- #1

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Where is the mistake?

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- I
- Thread starter Enryque
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- #1

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Where is the mistake?

- #2

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Edit: Also note that the A-level tag indicates that you have an understanding of the subject at the level of a graduate student or higher. As your questions suggests that you do not, I have changed the thread level to I.

- #3

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Edit: Also note that the A-level tag indicates that you have an understanding of the subject at the level of a graduate student or higher. As your questions suggests that you do not, I have changed the thread level to I.

Thanks for your soon response and adjust the level.

It seems I agree with you about the locality and causality; however the problem is no clear for me. I suppose that this problem can be addressed clasically, with the idea that the force on a charge equals the product of the charge value by the local electric field .

Imagine two external forces such that maintains the motion state of the two charges : namely one at rest and the other with uniform velocity. If we apply the basic mechanics, the external forces must balance the internal ones if the motion state is preserved; and to a external observer, the sum of external forces must be null if the motion of the center of mass is uniform. Also the field is stationary and there is no wave phenomena. So I do not understand well, why the internal forces are not of equal magnitude and opposites.

- #4

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No, you cannot address this classically. Electromagnetism is an inherently relativistic theory. If you take the classical limit, the electric field of the charges is the same and you do not have a problem.I suppose that this problem can be addressed clasically, with the idea that the force on a charge equals the product of the charge value by the local electric field .

If one of the particles is moving, the EM field is not stationary.Also the field is stationary and there is no wave phenomena

- #5

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I don't think that this is correct. In the scenario you describe I think that the internal forces are equal.So I do not understand well, why the internal forces are not of equal magnitude and opposites

Have you actually worked out the math on this?

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I don't think that this is correct. In the scenario you describe I think that the internal forces are equal.

Have you actually worked out the math on this?

As I belive, the fields of the two puntual charges are, in modulus,like this (R.K. Wangsness - Electromagnetic Fields)

E

if we put the two charges aligned with the relative velocity θ=0 and we have

E

so the force on the charge at rest is less intense than the force on the moving charge.

- #7

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I don't know the assumptions of that equation, so I don't trust it. However, I did the calculation using the Lienard Wiechert potential and got a similar result.As I belive, the fields of the two puntual charges are, in modulus,like this (R.K. Wangsness - Electromagnetic Fields)

E_{rest}=q/4πεr ; E_{motion}=E_{rest}f(v,θ)

if we put the two charges aligned with the relative velocity θ=0 and we have

E_{motion}=E_{rest}(1-v^{2}/c^{2})

so the force on the charge at rest is less intense than the force on the moving charge.

However, it is important to note that the direction of the force changes when the charges pass each other. Thus, even though the force on the charge at rest is always less intense, the direction of the change in mechanical momentum flips as the charges pass each other. So on one side there is mechanical momentum going into the fields from the system and on the other side the flow of momentum between the fields and the charges is reversed. Unfortunately, I don't know how to deal with the singularities to demonstrate it, but Poynting's theorem guarantees it.

- #8

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so the force on the charge at rest is less intense than the force on the moving charge.

Well that is not very true at all, whatever the direction of the motion is.

A moving electric field is kind of concentrated to an area. It's kind of length-contracted.

So therefore:

The force on the charge at rest is more intense than the force on the moving charge, when the charge at rest is located somewhere on the area with the concentrated electric field.

On some other areas the force on the charge at rest is less intense than the force on the moving charge.

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