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I didn't think that a uniform magnetic field was possible (except as an
approximation).
Three thoughts (not-coherent)
1. The assymetry is that electric charges exist, and magnetic monopoles
do not. (Cabrerra notwithstanding) This means that all
real electric and magnetic fields are the superposition of
relativistically transformed electric fields. (N.B. the superposition
of transformed fields need not be the transform of a single field.)
2. What about the intrinsic magnetic moments of elementary particles.
These are relativistic in origin, but need not represent moving
charge.
3. Since charge cannot be created, perhaps we should believe that
current rather than charge is intrinsic. Maybe all electric fields
are transforms of magnetic fields! Isn't duality fun! Pick your
basis.