# Accelerating charges

1. Jun 2, 2005

### Cheman

According to source i read, in classical theory it its believed that charged particles radiate when the accelarate - but do they have to be accelerating or can they just be moving? So if we had an electron gas, each time "collision occured" light would be radiated as the particles decellerated, but not inbetween when they are traveling at constant speed?

2. Jun 2, 2005

### dextercioby

Check out the Liénard-Wiechert potentials and fields in any serious electrodynamics book,J.D.Jackson being the first to turn to.

Daniel.

3. Jun 2, 2005

### shyboy

yes, there is certainly some radiation called Bremsstrahlung, produced by electrons colliding with ions. I am not so sure about electron-electron scaterring.

4. Jun 3, 2005

### pmb_phy

No. Charges moving at constant velocity do not radiate. The charges must be accelerating to radiate.

Pete

5. Jun 3, 2005

### dextercioby

How do you prove the charges moving at constant velocity do not radiate...?I have a hunch they do radiate.

Daniel.

6. Jun 3, 2005

### pmb_phy

Take my word for it when I tell you that this kind of derivation is not something I can remember. With me physics is a "Use it or loose it" situation.

The power radiated by a charged is proportional to the magnitude of the acceleration. The derivation can be found in Jackson. A buddy of mine is an expert in this area. He did a lot of work on this subject. Unfortunately he's on an extended vacation. Basically he says that classical radiation is defined as when the EM field "breaks away" from the field of the charge.

However that does not mean that there is no energy flux when the charge is moving at constant velocity. The Poynting vector is not zero. In fact anytime you have a non-zero Poynting vector there is a flow of energy - as surprizing as it may seem. This fact is well worth your attention. I'll dig out the references it you'd like? One of them is in Shadowitz's text on radiation. There is also 1 or two articles in the American Journal of Physics on this as I recall. I think I have them in fact.

Pete

7. Jun 3, 2005

### Andrew Mason

But do they radiate because they accelerate? Or do they accelerate because they radiate? After all, no one has been able to detect radiation from a charge accelerating due to gravity.

According to Feynman, the radiation of a charge depends on the third time derivative of position (ie non-uniform acceleration). So constant acceleration does not produce radiation. This is still somewhat controversial. see: Does A Uniformly Accelerating Charge Radiate?

AM

8. Jun 3, 2005

### dextercioby

Alright,Pëte.Computing the Poyting vector for a Liénard-Wiechert field generated by a constant velocity moving electric charge,one gets a nonzero result.Ergo,radiation is being emitted.

I'm aware people always ponder about Larmor's formula,but this case must not be excluded.

Daniel.

9. Jun 3, 2005

### dextercioby

It is a thorny subject indeed.But i'm sure i was not referring to a generally covariant theory of classical electrodynamics,but only about a Lorentz invariant theory.

Daniel.

10. Jun 3, 2005

### Cheman

So when we say an accelerating charge "radiates" what do we actually mean? I mean, say we have an electron moving around at constant velocity - this is clearly exerting an electric/ megnetic field on any charged particles near it. How come as soon as it accelerates this field suddenly becomes light? How come a charge accelerating would cause an oscillating "light field"? How does this field become different to be classed as light rather than just an electric field? How is classical light absorbed? eg - people would have said that things were green because they reflected green light and absorbed everything else - what would they say it would have been absorbed by? Would it be electrons, as in quantum theory, and if so how is this "force" absorbed> ( ie - if light is just a force field oscillating as the theory suggests, then how could it be "absorbed"? I mean, afteral, if you had an electron and put a proton near it and then another one behind that, the second protons energy is not altered due to force/ energy being absorbed by the proton in front and thus weakening the force - the only thing that makes the force from the electron slightly weaker for the 2nd proton is that this proton is further away? (if we say that the protons do not hypothetically repel each other.) Forces at a distance cant have their energy absorbed by objects the act on - so why does this happen with classical light?

I always feel that the classical model of light is always completey over looked in my studies - we are told "its wave - the end" and then quantum begins to be mentioned - but no one actual explains what people before quantum believed light to be like, and what form it took. I would be very interested if anyone could explain to me from scratch what classical light is like, how its acts, is formed, and was believed it would act with particles. (obviously, this was wrong as later proved by photoelectric effect,etc.)

11. Jun 3, 2005

### McQueen

cheman
According to source i read, in classical theory it its believed that charged particles radiate when the accelarate - but do they have to be accelerating or can they just be moving?

One explanation that is given is that charged particles moving with uniform velocity , give rise to magnetic fields while accelerating charges give rise to electromagnetic fields. For instance in a DC circuit as soon as the current is established it ceases to effect conductors in its vicinity although it will still deflect a compass needle , attract or repulse another wire carrying a current and so on. An AC circuit would induce a current in conductors in its vicinity..

12. Jun 3, 2005

### dextercioby

That's not true.Do some reading,okay and stop posting inaccurate info.

Daniel.

13. Jun 3, 2005

### McQueen

Dextercioby
That's not true.Do some reading,okay and stop posting inaccurate info.
Check out this site , I think the author is saying more or less what I said in my post , although he uses the word a changing field as opposed to accelerating charges.
http://www.ch.ic.ac.uk/local/physical/mi_5.html

14. Jun 3, 2005

### dextercioby

I give you this formula

$$\vec{E}_{\mbox{Lienard-Wiechert}} =\frac{q}{4\pi\epsilon_{0}}\frac{1-\frac{v^{2}}{c^{2}}}{\left(R-\frac{\vec{R}\cdot\vec{v}}{c}}\right)^{3}} \left(\vec{R}-R\frac{\vec{v}}{c}\right)\left|_{t'}\right +\frac{\mu_{0}}{4\pi}\frac{q}{\left(R-\frac{\vec{R}\cdot\vec{v}}{c}}\right)^{3}} \left\{\vec{R}\times\left[\left(\vec{R}-R\frac{\vec{v}}{c}}\right)\times\vec{a}\right]\right\}\left|_{t'}\right$$

,where t' is the retarded time,$\vec{v}$ is the velocity of the charge "q",$\vec{a}$ is the acceleration of the charge and

$$\vec{R}=\vec{r}-\vec{r}_{0}(t')$$

,where $\vec{r}_{0}(t')$ is the position of the charge at retarded time.

Daniel.

P.S.The magnetic field is obtainable from the expession of the electric one.

15. Jun 3, 2005

### dextercioby

One sees that there's a nonzero time dependent component of the electric field (and of the magnetic one of course),even in the absence of acceleration (case in which the second term of sum in the electric field's expression vanishes).

Daniel.

16. Jun 3, 2005

### Cheman

So suppose I had a highly charged rod - if i moved it across at constant velocity from one side to another we would not class its field as light. Yet if we wave it side to side it IS electromagnetic radiation. Why? Surely the fields are exactly the same and both do exactly the same things?! (ie - impose force on other charged objects.)

(NB - if anyone can answer the questions on my previous post that would also be useful. )

17. Jun 3, 2005

### Cheman

Also, how does classical wave theory of light explain why light is absorbed? Eg - if we put a green filter infront of our eyes all other light is absorbed - but how according to classical theory? It obviously cant use the resonace idea ( like people tried to use on the photoelectric effect, even though attempts at getting this to fit failed. ) since that would not cause the wave to be absorbed as it is, in essence, simply a long distance force. However does this force field, except for the force feild of green, in this example with a green filter, manage to be absorbed and not poass through the filter according to classical wave theory? Was it even related to the atomic structure of matter at all, or to something elese?

18. Jun 3, 2005

### Cheman

Or would it be (now that ive had a think about it. :rofl: ) anything to do with if the light frequency casued "particles" (electrons or whatever ) to resonate, then they will do it in anti-phase to the light - therefore setting up their own light which destructively interferes with it? I think i'm confussing myself now.... lol.

Any help appreciated! :tongue2:

Thanks.

19. Jun 6, 2005