Consult this document by Hans de Vries:
[The simplest, and the full derivation of Magnetism as a Relativistic side efect of ElectroStatics][1]The simplest, and the full derivation of Magnetism as a Relativistic side efect of ElectroStatics
He uses only Electrostactic field and the non-simultaneity to derive the Magnetic Field.
It appears that the Magnetic field is a side effect of movement of charges in the electric field.
If we pretend that the magnetic field exists beyond a mere artifact then the following question must be answered: How can the particles communicate information about its position and velocity so that, in the past, they can adjust the source of the electromagnetic energy?
(*) Hans de Vries has a very interesting online book (not yet finished) in his site.
added:
Magnetic forces are induced by the motion and, much like Coriolis force, is not a real force. ...
wikipedia ..the Coriolis effect is an apparent deflection of moving objects when they are viewed from a rotating reference frame. (a moving frame induces forces, there is no need to be a rotating one)
ps: it is frustating to be down voted without a comment :( it´s an injustice......yes it is - Calimero. [1]: http://physics-quest.org/Magnetism_from_ElectroStatics_and_SR.pdf