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I might have asked this to many times but there just does not seem a good understandable answer about this.

From the following Link

A charge moving at constant velocity also cannot produce electromagnetic waves as the constant motion means that there is no change in the electric and magnetic field of the moving charge.

if charge moves in a constant speed, there is definately electric and magnetic fields changing at each point due to distance between the charge and each point increasing or decreasing so we got time varying electric and magnetic field at each point in space.

Why then does the quote say that there is no change ? I am saying it is. Maybe observer should not be considered as a point in space but then who should he considered observer ?

Giorgi Lagidze
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  • I am not sure if this is the right answer to your question but I think you should consider what a wave is. So, an electromagnetic wave is not any random change in E and B fields but rather a synchronous change that obeys the wave equation. – physicopath May 30 '23 at 14:22
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    A question related to yours was asked yesterday. Why does the kink has the following vector direction? – mmesser314 May 30 '23 at 14:27
  • @physicopath i know that but why dont we have synchronous change in E and B for constant velocity case ? – Giorgi Lagidze May 30 '23 at 14:45
  • @mmesser314 that does not answer my question – Giorgi Lagidze May 30 '23 at 14:45
  • I see your point. If you drag your finger through water at constant velocity you get ripples spreading out over the surface. For a charge, why do you need acceleration to get this? This has been asked a number of times - How and why do accelerating charges radiate electromagnetic radiation?. The answer is "because Maxwell's equations". Sometimes a diagram is added like the one in the link above. But these don't answer your question, at least not intuitively. – mmesser314 May 30 '23 at 15:00
  • Even if one learns maxwels equations, it does not still answer my question intuitevely. Everybody brings an example of kinks for the acceleration case but nobody explaine why kinks are not produced for constant speed charge. If one explains kinks for acceleration, one should explain why it does not happen for constant speed. This is why i am kind of confused and angry. It would be even better not to mention kinks at all then. – Giorgi Lagidze May 30 '23 at 15:17
  • Time varying E gives B. E remains constant but generates a magnetic field. if the velocity is constant this magnetic field is also constant. – M06-2x May 30 '23 at 16:50
  • For uniform motion of a point charge, the electric field can be shown to simply be radially outward from the current position of the charge. (However its magnitude is not spherically symmetric.) A purely radial field obviously has no kinks. – Ghoster May 30 '23 at 20:23
  • The field obviously has to change as the charge moves. But it changes in a way that keeps it exactly radial at all times from the moving position of the charge. Thus there are no kinks and no radiation. It’s that simple. – Ghoster May 31 '23 at 03:54
  • I think the main idea is that. Maxwell's equations tell us that an EMW is a wave that travels with speed of light and for which E, B and direction of propagation are all perpendicular to each other. And the only way to produce such a wave with a charge is to accelerate the charge. Have a look at these two videos. https://www.youtube.com/watch?v=xYrvt_S_5Co https://www.youtube.com/watch?v=cXk9WDafPHo – physicopath May 31 '23 at 11:47

3 Answers3

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You are getting caught up in the difficulty of using words to express the concept.

Under no circumstance are the people who are telling you the correct information are saying that the E and B fields are invariant in time, because as you have correctly noted, the E and B fields everywhere will be changing with time as the charge passes by in its constant velocity.

The statement, however, is that such a changing E and B field do not make electromagnetic waves.

One needs accelerating charges to get electromagnetic waves. Constant velocity is zero acceleration, and so there will not be electromagnetic waves, no kinks.

The obvious way to see that constant velocity will not get you electromagnetic waves is to do a Lorentz transformation to make the charge stationary. Then it will be a pure E field that is time-invariant, and so obviously no electromagnetic waves.

You can work through the horrendous mathematics to get the Lorentz transform of the fields to get you the correct answer, or you can think of things in any form of relativity (even Galilean, even though that cannot get the maths down correct). Or any other argument that will convince you.

naturallyInconsistent
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  • Question 1. How does the E and B change happen in accelerate mode of the charge versus constant speed that does not cause EM wave ? Should it be ONLY oscilation of E and B in order to produce em wave ? Such as if E and B only increases, it wont produce EM wave but if E and B increase then decrease then increase, then it produces EM wave ? – Giorgi Lagidze May 30 '23 at 17:31
  • Question 2. Trying to see in the kinks way why there would be no kinks in the constant speed case but seems like nobody explains this. Any advice on this ? – Giorgi Lagidze May 30 '23 at 17:32
  • Q1) you should think of a Lorentz squashed E field that is moving along with the charge, and also a B field moving along with the charge. At any fixed point the E and B fields increase and then decrease. That is not the problem. You need to increase and decrease in a specific way to get EM waves. Yet another way to see it is to derive that EM waves are made, proportional to the acceleration of charges. – naturallyInconsistent May 30 '23 at 17:50
  • Q2) is actually also answered above: if you have const velocity, the E and B fields can just move in and out rigidly, as if there is nothing more to say about it. Only if you have an acceleration does the E and B field have to develop kinks. – naturallyInconsistent May 30 '23 at 17:52
  • Lets imagine a charge moves with constant velocity on a x-axis linearly to the right and as we know, it produces electric field. Lets say this charge has the speed = v. We know that electric field spreads in every direction in a speed of light, but in addition to this, does this mean that electric field itself has the same speed in the same direction as the charge moves ?
    If thats how it is, then at the time of charge stopping, electric field should continue moving along x-axis to the right inertially, bending electric field, creating kink and producing EM wave?     – Giorgi Lagidze May 30 '23 at 18:12
  • Is that logic close to the truth? Mostly interested in the fact if electric field has the same speed as the charge in the x axis to to the right(the same direction of the charge) - I am curious in this as I am trying to understand why there is no kink when charge moves in constant speed. – Giorgi Lagidze May 30 '23 at 18:12
  • Yes, the E and B field of a charge moving at constant velocity necessarily has to move at the same constant velocity, and if you suddenly accelerate the charge, the E field will take some time to realise it should not be moving at that velocity anymore, hence kinks – naturallyInconsistent May 30 '23 at 18:16
  • Let us continue this discussion in chat. – Giorgi Lagidze May 30 '23 at 18:17
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The question in the link asks about electromagnetic waves, not the one time change of an electric field at some place, wich will occur, if a charge particle moves with constant speed moves along one line relative to an observer.

trula
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  • Why would it happen one time ? If charge moves constant speed, each time it increases the distance from it to the observable point and hence electric field decreases each time(not just one time) – Giorgi Lagidze May 30 '23 at 15:14
  • if it moves with constant speed this means constant direction and constant size. so the distance first diminishes and than increases, no periodic . moving in a circle is an accelerated movement and produces EM waves. – trula May 30 '23 at 17:32
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One key difference between water and EM waves is there is a medium for water waves. Your finger has a velocity with respect to the water. For EM, there is no medium.

Suppose you see waves from a charge moving at constant velocity. If you run alongside a moving charge at constant velocity, you see the same waves. That would mean you get waves from a charge at rest.

This shows that you don't get waves. But it isn't very satisfying. Perhaps a better answer might be an elaboration on "because special relativity."

mmesser314
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  • With your argument, I can also run with charge with the same acceleration and then I would see the waves as at rest. This argument is very poor and does not hold true for accelerwtion case. If it does, how ? – Giorgi Lagidze May 30 '23 at 15:13
  • Special relativity is all about inertial frames of reference - frames with no acceleration. If you used a frame that followed an accelerating charge, you would need general relativity. It would show that there are waves. – mmesser314 May 30 '23 at 15:15
  • You are fight. My answer isn't very complete. Perhaps someone will have a better one. – mmesser314 May 30 '23 at 15:16
  • Everybody brings an example of kinks for the acceleration case but nobody explaine why kinks are not produced for constant speed charge. If one explains kinks for acceleration, one should explain why it does not happen for constant speed. This is why i am kind of confused and angry. It would be even better not to mention kinks at all then. – Giorgi Lagidze May 30 '23 at 15:18
  • See the link I posted in the comments. The kink is produced when the charge suddenly started moving. Suppose the charge had always been moving. The fields would be like the red region inside the bubble. No kinks. If you think about that for a while, you might see why. Physics is often confusing and takes thought to become clear. The poster for the linked question found it confusing too. That question has a link to chat where the discussion continued. – mmesser314 May 30 '23 at 15:23