday if needed.

 

[kof9595995]

Ok, i think maybe I'll just ignore it for the moment.