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This question is related to this one but is much more specific:

As answered in the linked question, it can be shown that a new force that we will call magnetic force must appear in the system of electric wire, just by using fundamental principles of special relativity.

My question is whether this procedure can be generalized to every system and not specifically to the above example.

Specifically, can we derive the Biot-Savar law?

I tried to do it few years ago and it didn't worked for me and until this day I am not really sure if someone really have an answer for that.

ziv
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    For uniformly moving charge, assuming the Coulomb law and special relativity, one can derive more than that - all Maxwell's equations. See e.g. http://richardhaskell.com/files/Special%20Relativity%20and%20Maxwells%20Equations.pdf – Ján Lalinský Feb 19 '23 at 01:46
  • One can imagine a straight current-carrying wire is made of charges that stand still and charges that move uniformly, so the derivation should also be able to recover the Biot-Savart law for straight wire. – Ján Lalinský Feb 19 '23 at 01:47

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