Abstract
The magnetic force between parallel uncharged current-carrying wires is derived by considering the forces on a boosted electron in the presence of a current-carrying wire. The magnetic force is seen to be caused by Lorentz contraction, which is extraordinarily tiny for typical lab demonstrations. The puzzle that large magnetic forces are due to tiny relativistic effects is resolved in numerical examples where the hugeness of Avogadro's number proves essential. Electrodynamics is formulated in covariant notation so the principles of relativity become manifest. The antisymmetric electromagnetic field strength tensor is developed to describe electric and magnetic effects in any reference frame. A field theory of charged matter is seen to be the next step in developing a relativistic and consistent theory of charged relativistic matter and electromagnetic fields.
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