I've read an explanation about 'how moving charges produce magnetic field' according to special relativity. It proves how magnetic force is just another artifact of electric force viewed from a different reference frame. Here's a veritasium / minutephysics video explaining the same : https://www.youtube.com/watch?v=1TKSfAkWWN0 Now this explanation is fine. But then how this explanation can work with a single charged particle? How can a single moving charged particle produce magnetic field?
I hear you. How to length contract a single charge to fit the popular examples given of more charges present from length contraction. Length contraction was a popular idea in 1905. In order to set himself apart Einstein said simultaneity time not length contraction. The phrase "length contraction" can not be found in the original paper on the electrodynamics of moving bodies. Special relativity as it is known today was the result of team work mostly Hermann Minkowski Einstein's old math teacher where length contraction was put back in. Use the Lorentz gamma and apply it to the Coulomb force for the charge and it will work without the conflict you brought up. Also do not use this as an answer on an exam. For that you memorize then spit it out , you know the drill.