A Classical Basis for Electromagnetics
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.