Volume 3: Pages 117-121, 1990
On Ampère Electrodynamics and Relativity
P. T. Pappas 1
1Center for Electromagnetics Research, Northeastern University, Boston, Massachusetts 02115 U.S.A.
Difficulties with the concepts of motion of charges at the end of the nineteenth century motivated the Lorentz law instead of the assumed cardinal law of electrodynamics of Ampère. The two laws are different for nonclosed currents, which were at the same time supposed not to exist. Thus the two laws were assumed to be always identical as far as electrical currents were concerned. However, recent mathematical elucidations prove that the two laws are also identical for isolated charges moving in steady magnetic fields. Nevertheless, the cardinal law, correct for velocities with respect to the laboratory, is, in general, not relativistic or Lorentz invariant and violates energy conservation. The Lorentz law is relativistic or Lorentz invariant for isolated charges, but violates action and reaction and the conservation laws. Clearly, for closed circuits with uniform charge mobilities, both laws' deficiencies vanish, and both laws become identical. However, the two laws are different in certain other cases, and it is possible to distinguish them experimentally.
Keywords: original Ampère law, cardinal law, Lorentz force law, Grassmann, Biot‐Savart law, equivalence, (non) closed circuits, longitudinal forces, contact and interface (longitudinal) forces, action‐reaction preserving law, electrodynamic momentum, energy conservation, relativistic, Lorentz invariant electrodynamic law
Received: November 21, 1988; Published Online: December 15, 2008
