This talk describes how an electromagnetic field is the direct result of electric charge plus special relativity. (Permanent magnets are much harder to explain.) This shows that electromagnetism is essentially two-dimensional. It works the same in all Minkowski spaces with dimension of 2+1 or more.To calculate the magnetic force between a current flowing in a straight wire and a free charge in standard 3+1 space, do the following. Determine the plane defined by the line of the straight wire and the location of the free charge. Project the velocity vector of the free charge onto that plane. Rotate 90 degrees, depending on the direction of motion and the signs of the charges involved. The resulting vector shows the acceleration on the free charge due to the magnetic field.The magnitude of the magnetic field vector is proportional to the dot product of free charge and the velocity vector of the charge in the wire.All this has been known for decades. It seems that the most elegant way to calculate these things is with tensors, which I may or may not someday understand.
I didn't find the right solution from the Internet.
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Everything about Robert Distinti's Ethereal Mechanics, New Electromagnetism theories and Q-Vector Algebra.
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