In the late 1800’s Appel wrote this, and differentiated it to yield ELECTRIC and MAGNETIC fields both. These are part and parcel, together, and the form reads, E + iH, ‘E’ being electric field, and ‘H’ the magnetic.  Yet these theta-components are associated with the SPIN…… hmmmmm. We have already used the ‘i’ trick… I SHALL BE PICKING AWAY HERE, like the archeologist in Egypt who was picking away slowly at a dig, and actually fell thru into something like….
The direction of the magnetic field is not the same, there may be room to construct this. If I can, I wil blow Burinskii away. OK scratch my last statement, the mag. field is in the same direction as E_theta and E_r.
This became clear chewing a good breakfast. However, in EM we usually construct a 4-vector POTENTIAL… HERE could be opportunity. I am sensing some elbow room for construction, there is something hollow, here.

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