Understanding Electric Field Direction in Relation to Moving Charged Particles

[asdf60]

Consider a uniformly moving charged particle (moving along the x-axis say). Consider an observer a light minute away from the origin, on the y-axis. Now, when the particle crosses the origin, the observer measures that the electric field points towards the origin. Why is this?

This seems really weird to me. Why isn't it the case that the observer instead measures the electric field as if the particle is where it was a minute before crossing the origin?

Would it be the case then, that an observer capable of seeing the particle (perhaps say instead that it was replaced with a large sphere), would then see the electric field eminating from a point ahead of the sphere?

 

[Cyrus]

I don't quite understand your question. What do you mean by measure the E field "before the particle as where it was a minute before crossing the origin"

For your setup, are you saying this body moves along the x-axis and the observer is stationary 1 light min up from the x-axis? The person is at point (o, 1lt-min) and the body is moving along the path (x,0)?

 

[asdf60]

Yes, that's correct.
What I really mean is this:

Say, for example, there is a star, 15 light years away, moving uniformly very fast relative to me and in a transverse direction (that is not along the line of sight). Now any time I see the star, the star is in fact (15 years * velocity of star) ahead of where I see it now. This is pretty obvious.

Now the confusion is this: suppose the star is very strongly charged, so the electric field of the star is quite discernable here on earth. Now according to what I understand, if i measure the electric field of the star, it points to where the star instantaneously is, not where I observe it! Is this true?

 

[Cyrus]

Lets try to be clear:

Any time you see the star, it will be

$$15*9.461 (10^{15}) + \int^{t_1}_{t_0} v(t)_{star} dt$$ away from you. A light year is a misnomer, it is a unit of length. The distance you observe it at any time will be its initial distance, plus how ever much distance it moves away or towards you in a given instant, which would be equal to the integral.

In general, the electric field of a charged body will vary in direction based on how the charge is distributed within the body, the shape the body takes, the magnitude of the charge, and the square of the radial distance. For simplicity, let's assume the star is a perfect sphere with uniform charge on its surface. Then in this example, the electric field would be given as $$E = \frac{ q } { 4 \pi \epsilon_0 r^2}$$ Where r, the radial distance, is given by the first equation, at any instant in time. At any given instant, you should observe the star at some position away from you, and it should have an electic field value associated with that position at that given instant in time, based on that radial distance. Then time will increment, the star will move away or towards you, and the distance will change, and the E field will change at that instant as well. They are related.

Im not a physics major, so I am not 100% sure, or even 1% sure I am right. There are probably many more factors at work. The E field I gave was for a static case. I assume it would hold true if the star is moving with uniform velocity. If the star is accelerating, more than likely all bets are off. Also, I don't know if the movement would have a dopler effect on the E field. I also don't know if there will be a lag time for the E field to change. The E field might take some time to propogate. If it does, it should give you an E field value that is slightly offset in time from the E field at that instant. It would lag as you are saying. Maybe a smart guy like Marlon can help us out.

 

[Meir Achuz]

Consider a uniformly moving charged particle (moving along the x-axis say). Consider an observer a light minute away from the origin, on the y-axis. Now, when the particle crosses the origin, the observer measures that the electric field points towards the origin. Why is this?

This seems really weird to me. Why isn't it the case that the observer instead measures the electric field as if the particle is where it was a minute before crossing the origin?

You probably know that the case you describe is actually quite complicated. It is treated in advanced EM textbooks.
The E field from a charge moving with constant velocity does point directly at an oberver, even though it is more complicated than just
qr/|r|^3. The fact that it points toward the observer even after using the retarded time and a Lorentz transformation comes after a long and tricky derivation.
There might be some simple reason why it still points that way, but I can't think of one, although I have tried.

 

[asdf60]

You probably know that the case you describe is actually quite complicated. It is treated in advanced EM textbooks.
The E field from a charge moving with constant velocity does point directly at an oberver, even though it is more complicated than just
qr/|r|^3. The fact that it points toward the observer even after using the retarded time and a Lorentz transformation comes after a long and tricky derivation.
There might be some simple reason why it still points that way, but I can't think of one, although I have tried.

I'm quite aware of this. I've seen the derivation, but the derivation I saw doesn't satisfy me (from purcell's E&M textbook). I was hoping that someone could provide a better derivation or explanation.

 

[Meir Achuz]

There are better derivations in more advanced texts than Purcell.
They are complicated, but follow step by step and are rigorous and satilsfying if you can follow the math. I haven't seen Purcell, but my guess is that he has to short circuit some of the math, which might make his derivation look fishy.

 

[bernhard.rothenstein]

Relativistic derivations of the electric and magnetic fields generated by an electric point charge moving with constant velocity
Authors: Bernhard Rothenstein, Stefan Popescu, George J. Spix
Subj-class: Physics Education

We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the fields are measured. The same equations were previously derived in a relatively complicated way2 based exclusively on general electromagnetic field equations and without making use of retarded potentials or relativistic equations
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Links to: arXiv, form interface, physics, /find, /abs (-/+), /0601, help


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Relativistic derivations of the electric and magnetic fields generated by an electric point charge moving with constant velocity
Authors: Bernhard Rothenstein, Stefan Popescu, George J. Spix
Subj-class: Physics Education

We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the fields are measured. The same equations were previously derived in a relatively complicated way2 based exclusively on general electromagnetic field equations and without making use of retarded potentials or relativistic equations
Full-text: PDF only
References and citations for this submission:
CiteBase (autonomous citation navigation and analysis)

Which authors of this paper are endorsers?


--------------------------------------------------------------------------------

Links to: arXiv, form interface, physics, /find, /abs (-/+), /0601, help


--------------------------------------------------------------------------------
Please have a look at the paper mentioned above

 

[Meir Achuz]

Relativistic derivations of the electric and magnetic fields generated by an electric point charge moving with constant velocity
Authors: Bernhard Rothenstein, Stefan Popescu, George J. Spix
Subj-class: Physics Education

We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the fields are measured. The same equations were previously derived in a relatively complicated way2 based exclusively on general electromagnetic field equations and without making use of retarded potentials or relativistic equations

Links to: arXiv, form interface, physics, /find, /abs (-/+), /0601, help


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Please have a look at the paper mentioned above

At first I was confused by your article, which seemed to derive two different equations [(1) and (3)] for the same electric field. But then I realized, after looking also at Jefimenko, the the r's in the two equations are not the same. The r in your Eq. (1) is at the observation time, while the r in your Eq. (3) is at the retarded time. This is mentioned in Jefimenko, and in textbook derivations, but, for some reason, not in your paper. Did I miss it somehow? In any event, it is still clear that the observed electric field points directly away from the present position of the constant velocity charge.

Straightforward (but complicated) derivations for each equation, as well a graphical demonstration of their connection are given in graduate texts by Jackson, "Classical Electrodynamics", and
Franklin, "Classical Electromangetism".

 

[bernhard.rothenstein]

I have not mentioned the concept of retardation prefering instead the concept of propagation of information about the creation of the field from the source to the point of observation. have you seen somewhere a relativistic derivation of the formula (3) in my paper?

 

[Meir Achuz]

Your Eq. (3) is the constant velocity term in the Lienard-Wiechert field of a point charge. It is Eq. (14.14) in Jackson or (15.103) in Franklin
(as well as other texts). Each text also shows a graphical connection between that and your Eq. (1) that is similar to your derivation of your Eq. (3).

 

[bernhard.rothenstein]

I have no access to the sources you quote. Are in the derivations you mention the space coordinates of the point where the measurement of the field takes place determined using the radar detection?

 

[Meir Achuz]

I believe what you call "radar detection" is more usually referred to as using the retarded time, which both of those texts use to derive your
Eq. (3). Your derivation is much simpler than that in the texts, because they are more interested in the acceleration fields which lead to radiation. The velocity fields are just a by product in the derivation.
Each text shows the connection between your (1) and (3) in a fairly simple derivation, which is somewhat like your derivation of (3).
Jefimenko refers to such derivations.
I could fax you (if you can receive a fax) or send you a brief PDF
of these other derivations if you want.

 

[bernhard.rothenstein]

electric field

thank you. a pdf will be appreciated. if you compare my derivation with Jefimenko's one I think mine is a "two line" one.

 

[DaTario]

Claude Cohen Tannoudji in his "Photons and Atoms - an introduction to quantum electrodynamics" (initial pages) discusses this topic in an interesting way.

Best Regards

DaTario