If two stationary charges experience 1N of force, two moving charges should experience 1N of force as well right? (Due to the fact the the moving charges see each other as stationary.)
So can we use only coulomb law to explain every phenomenon in electromagnetism especially magnetism?
Indeed, what you say is true and this is exactly the approach that is taken in the undergrad textbook Electricity and Magnetism by Purcell and Morin. The entire chapter 5 is dedicated to showing that the magnetic field has to be consequence of electrostatic force and special relativity.
Indeed you do not need the Lorentz force to describe the force between stationary charges. For such cases a scalar Coulomb potential suffices in the rest frame of the charges. For all other cases you need tbe Lorentz force. Notably, induction cannot be explained in any frame with only the Coulomb force.
If two stationary charges experience 1N of force, two moving charges should experience 1N of force as well right? (Due to the fact the the moving charges see each other as stationary.)
So can we use only coulomb law to explain every phenomenon in electromagnetism especially magnetism?
If two stationary charges experience 1N of force, two similar co-moving charges will exhibit less than 1N of force.
Due to the fact the the moving charges see each other as stationary, the charges themselves see the force as 1 N.
So we can use only coulomb law to explain this phenomenon in electromagnetism, if we say that same Coulomb force is different in different frames.
(This phenomenon has the old name "Lorentz force")
