9. Mario J. Pinheiro, Do Maxwell's Equations Need Revision? A Methodological Note

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Volume 20: Pages 267-275, 2007

Do Maxwell's Equations Need Revision? A Methodological Note

Mario J. Pinheiro 1

1Department of Physics and Institute for Plasma and Nuclear Fusion, Instituto Superior Tecnico, Av. Rovisco Pais, 1049001 Lisboa, Portugal

We propose a modification of Maxwell's macroscopic fundamental set of equations in vacuum in order to clarify Faraday's law of induction. Using this procedure, the Lorentz force is no longer separate from Maxwell's equations. The Lorentz transformations are shown to be related to the convective derivative, which is introduced in the electrodynamics of moving bodies. The new formulation is in complete agreement with the actual set of Maxwell's equations for bodies at rest, the only novel feature being a new kind of electromotive force. Heinrich Hertz was the first to propose a similar electrodynamic theory of moving bodies, although its interpretation was based on the existence of the socalled ether. Examining the problem of a moving circuit with this procedure, it is shown that a new force of induction should act on a circuit moving through an inhomogeneous vector potential field. This overlooked induction force is related to the Aharonov—Bohm effect but can also be related to the classical electromagnetic field when an external magnetic field is acting on the system. Technological issues, such as the socalled Marinov motor, are also addressed.

Keywords: classical electromagnetism, Maxwell equations, classical field theories, special relativity, general physics

Received: May 24, 2006; Published Online: March 26, 2009