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When you launch this applet you can notice, that in the beginning the force lines are propagating from a charge, with some speed(speed of light, probably).

The force lines means, that in every point of the space there are force with straight-defined direction, according to charge position. When charge is changing it's position, the force direction and density should change too.

So, how does a classic physics describes the electric charges forces propagation speed?

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  • Relativity is usually considered classical physics. Is there any particular reason you think that applet is non-relativistic? – jacob1729 Aug 22 '18 at 19:46
  • @jacob1729, didn't understand You. I didn't write that the applet is non-relativistic –  Aug 22 '18 at 20:21
  • Related : Electric field associated with moving charge – Frobenius Aug 23 '18 at 18:42
  • @Frobenius, yeah, almost. But how does classic physics explains that? Is there any laws? –  Aug 23 '18 at 18:49
  • Take a look in the @probably_someone answer in above given link. It's qualitative. I hope that I find a full answer in the future. It's relativistic classical physics and I am confident that the proof must be given via Lienard-Wiechert potentials. – Frobenius Aug 23 '18 at 19:31
  • @Frobenius, so the answer, probably is Lienard-Wiechert potentials, and derivatives by time for acceleration case? –  Aug 23 '18 at 19:45
  • Take a look in my answer there : Fields of a moving electron. The expression (14.14) for $\mathbf{E}(\mathbf{x},t)$ is produced from Lienard-Wiechert potentials. The first term in the rhs depends on velocity $\boldsymbol{\beta} = \boldsymbol{\upsilon}/c$ only while the second term depends on acceleration $\dot{\boldsymbol{\beta}} = \dot{\boldsymbol{\upsilon}}/c=\mathbf{a}/c;;$ also. Since the charge is going at rest suddenly we must use the Dirac $\delta-$function (difficult). – Frobenius Aug 23 '18 at 20:52
  • @Frobenius am I a single who seeing glitch instead of normal expressions exactly in 14.14? The symbols are very tiny –  Aug 24 '18 at 07:20
  • Yes, it's probably a problem of your browser and/or your device. Anyway, I edit these equations to normal size fonts before 5 minutes. Also, you could see these equations in Jackson's textbook, if you have a copy of it. – Frobenius Aug 24 '18 at 07:30
  • @Frobenius, thank You. I have a one more question: why a constant magnetic field according to Lorenz force, for example, has a perpendicular component, if, as You can see from the same applet, there is no perpendicular lines, when charge is moving constantly? –  Aug 24 '18 at 07:37
  • @Frobenius The thing that confusing me is why does there is actually no curves due to constant moving? Light propagates with finite speed, so even if charge moves constantly, there should be curves, but in the applet lines change instantly(due to constant moving). –  Aug 24 '18 at 07:41
  • There exists a magnetic field perpedicular to the plane but variable in magnitude : Magnetic field due to a single moving charge. See also my video here Electric field of a uniformly moving point charge. I post this in an answer of mine but I don't remember in which one. – Frobenius Aug 24 '18 at 08:00
  • @Frobenius, yeah, but You are saying there about $B$, but I'm talking about the case where there there is only field lines like in the applet. I think the answer is why a particle feels perpendicular force from another particle with "magnetic" field is the fact that magnetic field a priori means that we deals with particle that is moving relative to another, and.. Well it's hard to explain by the words.. –  Aug 24 '18 at 08:19
  • @Frobenius, and I don't understand why in the video there are two charges, and one of them retarded? –  Aug 24 '18 at 08:25
  • We can not continue with so many comments. You are missing so many important in Classical Electrodynamics. Choose some introductory textbooks and study about them (for example, if you don't know about retarded, present and advanced positions and time moments how it's possible to know about Lienard-Wiechert potentials and the propagation of the electromagnetic interaction with the finite speed of light $;c;$, about special relativity, Lorentz tranformation etc ???). – Frobenius Aug 24 '18 at 09:05
  • Now, may be my answer here : Electric field associated with moving charge it's useful to you. – Frobenius Sep 06 '18 at 12:43

2 Answers2

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Considering Maxwell's equations as "classical" physics, the propagation speed of a change in the electric field strength can be calculated from those equations. Maxwell himself did this and discovered that this speed was equal to the speed of light.

niels nielsen
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  • And how it can be calculated? –  Aug 23 '18 at 07:38
  • c is equal to 1/sqrt(ue) where u is the permeability of the vacuum and e is the permittivity of the vacuum. u is a constant of nature that describes how magnetic fields affect free space and e does the same for electric fields. – niels nielsen Aug 23 '18 at 16:32
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EM interactions are mediated by photons. Photons are massless particles that travel at speed c in vacuum when measured locally. All massless particles travel at speed c, like gluons and theoretically gravitons.

Originally in classical physics Maxwell's equations described the classical EM waves and their propagation. In that theory, a changing E field induced a changing M field, and a changing M field induced an E field, and this is how classical EM waves propagate.

Now these equations of Maxwell have a solution for the propagation speed of the classical EM waves, and that speed is c, in vacuum, when measured locally. In the classical theory, this speed has a relation to the permeability and permissivity of vacuum.

Nowadays, the speed of light is defined exactly as 299,792,458 m/s. It is a universal constant, and its value is exact, because the meter is defined as the distance traveled by light in 1/299,792,458 seconds.

Today, we know that not only EM waves, and photons travel at this speed, but all massless particles, and gravitational waves too.

When you say force lines, and charge position, if you talk about an electron, a charged particle, that has rest mass, and cannot travel at this speed. Nothing, no macro object and no elementary particle with rest mass can travel at this speed.

Photons do not carry charge. Now the QM description of EM waves is a herd of photons traveling as waves, and the classical EM wave works good with the QM theory.

If you are talking about charges traveling, like electrons, in a metal wire, the drift speed of electrons, to travel from one atom to another one, is slow. But, since, the electrons in the metal are so densely packed, the EM charge travels inside the metal with speed near c, that is why your applet is relativistic.

You are asking about force fields and based on the correct comments:

Let's take an electric charge like the elementary charge, the electron. It has field lines around it, those are mediated by virtual photons. We call them virtual because they describe the math. They too do not have to obey some laws that real photons have to obey, for example they are not limited by the speed of light. As the electron travels in space, the force field travels with it. The direction of the force field does not change, relative to the electron, the force field lines look constant.

Árpád Szendrei
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  • Did You read well? I asked exactly about the classic explanation, where there is no photons, so 50% of Your answer doesn't match the question. I know about Maxwell's equations, but there is no $c$ there, and describes exactly E and B fields, but not forces –  Aug 23 '18 at 07:23
  • Yes, I wrote about the classical, where c is the solution to the equations. That is how they defined c back then, but nowadays c is defined differently, and that is why I wrote about the current QM description. Now I will add to my question a few words about the force field. – Árpád Szendrei Aug 23 '18 at 17:08
  • Your edited that, force field travels, with electron, and it always constant for electron frame, I agree, but the question was exactly about non-electron frame. I edited my question, if You can, check it, please –  Aug 23 '18 at 17:57
  • Can you please tell me if it is not about an electron, then what charge are you specifically asking about? – Árpád Szendrei Aug 23 '18 at 18:12
  • I'm asking about electron –  Aug 23 '18 at 18:18
  • And I wrote about the electron. Is that not OK? – Árpád Szendrei Aug 24 '18 at 00:08
  • Yes, electron, but the question was about its electric field propagation. However, the answer seems to be Lienard-Wiechert potentials –  Aug 24 '18 at 07:14