Ok, let's pit FB against UF and let's see where do I get the best answer.
We know that charged particles in movement generate a magnetic field.
In fact, if we let two parallel electric cables carry a current I, the two will attract each other with force density proportional to I squared.
That's because the electrons are moving.
Now, let's remove everything but two electrons freely running along parallel paths.
They will be repelling each other due to their charge, but this effect will be slightly weakened by their mutual magnetical attraction, because both are moving and generating a magnetig field.
Now, let ourselves be in the reference frame of one of those electrons.
Since the speed relative to the other electron is zero, the magnetif force between the two of them, is zero.
Turns out that the magnetic field is just a relativistic correction of the electric field.
Ok, no problem so far.
Now let's go back to our two parallel cables.
Let's stay in the (average) reference frame of the electrons.
Again the two flow of electrons are still with respect to each other.
But now we have protons, that move in the opposite way with the same speed and opposite charge, and therefore generate exactly the magnetic field that the electrons generate in the lab reference frame.
The results of the mental experiment with only two electrons and the mental experiment with also the protons do not match.
What am I doing wrong?