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Considering that the forces between a moving charge and its target are developed as elementary forces at each point in both charge fields leads to the Lorentz Transform. The elementary forces propagate outwards in both fields at the speed of light relative to their centers. The derivation suggests that when a charge approaches a target, its surrogate, formed in the target's field by the sum of a set of these elementary forces, is observed, not the charge itself. The surrogate grows faster than the charge moves, thereby explaining the increase in the charge's momentum over its Newtonian value; the charge's mass doesn't change. The fast moving charge's time doesn't slow down ? it just seems to because the target senses the surrogate coming out of the field so it is sensed as it was at an earlier time.

The interaction between electric charges is here assumed to take place in their fields, where there is an isotropic propagation at the velocity of light with respect to the individual charge centers. This leads to an increase in the mutual energy between two charges if one is in motion with respect to the other, the amount depending on whether the motion is transverse to or along the line of their separation; this provides the basis for a classical derivation of the differential relationships of electromagnetics. It is shown that induced electric forces arise from the energy changes when one charge accelerates, and that magnetic forces arise from the cross-product term in the mutual energy when both charges are moving; the squared velocity terms in the mutual energy are canceled by the energy associated with the moving charges interacting with the fixed ions in the conductors that are left be?hind by the moving charges. The derivations are directed to the behavior of charges in conductors, where conditions are essentially static and retarded fields need not be considered.

A moving particle, represented by its associated plane wave, is assumed to interact with a stationary target particle by the generation of Huygens' sources in the local media. These sources add along a continuum of cones whose apices are on the moving particle and, in combination, constitute a wave that converges on the target along a cone that is orthogonal to them. It is shown that the x' and t' coordinates of the Lorentz transform describe the motion on the orthogonal cone that corresponds with the motion of the particle as described by the x and t coordinates.

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.

Two potentials associated with a moving charge are derived by assuming that the mutual energy between it and a stationary test charge are generated in their fields and that the generation involves as random propagation at the velocity of light relative to a stationary point. Expressed in terms of B, the velocity of the charge divided by the velocity of light, the potentials are: (1) the static potential of the moving charge divided by 1 - B^₂ if the velocity is along the radial to the test charge; and (2) the static potential divided by [] if the velocity if transverse to the radial. The low velocity approximations of these potentials lead to very direct derivations of the differential relations for the induced fields associated with changing currents and for the magnetic forces associated with stationary currents. They thereby provide a basis for the development of electromagnetic theory.