Although this incompatibility of the relativistic view with electrodynamics does not come as a surprise given the mathematical inconsistencies in the Lorentz Transformation itself, it is probably important that the suggested velocity dependence of the electrostatic and magnetostatic forces would actually not explain the Lorentz force in terms of electrostatics either as again the field would decrease like 1/r4. This would suggest that the magnetic field is in fact primarily a different physical phenomenon and can not be explained in terms of electrostatics (see the home page entry regarding Maxwell Equations for more in this respect). On the other hand, it is hard to believe that the apparent velocity dependence of the electrostatic force observed in accelerators for instance is not real, so one would have to assume the existence of two components which are identical for the near field but are different in the indicated sense for the far field. Clarification in this respect can probably only be achieved by making exact measurements of the magnetic far field of current systems.
http://www.physicsmyths.org.uk/lorentzforce.htm
http://www.physicsmyths.org.uk/lorentzforce.htm
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