# Energy stored in a field

1. May 4, 2005

### myself

How exactly is energy stored inside an electric or magnetic field? I read some formulas in a book, and I get the derivations, but I do not see how there is energy in the electric field, of say, an electron. Does anyone know how conceptually, energy is stored in a field?

2. May 5, 2005

### shyboy

If we are talking about static or quasistatic field, then energy stored in a field is an energy which can be released by through a field source if that field is changed. So the energy could be attributed not to the field, but to sources of the field. For example, the energy stored in a superconducting coil may be released an transformed into heat by terminating the coil on a resistor. The same way the energy of the electric field may be attributed to the potential energy of the charges, so the change in the field energy will lead to a change in the kinetic (or other) energy of that charges.

However if we are dealing with electromagnetic radiation, then we should to consider the energy of the electromagnetic field as a separate entity. On a microscopic level it is carried out by photons. As to the macroscopic approach, scientists spent a lot of time with the ether because it was difficult to comprehend how energy could be transfered without medium. So , eventually they said that EM radiation is a materia itself.

3. May 9, 2005

### Chi Meson

Another situation where it is popular to say that "energy is sored in the electric field" is in the case of a charged capacitor. Between two paralel plates that have had a separation of charge, there will exist an electric field. The capacitor stores energy, not charge, so where is the energy? "The energy is stored in the field itself." Another way to think this: " the presence of the electric field is evidence of the stored energy."

Also, consider a simple circuit: when a switch is closed, charge begins to flow simultaneously through the entire circuit. THe actual net flow of the electrons is very slow, but the transmission of energy through the circuit is near instantaneous because the electric field is established through the wire almost instantaneously. So again, the energy is contained in the field itself.

4. May 9, 2005

### pmb_phy

Its a very bad idea to speak of energy stored in a field. Its unfortunate that many people do this.

Pete

5. May 9, 2005

### Crosson

What if the energy is real, as in the case of electromagnetic waves? Such waves carry energy through a vaccum, and they are nothing more than oscillating electric and magnetic fields.

You might say that the only way to measure this energy is using a test charge, and then argue that we can explain this energy as charge-to-charge interaction. This argument is flawed because energy cannot transfered faster then light, and so it is not as if the energy waits a few seconds at charge A and then teleports to charge B. No, the energy travels from A to B in the form of a field.

Remember that there is not one right formulation of physics, and any physics which fits the data ought to be consider acceptable. I can say this: It is entirely consistent and in my opinion more elegant to consider the energy as stored in the field itself; both in E&M and gravity.

6. May 10, 2005

### Staff: Mentor

In what sense is energy "real?" In what sense are electric and magnetic fields "real?"

To the original poster ("myself"): You're venturing (probably without realizing it) into very deep philosophical matters here. Electric fields, magnetic fields, energy, and many other things, are all concepts that we use to explain the observed relationships involving physical objects and their motions. But "energy" is not a substance in and of itself; it exists only in the context of two or more objects. We cannot observe energy in isolation, or measure it directly. We can only infer the amount of energy involved in any process by measuring the positions and locations of objects before, during, and/or after that process, and performing some calculations.

Similarly for electric and magnetic fields. After all, we define the presence of electric and magnetic fields by the observation that certain objects placed in proximity to each other move in ways that cannot be explained by simple contact-type pushes or pulls.

I'm not trying to denigrate or belittle these concepts, or suggest that there's any useful replacement for them. They're amazingly useful, and I would not want to try to do physics without them. But we need to keep in mind the dangers of excessive reification of the concepts that we invent to explain what we actually observe. That is, we need to be careful not to associate "too much reality" to them.

Again to the original poster: don't worry too much about this stuff, except maybe when you have some free time. If you think energy in electric and magnetic fields is weird, just wait until you get to quantum mechanics, and you have to wrap your mind around the $\psi$ function!

7. May 10, 2005

### pervect

Staff Emeritus
*boggle boogle*. The idea that electromagnetic fields store energy (and momentum, for that matter) is very standard & basic.

For instance, it is necessary to include the momentum in electromagnetic fields to have a conserved momentum when particles interact magnetically (see Goldstein's classical mechanics). Similar concerns about energy conservation require that E&M fields carry energy. Electromagnetic radiation is a prime example of how E&M fields carry energy, as various other posters have mentioned.

8. May 10, 2005

### Chi Meson

THe debate is not so much philosophy as it is sematics. The energy is there and it is stored. THe requirements for this storage is a particle-field interaction. Our spoken language fails at providing a word that perfectly encapsulates the concept, so the language of mathematics is used as the ultimate authority on the definition of what we mean. After using all those formulas over and over, they start to mean more than the mathematical equation themselves. Trying to truly understand the Maxwell equations, for example, will lead to a fuller conceptual understanding of electricity, much more so than words will convey.

In the mean time, to echo a previous post, don't worry about it too much, just think about it.

9. May 10, 2005

### pmb_phy

Umm .. that's why I said Its unfortunate that many people do this. I agree that it's standard and basic, But its very bad to think this way. However when each participant in a conversation understands this then it can be easier to talk about things.
Where did you get the idea that something I said would contradict this?

If you want to know the details of what I mean exactly then read the entire page at 0 http://www.geocities.com/physics_world/mech/what_is_energy.htm

Pete

10. May 10, 2005

### da_willem

Are EM fields not included in the energy-momentum stress tensor in GR? As this is a function of the spatial and time coordinates doesn't this indicate that the location of the energy is in the fields?

Furthermore when you want to calculate the field energy you integrate the (square of) the fields over all of space. You could probably find a way out of thinking of the energy not stored in the fields, but (for me at least) it sure makes it a lot more insightfull.

11. May 10, 2005

### pmb_phy

All this seems to give the impression that there is only one way to view the localization of energy whereas there are three views. They are described in The Electromagnetic Field, Albert Shadowitz, Dover Pub., pages 174 - 176.

Pete

12. May 10, 2005

### pervect

Staff Emeritus
Given that the alternative to allowing E&M fields to carry momentum and energy would be to say that neither momentum nor energy is conserved, it seems like a slam-dunk to me to say that E&M fields do carry momentum and energy. I don't really see why there is any question about it.

13. May 10, 2005

### pmb_phy

Its an exercise in what one can against what one must do.

So what is this alternative you speak of?

Pete

14. May 11, 2005

### pervect

Staff Emeritus
It's not my alternative - I'm perfectly happy with saying that E&M fields carry momentum and energy, and that energy and momentum are conserved quantities.

15. May 11, 2005

### Juan R.

Unfortunately, EM and GR are both inconsistent view of nature.

Since EM is more studied, I focus on it.

There is not real fields on nature. Therefore the idea of energy stored somewhat in space in free fields is not consistent. In fact, anyone studying EM seriously know that Maxwell EM is inconsistent.

One of recently found inconsistencies is that the LW potentials does not verify Maxwell equations. Other inconsistencies with the field approach are:

- The use of retarded signals. It is not true. Morever it has been computed that gravitation interaction is not bounded by c. There is also instantaneous interaction in EM.

- The idea of that EM field is an entity on his own right. This is true from Maxweel equation for potentials but if you do q=0 and j=0 on LW potentials or similar ones you find that E and B are zero. There is not field without charges and currents.

- The violation of third law of Newton.

- The problem with infinites, renormalization, mass, self-action, etc.

Moreover, the concept of field does not solve the misterium about interactions. See my criticism to GR in www.canonicalscience.com.

See also www.canonical.chemicalforums.com [Broken] for an outline of my work in canonical eelctrodynamics

Last edited by a moderator: Apr 21, 2017 at 3:29 PM
16. May 11, 2005

### marlon

Good question. Let's take the example of the capacitor. When an EMF is applied, the capacitor will be charged until the EMF is counterbalanced by the charges on the capacitor plates. Because of these induced charges, the insulating dielectric in between the plates will be polarized. Thus, an electric field will be generated that opposes the electric field coming from the induced charges in the plates. The energy in this case directly comes from the induced charges but one says the energy is stored in the electric field because it is this electric field that is able to move charges around via the Coulomb force. So energy stored in a field expresses the fact that this field is able to make certain things happen, like moving charges or changing he orbit and velocity of charged particles.The energy (measured in joules, in SI) stored in a capacitor is equal to the amount of work required to establish voltage. But this voltage V is directly related to the electric field E, so we can also say 'the amount of work necessary to establish the electric field E'. We had to do work in order to establish the E-field, thus this field must have energy. It's just like pushing up an object. The more work you do, the higher it gets and therefore it has more potential energy. That's all.

The dielectric constant is a physical entity that expresses how well a certain material is able to hold on charges (think of a sponge and water). This constant is directly related to the capacitance, which can also be defined this way. If we apply a voltage V over the capacitor, charges Q will arise on the plates. Now, if the dielectric constant is big then more charges Q will be induced on the plates for the same voltage V. These socalled High K dielectrics are of fundamental importance to research in nanotechnology because they are the most promising answer to the difficulties that arise in the miniaturization of transistors. read my journal for more info