I am looking for a different approach that of the relativistic effect of Einstein. enter image description here

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    $\begingroup$ Will you accept a classical magnetic explanation? $\endgroup$ – The Photon Mar 3 at 17:21
  • $\begingroup$ The question would gain clarity, if you would write a little bit more. $\endgroup$ – Semoi Mar 3 at 18:31
  • $\begingroup$ @The Photon yes $\endgroup$ – Fred Caston Mar 3 at 20:38

Physics does not have an explanation why electromagnetism exists, but it does describe how it works. One could argue that parallel currents attract because of the Lorentz force and Ampère's law. Conversely, these laws are what they are because parallel currents attract. In the end the laws are as they are to explain, among others, this observation.

  • $\begingroup$ Could you go into more detail? $\endgroup$ – Fred Caston Mar 3 at 21:25
  • $\begingroup$ We know that currents behave like this and we have a very complete and successful model that describes this and a lot more. Perhaps one day we will have a deeper theory from which electromagnetic and other forces follow, but not yet. $\endgroup$ – my2cts Mar 3 at 22:12

Faraday might have used an argument like this one... The magnetic fields due to two wires carrying currents in the same direction tend to cancel between the two wires, but re-inforce beyond the two wires (applying right hand grip rule). Magnetic field lines behave as if under tension but exerting lateral pressure, so if you draw the pattern you will see that the wires are forced together. By a similar argument, wires carrying currents in opposite directions are forced apart.

Too hand-wavy? Well, you don't want Einstein's approach and I guess that you know the mainstream argument based on the Lorentz force.

  • $\begingroup$ I don't know Lorentz force extensively actually you could explain that argument actually $\endgroup$ – Fred Caston Mar 3 at 21:27
  • $\begingroup$ Refer to your top left diagram. Using the right hand grip rule, the right hand wire produces a magnetic field that, in the vicinity of the left hand wire, is down the screen. Electrons in the left hand wire are moving out of the screen. The magnetic Lorentz force on each moving electron is $\mathbf F=-e\mathbf v \times \mathbf B$, which is therefore to the right. $\endgroup$ – Philip Wood Mar 3 at 22:35
  • $\begingroup$ Incidentally, the arrows on the field lines in your diagrams are pointing in the reverse directions to the way they should, and the lines merge together unrealistically in the right hand diagram. Where did you get these diagrams? $\endgroup$ – Philip Wood Mar 3 at 23:08
  • $\begingroup$ why do we generalise circular the magnetic field from the right wire to be moving to the left? $\endgroup$ – Fred Caston Mar 3 at 23:25
  • $\begingroup$ @Fred Caston. I'm sorry but I don't understand your last comment. In particular, what movement are you referring to? $\endgroup$ – Philip Wood Mar 4 at 19:22

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