Purcell has a paper in which he derives the magnetic field by assuming a charged particle travels alongside a conducting wire at the same velocity as the conduction electrons in the wire. The conduction electrons and the test charge are moving together but the positive charges are moving backwards with respect to the electrons and the test charge. The positive charges undergo a length contraction as explained by special relativity. The unbalanced charges then produce the magnetic field. Is it possible that there is more to this. That there are things we don't understand yet. Is it possible to totally explain the magnetic field with special relativity?