Maxwell—Out of Newton, Coulomb, and Einstein

The electromagnetic field of an accelerating charge is obtained starting with (1) Coulomb's law in extended form (a stationary source charge exerts a Coulombic force on an arbitrarily moving test charge), (2) the special relativity transformation relations for coordinates and forces, (3) charge conservation, (4) Newton's third law, and (5) the assumption that electric effects are transmitted with the velocity c. This method can also be used to investigate the fields of hypothetical “charges” obeying a “Coulomb law” $F = q1q2/rn$⁠, where $n$ is different from 2.