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Lets have 2 electrons travelling with some speed relative to a static observer.

The force between those 2 electrons will be the Coulomb force and the magnetic force.

Is it forbidden from the laws of nature the magnetic force to have the same magnitude with the Coulomb force?

I tried to find a case where it is true and it came out that the charged things must travel at speed c which is impossible for every frame of reference.

Lets take 2 electrons moving at the same speed relative to a static observer.

From the frame of reference where the electrons are immobile , space is moving to the opposite direction.Due to length contraction of space , less electrons now fit the contracted space and the coulomb force is different.The difference of the coulomb force between the 2 frame of references is the magnetic force.

Now for the magnetic force to be equal to electric force the length of the space in the frame of reference where the electrons are immobile must be 0 meaning velocity c.

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    \$\begingroup\$ Shouldn't your name be Mrs Physics rather than Mrs Chemistry? Perhaps this should be asked on the physics board? FWIW I don't think there's any arbitrary requirement on the equality or otherwise of electric and magnetic forces as you move between frames of reference. As you say, there is a prohibition on travelling at c. I would think therefore that the latter trumps the former. \$\endgroup\$
    – Neil_UK
    Nov 25, 2019 at 9:11
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    \$\begingroup\$ It is not clear what you asking. Do you want to compare the situation observed from two different frames of reference (one at rest ("static oberver"); one moving with the electrons)? BTW are the electrons moving at the same speed? You have to make this clear! Why do you think there are any restrictions ("forbidden to have same magnitude") concerning the electric and magnetic force? How did you "try to find a case where this is true"? Why don't you show what you tried? We can not read your mind! \$\endgroup\$
    – Curd
    Nov 25, 2019 at 9:34
  • \$\begingroup\$ Neil_UK i am a chemist with an interest in physics , electrical engineering and psychology. However my university degree is the chemist's one. \$\endgroup\$ Nov 25, 2019 at 10:15
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    \$\begingroup\$ Are you familiar with the non coulomb electric force? Are you familiar with the fact that the magnetic force is a classic, non relativistic force that can be replaced with relativistic theory? Have you tried to read any of the very excellent Feynman lecture series freely available on the web, and in particular volume 2? Are you familiar with the idea of the A-field? (See chapters 14 & 15, vol. 2.) Could you show us here any quantitative development for your question? Your question asserts things not shown. I'd like to see a better argument. \$\endgroup\$
    – jonk
    Nov 25, 2019 at 10:24
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    \$\begingroup\$ MrsChemistry, if you write their name like @MrsChemistry (@ symbol + their name, just type the first few letters in their name and then press tab) then the ones you are talking to will be alerted the same way you were alerted when I wrote this comment. - Neil and curd and jonk has probably not seen your responses unless they've come back to this question a second time on their own accord. - Knowing Neil and Curd and Jonk I think all 3 of them has come back to this question on their own accord already. \$\endgroup\$ Nov 25, 2019 at 11:32

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If you have just 2 electrons moving there is no point in saying "less electrons now fit the contracted space" There will still be exactly two electrons no matter what frame of reference you are using.

I guess what you have in mind (still some mind reading required with your question) is looking at two parallel wires with a given current (which is reflected by a given charge density (charge per length) and speed) when observed from rest and from a frame of reference moving with the electrons.
There will be difference in Coulomb force because of differences in charge density due to relativistic effects (length contraction) depending on the frame of reference; and the difference will exactly match the difference of magnetic force which will be present only when observed from a frame of reference not moving with respect to the electrons.

This is a well known illustration of the fact that magnetic force is just a relativistic effect of electric force.

You can find it discussed e.g. in Feynman Lectures of Physics, Volume II, "Mainly Electromagnetism and Matter": 13–6The relativity of magnetic and electric fields

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  • \$\begingroup\$ Corson and Lorrain may also, with their many examples, assist the understanding. \$\endgroup\$ Nov 25, 2019 at 11:17
  • \$\begingroup\$ You can't move at c. And what do you mean by "space becomes 0"? And where do you think would the electrons go? Leave the universe? \$\endgroup\$
    – Curd
    Nov 25, 2019 at 11:24
  • \$\begingroup\$ "Space" doesn't move at all. You seem to still have the concept of aether in mind which had to be given up more than 100 year ago. And: a frame of reference moving with c doesn't make sense. \$\endgroup\$
    – Curd
    Nov 25, 2019 at 11:55
  • \$\begingroup\$ @mrsc Only to bosons is space-time absent. To large population fermion statistics, via bosonic entanglements, space-time becomes an emergent phenomena. You should read Mach's philosophical arguments made more than a century ago. Or just think about the implications of the axioms used by Einstein in his very simple special theory of relativity. \$\endgroup\$
    – jonk
    Nov 25, 2019 at 13:42
  • \$\begingroup\$ I once heard that ya can't change the laws of physics... \$\endgroup\$
    – Nedd
    Nov 25, 2019 at 15:50

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