The Differential Forces of Electromagnetism
Keywords: electromagnetism, magnetic forces, currents
The basic relationships of electromagnetism are derived from the two postulates of relativity theory while avoiding an unstated third postulate of the theory, namely that the effects of motion on forces both transverse and parallel to the motion are subject to a common transform. This results in a theory in which the static mutual energy of two charges, M, transforms to [ ] if one charge is moving with normalized velocity B transverse to the line joining them but to [ ] if the motion is along the line. The first transform has two important consequences whose effects dominate electromagnetic theory: (1) as a charge accelerates the increasing mutual energy results in electric forces on other charges; and (2) the square of the relative velocities between moving charges have a cross product term that gives rise to the magnetic forces (the squared velocity components are compensated by forces developed with the stationary ions in the conductors.) The second transform is required to explain the forces between orthogonal current elements but has no other effect on the forces between conductors carrying currents. The analysis suggests that the energy associated with moving charges is more closely related to the vector potential than it is to the magnetic field.