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Well, here I see we meet a serious problem, perhaps the barrier to
our efforts:
1. There is no such thing as an *almost* inertial reference frame.
2. Magnetism is *intrinsically* a relativistic effect. There is
never a justification for ignoring relativity when treating
questions of this sort. Purcell is a good source for teaching
E&M with this fact held constantly in view, as is Feynman.
(These two texts were published within a year of one another.)