Light waves are one half kinetic and one half potential energy

[liometopum]

Water waves are one half kinetic energy and one half potential energy. The quote below comes from the Wikipedia wave power article.

I assume that it is the same with light waves. Do people here agree?



"...E is the mean wave energy density per unit horizontal area (J/m2), the sum of kinetic and potential energy density per unit horizontal area. The potential energy density is equal to the kinetic energy,[3] both contributing half to the wave energy density E, as can be expected from the equipartition theorem."

 

[Bill_K]

No indeed. Light waves and water waves have almost nothing in common. Light waves do not have kinetic energy or potential energy.

The energy density in a light wave is proportional to E² + B², so you could say that half of it is electric and half of it is magnetic. But note that E and B are in phase: they reach their maximum value simultaneously, and are zero simultaneously, so the energy density is not constant. To get a meaningful value one needs to average the energy density over a cycle.

 

[Naty1]

Seems like water waves would be more related to sound waves: both are longtitudional, both involve matter(mass) ,etc,etc.

 

[liometopum]

Good points.
Let's try it differently... let's say an material object is moving at just below light speed, as close to light speed as imaginable.

Then, would kinetic energy and potential energy be almost the same?

 

[Philip Wood]

Taking up the point about a 'material object'...

Potential energy is energy (ability to do work) measured with respect to a reference point (a point where, by convention, we say that the potential energy is zero).

This implies that whether PE and KE are equal or unequal is dependent on this convention, and cannot, in general have any fundamental significance. It is changes in potential energy which are of physical significance. An object traveling near the speed of light, or indeed at any speed, may or may not be changing its potential energy. Depends on whether or not it’s in a field.

 

[JeffKoch]

Water waves are one half kinetic energy and one half potential energy.QUOTE]

Because water is in a gravitational field where the concept of potential energy makes sense, and you can chose to classify energy in terms of kinetic and potential energy. Potential energy here relates to the earth, specifically to differences in potential energy due to differences in distance away from the center of mass.

 

[liometopum]

1. BillK: Light does have kinetic energy. Some calculate it from Planck's constant times the frequency.
2. BillK: Light waves and water waves have a lot in common. They are both waves, traveling disturbances carrying energy. Both show interference. They are both waves. Basic energy characteristics should be the same for all waves.
3. Naty1: What?? Sound waves are longitudinal (compressional) and water waves are transverse.
4. JeffKoch: But the sound wave is a good point. It is not gravitationally-effected like the water wave, so we can eliminate gravity. Rephrase the question I asked to sound waves. I am sure a sound wave is half kinetic and half potential as well. And I am positive that light is the same too. It must be a characteristic of all waves, regardless of medium of travel.
5. Phillip: If all waves have both PE and KE, then maybe there is no need for a frame of reference for PE, except the existence of the KE.
6. JeffKoch: Potential energy exists in many forms and is not restricted to gravitational fields.

 

[Ken G]

Perhaps sound waves are easiest to imagine, so we can contrast them with water waves. Sound waves are all kinetic energy-- no potential energy at all. So why doesn't the virial theorem apply there? It has to do with what the restoring force is. For a water wave, or a wave on a slinky, the restoring force is conservative. There's a "real" force there doing the restoring, and it soaks up kinetic energy by having work done on it, only to release that energy by doing the work back. But in a sound wave, the "restoring force" is not a conservative force, it's a kind of make-believe force that shows up when you treat the particles collective behavior as a fluid. It has no potential energy associated with it, and the assumptions that go into the virial theorem don't apply. But maybe there is some way to build an equivalent concept, I don't know. Still, without some work to build an equivalent concept, we see that the half-and-half idea is not a general property of waves.

 

[JeffKoch]

Rephrase the question I asked to sound waves. ...And I am positive that light is the same too. It must be a characteristic of all waves, regardless of medium of travel.

Sound is compression of a medium that is capable of pushing back, like a spring - which also can have potential energy. There is no medium for light waves, unless you wish to believe in the ethereal theory that was disproved in the 19th century. And if you are positive, why do you ask, and in what sense do you think a light wave has potential energy associated with it?

 

[Redbelly98]

Good points.
Let's try it differently... let's say an material object is moving at just below light speed, as close to light speed as imaginable.

Then, would kinetic energy and potential energy be almost the same?

No, not necessarily. In fact, the potential energy could even be zero or negative.

1. BillK: Light does have kinetic energy. Some calculate it from Planck's constant times the frequency.

That's not kinetic energy, that's electromagnetic energy.

 

[liometopum]

Thanks KenG. And of course, thanks to everyone for your input!
Regarding the potential energy of sound waves:

From Wikipedia, Sound: (http://en.wikipedia.org/wiki/Sound)
"The energy carried by the sound wave converts back and forth between the potential energy of the extra compression (in case of longitudinal waves) or lateral displacement strain (in case of transverse waves) of the matter and the kinetic energy of the oscillations of the medium."

But I see that JeffKoch spotted this too. The back and forth aspect of any wave implies a transition between kinetic and potential energy. For example, the Wikipedia article on "Vibration" states "... Thus oscillation of the spring amounts to the transferring back and forth of the kinetic energy into potential energy."

All waves oscillate. It is part of being a wave.

JeffKoch: I ask in part because I need to bounce some ideas off people and this forum is the only option for me.

Redbelly: Maybe the interpretation of it being electromagnetic energy is analogous to kinetic energy turning to heat after a moving object hits something. The kinetic energy of light is transferred as electromagnetic energy upon interaction with the receiving object.

Redbelly: If PE+KE=a constant, and you go negative with the PE, that means you have to go above the initial kinetic energy. And now we are entering a strange area of talk and we might want to not go there.

All: Do you notice how much confusion exists over potential energy? Or might I say energy in general?

 

[Ken G]

Sound is compression of a medium that is capable of pushing back, like a spring - which also can have potential energy.

It can be that, but the most common example, sound in air, isn't like that. For sound in air, there's no conservative force, and no potential energy anywhere.

 

[Ken G]

T
Regarding the potential energy of sound waves:

From Wikipedia, Sound: (http://en.wikipedia.org/wiki/Sound)
"The energy carried by the sound wave converts back and forth between the potential energy of the extra compression (in case of longitudinal waves) or lateral displacement strain (in case of transverse waves) of the matter and the kinetic energy of the oscillations of the medium."

I haven't read the entry, but on the surface, that's just nonsense. The vast majority of our experience with sound is in air, and that entry makes no sense at all for sound in air. Maybe they specify somewhere they are talking about sound in an elastic medium, for which the restoring force is a conservative force. Air isn't like that at all, the restoring force is just freely flowing momentum flux, it's not really much of force at all-- it just acts like one in a fluid description.

 

[JeffKoch]

It can be that, but the most common example, sound in air, isn't like that. For sound in air, there's no conservative force, and no potential energy anywhere.

A sound wave is a compression wave, which results in a local increase in air pressure above ambient (the RMS is the sound pressure, which can be related to a number in decibels), so in a sense it is like a spring. I personally don't think of sound waves in terms of potential energy, but I suppose one could do so.

 

[Ken G]

A sound wave is a compression wave, which results in a local increase in air pressure above ambient (the RMS is the sound pressure, which can be related to a number in decibels), so in a sense it is like a spring. I personally don't think of sound waves in terms of potential energy, but I suppose one could do so.

I can't really see how potential energy would make much sense for sound in air, but I agree with you that the mathematics can look kind of similar. When you compress air, there is the potential to re-expand, but no potential energy is involved.

 

[Phrak]

Water waves are one half kinetic energy and one half potential energy. The quote below comes from the Wikipedia wave power article.

I assume that it is the same with light waves. Do people here agree?

So you think light has energy. Really? Light energy is usually given in terms of the Poynting vector, P. <P> makes people happy because it let's them get energy from one place to another in a continuous manner without raising any hard questions. But as I recall, application of the Poynting vector is an example of junk physics. In the derivation of the Poynting vector, it is initially assumed that charge density over a region in question is non-zero. Charge density then calcels out, and for some reason the Poynting vector is still faithfully applied where there is no charge density at all. Where charge density is zero, the equation yields 0=0. Properly applied, Mr. Poynting's formula does not include the vacuum.

 

[Philip Wood]

Sound Waves in air
Although Robert Boyle (of Boyle's Law fame) wrote about "the spring of the air" we now know that the mechanical properties of gases at 'ordinary' temperatures and pressures are well described by the kinetic model, in which the gas consists of molecules in rapid random motion, and for which the energy is wholly kinetic.

When sound is traveling through air, the energy associated with the oscillatory motion of the molecules might be thought, as in most oscillations, to be partly kinetic and partly potential. But here, the 'potential' part is due to "the spring of the air" and is, fundamentally, (random) kinetic. The 'kinetic' part is due to the organised superimposed motion of the molecules due to the passage of the sound wave.

Electromagnetic Waves
The energy of an e-m wave is electric field energy and magnetic field energy.
The energy per unit volume in an electric field of magnitude E is $\frac{1}{2} \epsilon_{0} E^2$.
The energy per unit volume in a magnetic field of magnitude B is $\frac{1}{2} \epsilon_{0}c^2 B^2$.
At any point in an e-m wave these are equal.

In circuit theory (and possibly in a wider context) there is quite a good analogy between B-field energy and kinetic energy, and between E-field energy and elastic potential energy. But it's only an analogy.

 

[Ken G]

In circuit theory (and possibly in a wider context) there is quite a good analogy between B-field energy and kinetic energy, and between E-field energy and elastic potential energy. But it's only an analogy.

I agree that's the bottom line here-- what the OP is noting is likely a fruitful type of analogy to look for in many situations, but it is also not something that should be taken too literally when more precise meanings of the words are in use. Langauge like potential energy can be used to mean something quite specific, or it can be generalized, we just have to be clear which one we are doing.

 

[Phrak]

No indeed. Light waves and water waves have almost nothing in common. Light waves do not have kinetic energy or potential energy.

The energy density in a light wave is proportional to E² + B²...

What does "indeed" mean. Could you supply a source and derivation of energy density = E2 + B2, please?

...
Electromagnetic Waves
The energy of an e-m wave is electric field energy and magnetic field energy.
The energy per unit volume in an electric field of magnitude E is $\frac{1}{2} \epsilon_{0} E^2$.
The energy per unit volume in a magnetic field of magnitude B is $\frac{1}{2} \epsilon_{0}c^2 B^2$...

Could you supply a source and derivation for this?


In dimensional analysis, I get

$E = E[MD/QT^2]$

$B = B[M/TQ]$

$1/\mu = 1/\mu [T^2Q^2/M^2]$

$\epsilon = \epsilon [T^4Q^2/M^2D^2]$

therefore

$B^2/\mu$ is unitless.
$E^2 \epsilon$ is unitless.

Neither represents energy. Anyone have a problem with this?

In skew differential forms I know of only one natural combination that yields terms in E^2 and B^2. This is the Faraday tensor with lower indices, F multiplied by it's dual, G (outer product multiplication).

$G_{\mu \nu} = {\epsilon_{\mu\nu}}^{\alpha\beta}F_{\alpha \beta}$

$G_{\mu \nu}\wedge F_{\alpha \beta} = 0$

The product G^F is generally covariant when G, F and epsilon are tensor densities. I know of none that are expressed in generally covariant form and are nonzero in local coordinates.

 

[Philip Wood]

Here's an unsophisticated plausibility argument for electric field energy.

Consider the uniform electric field inside a parallel plate capacitor of plate area A and plate separation b, for which capacitance C = $\epsilon$₀ A /b

We know that the energy U stored in the capacitor is $\frac{1}{2}C V^2$.

This can be written $\frac{1}{2} \frac{\epsilon_{0}A}{b} V^{2}$.

But the electric field strength, E, in the gap is given by E = V/b.

Expressing V in the energy formula in terms of E...
$$U = \frac{1}{2} \epsilon_{0}Ab E^{2}.$$
So the energy per unit volume of interplate gap is $u = \frac{1}{2} \epsilon_{0} E^{2}.$.

So far, so good. Nothing controversial. The leap is to attribute the capacitor's energy U to energy stored in the field, in which case the last formula gives the energy in the field per unit volume.

A similar argument can be constructed just as simply for magnetic energy by considering the energy stored in the uniform field in a long current-carrying solenoid.

 

[Phrak]

Here's an unsophisticated plausibility argument for electric field energy.

Consider the uniform electric field inside a parallel plate capacitor of plate area A and plate separation b, for which capacitance C = $\epsilon$₀ A /b

We know that the energy U stored in the capacitor is $\frac{1}{2}C V^2$.

This can be written $\frac{1}{2} \frac{\epsilon_{0}A}{b} V^{2}$.

But the electric field strength, E, in the gap is given by E = V/b.

Expressing V in the energy formula in terms of E...
$$U = \frac{1}{2} \epsilon_{0}Ab E^{2}.$$
So the energy per unit volume of interplate gap is $U = \frac{1}{2} \epsilon_{0} E^{2}.$.

So far, so good. Nothing controversial. The leap is to attribute the capacitor's energy U to energy stored in the field, in which case the last formula gives the energy in the field per unit volume.

A similar argument can be constructed just as simply for magnetic energy by considering the energy stored in the uniform field in a long current-carrying solenoid.

Nicely done! I like unsophisticated. It excludes sophistry.

Your textook equation for U should be corrected a little.

$$U = C\int V(t) + U_0$$

$U_0$ is a constant of integration, so the energy derived is not absolute but relative. This is a small matter, but might be found relevant.

Another relative, rather than absolute energy relationship can be formed considering separation of charges. To do this, take two charged parallel plates, initially separated by some given distance, and calculate the potential energy lost as they approach. This yields a dU/dx, and after integrating, also obtains a relative, rather than absolute energy. Assume the plate area is large compared to delta x.

So, in this way, if I'm not mistaken, energy needn't be attributed to fields without charge/current present. I would actually have to do the problem rather than talk about it to be sure. Maybe later.

By the way, this is an old question: Is the electromagnetic energy resident in the fields, or in the separation of charge?

 

[Phrak]

By the way, I must have made an error in the units calcuation of the energy units in vacuum. Now I calculate DE and BH as having units of energy.

Secondly, although the Poynting vector is identically zero, stating that electromagnetic fields carry no energy nor momentum (and therefore totally messing with the accepted electromagnetic stress energy tensor), there are derviatives of the covariant vector potential that are generally nonzero valued having line integrals expressing energy differences.

These only occurr in the presence of charge and current density: according to classical electromagnetic theory, when carefully derived, electromagnetic radiation carries no momentum or energy where charge/current is not present.

 

[liometopum]

Since the conversation is now on electrical/magnetic fields, here is something I'd like to hear comments on. I posted this under classical physics, but NOBODY replied:

There is a video uploaded by a Vietnamese physicist, Nhan Huynh Cong, at http://www.youtube.com/watch?v=06q57uAt4AI&feature=feedlik
The title is "Magnetic field is vortices with their own axis to create electromagnetic deflected axis interaction" (in case the link fails)

Also http://www.youtube.com/watch?v=3A2K...list=ULjrXwqOPDigM&lf=mfu_in_order&playnext=4

He shows, by a simple experiment, how the orientation of a spinning object interacting with another spinning object can mimic magnetism when you change the angle of interaction. You get attraction and repulsion. It is very interesting. I have not seen this experiment before. He does not speak English, so you have to watch and deduce what he is doing.

Do any of you have comments or viewpoints on this demonstration?

 

[Philip Wood]

Both links give the message 'Malformed video', I'm afraid.

Maxwell ('On Physical Lines of Force', c 1868) devised an elaborate mechanical 'ether' in which magnetic lines of force were represented by the axes of spinning vortices. Neighbouring vortices on adjacent lines were separated by 'idle wheels". The vortices (contracting along the axes and expanding sideways) mimicked the properties of magnetic lines of force. He developed the model mathematically, coming up with a set of equations whose solution was a wave. Later he dropped the mechanical model but retained the equations...

 

[liometopum]

I corrected the links. When I copied them over, I forgot to consider that the URL was abbreviated on the page and so the abbreviated link was plugged in. The links work now.

 

[Born2bwire]

What does "indeed" mean. Could you supply a source and derivation of energy density = E2 + B2, please?



Could you supply a source and derivation for this?

I would expect any undergrad EM book would have this. Off the top of my head, Griffiths, Balanis, Jackson and Chew's Waves and Fields texts would all have this equation.

 

[Philip Wood]

As you've seen, I gave a simple 'derivation' of the energy density in an electric field in post 20, and, in the same post, mentioned how to use a very similar method for that in a magnetic field.

 

[Phrak]

I would expect any undergrad EM book would have this. Off the top of my head, Griffiths, Balanis, Jackson and Chew's Waves and Fields texts would all have this equation.

If you would post anyone of them, I would point out the error I believe.

 

[Born2bwire]

If you would post anyone of them, I would point out the error I believe.

Jackson gives it in Equation (6.106) in my third edition. Griffiths gives it as Equation (8.13) in the third edition. Chew gives it in Equation (1.129). This is a rather straightforward exercise. You just have to derive the energy contained in the fields with regard to a point source and current.

 

[Phrak]

Jackson gives it in Equation (6.106) in my third edition. Griffiths gives it as Equation (8.13) in the third edition. Chew gives it in Equation (1.129). This is a rather straightforward exercise. You just have to derive the energy contained in the fields with regard to a point source and current.

Where would you place the energy of a charged capacitor. In the fields as E^2 or in regions containing charge--or some other partition of both?

 

[Philip Wood]

Going back - with apologies for being boring - to my post (hash20), we find that the energy in a charged capacitor with uniform field is proportional to the volume occupied by the field. This strongly suggests associating the energy with the field itself.

This is supported by considering other geometries of capacitor where the field is non uniform. We get the same value for energy stored using $U=\frac{1}{2}C V^2$ as by using $\int\frac{1}{2}\epsilon_{0} E^2 d(Vol)$ in which the integral is taken over the volume of the field.

So we can, it seems, associate a given amount of stored energy with each volume element of the region occupied by the field. That's as far as I'd want to go. I wouldn't really want to say that this is where you would find the energy, or this is where the energy hangs out. Though I suppose you could say this if you wanted to; it would certainly have more going for it than saying that the energy lives on the plates with the charges!

 

[Ken G]

A way to argue that this is indeed "where the energy hangs out" is to look at time varying fields and Maxwell's equations. Via the Poynting flux concept, Maxwell's equations can be cast in the form of conservation equations for currents of electromagnetic energy. So if you have a charge, with a static field, and you shake the charge, you set up a blip in the field that corresponds to a local increase in the field energy density. That local energy blip then propagates along the field, where it can deposit energy somewhere else if it is absorbed by another charge. At any time, if you want to know where to put another charge to absorb some excess field energy, the answer is, "in the region where the excess field resides." This makes it very straightforward to associate that energy with a kind of "location" within the field.

Indeed, those who view fields as just placekeepers for what charges are doing may benefit from switching hats, and viewing the charges as placekeepers for what the fields are doing. I don't think either concept stands alone very well-- they work off each other.

 

[fizzle]

... So we can, it seems, associate a given amount of stored energy with each volume element of the region occupied by the field. That's as far as I'd want to go. I wouldn't really want to say that this is where you would find the energy, or this is where the energy hangs out. Though I suppose you could say this if you wanted to; it would certainly have more going for it than saying that the energy lives on the plates with the charges!

Sounds like good advice to me. Heaviside, who came up with the Poynting Vector, warned against giving electromagnetic energy a "personal identity" and following it from place to place. That's especially important when trying to break it down into electric and magnetic energy since they can "vanish" at any given time when em waves intersect. For example, if you send equal step waves down each end of a transmission line, when they overlap in the middle the magnetic energy in the resulting field will go to zero while the electric energy doubles.

 

[fizzle]

Indeed, those who view fields as just placekeepers for what charges are doing may benefit from switching hats, and viewing the charges as placekeepers for what the fields are doing. I don't think either concept stands alone very well-- they work off each other.

What's interesting about that is the complete flip-flop in the viewpoint required. The photon viewpoint is extreme in that it appears to be purely charge-to-charge transfer of state. To see this, start with the old Bohr model of hydrogen (electron orbiting a proton at various stable radii/energy level) and do a semiclassical calculation of the fields and energies involved. Have the electron drop from a high energy state to the lowest state (ignore the various forbidden transition issues). It emits a photon of a certain energy which corresponds to a certain frequency. That frequency is somewhere between the starting orbit frequency and the ending orbit frequency, asymptotically approaching 50% as the photon energy increases. You can calculate the radial electric field for the frequency during this transition. The obvious physical picture from the Bohr model is that the electron, for whatever reason, doesn't emit an em wave in the stable states but does during the transition and some sort of mean frequency is assigned to the photon. Regardless of what actually happens, we now assume a photon of the given energy goes flying off into space.

Now for the extreme charge-to-charge state transfer part. There's an electron sitting out in space somewhere, minding its own business (stationary). Along comes the photon emitted by the hydrogen atom. It's incident on the electron and absorbed temporarily. Let's say the electron was along the axis of the original hydrogen atom so that the photon's em wave is circularly-polarized. Do a semiclassical analysis of this CP em wave interacting with the free electron - with the constraint that the electron's total energy is increased by the incident photon's energy. What do you get for the required electric field in the CP em wave to make the electron behave properly? Well, you get, essentially, the electric field strength of the original electron in the emitting hydrogen atom. The free electron mimics the motion of the original electron in the hydrogen atom. It behaves as if orbiting a central positive charge at a given radius and associated frequency; i.e. the state of the hydrogen electron has been transferred completely to the free electron, at least temporarily. The two most troubling things from a semiclassical viewpoint are:

1) The required electric field strength in the CP em wave is *very* high
2) The CP em wave's electric field strength is independent of the distance (instead of 1/r)

Either one of these would be a showstopper from a semiclassical viewpoint. This is why any attempt to reconcile electromagnetic theory with QM is mostly doomed to failure. I tried a handwaving explanation in a previous post a while back but it was deleted by the mods here, so I won't do it again and be banned. I just think that going through all the calculations is a fascinating exercise in semiclassical em theory that others might enjoy.