November 2, 2005
The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for the electric field of a moving charge predicts that, for the particular spatial configuration considered, the inductive force vanishes in the frame in which the magnet is in motion and the test charge at rest. In contrast, consistent results, in different frames, are given by the recently derived formulae of relativistic classical electrodynamics.
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The Faraday-Ampere laws of electro-magnetic induction are formulated in terms of plain and twisted differential forms, taking in due account the body motion in terms of Lie time-derivatives. Covariance of Lie derivatives with respect to arbitrary relative motions, and Galilei invariance of the electro-magnetic fields, imply Galilei invariance of the induction laws, contrary to most claims in literature. A noteworthy outcome of the theory is the conclusion that the so called L...
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I show that no force or torque is generated in cases involving a charge and a magnet with their relative velocity zero, in any inertial frame of reference. A recent suspicion of an anomalous torque and conflict with relativity in this case is rested. What is distilled as `Lorentz force' in standard electrodynamics, with relative velocity as the parameter, is an under-representation of two distinct physical phenomena, an effect due to Lorentz contraction and another due to the...
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A derivation of the electric field intensity and of the magnetic induction generated by a uniformly moving point charge is presented. The derivation is in accordance with the fact that the electric and magnetic fields of moving charge are propagating from the charge with speed $c$ in empty space. The derivation is tailored for a special audience who knows the transformation of space, time and fields and Coulomb's law in the rest frame of the point charge. It avoids the use of...
August 3, 2000
A general law for electromagnetic induction phenomena is derived from Lorentz force and Maxwell equation connecting electric field and time variation of magnetic field. The derivation provides with a unified mathematical treatment the statement according to which electromagnetic induction is the product of two independent phenomena: time variation of magnetic field and effects of magnetic field on moving charges. The general law deals easily-without ad hoc assumptions-with ty...
May 4, 2012
It has been recently argued that the Lorentz force is incompatible with Special Relativity and should be amended in the presence of magnetization and polarization in order to avoid a paradox involving a magnet in the presence of an electric field. Here we stress the well-known fact among relativists that such an incompatibility is simply impossible and show that the appearance of such a "paradox" is a mere consequence of not fully considering the relativistic consequences of ...
February 25, 2021
The force exerted by an electromagnetic body on another body in relative motion, and its minimal expression, the force on moving charges or \emph{Lorentz' force} constitute the link between electromagnetism and mechanics. Expressions for the force were produced first by Maxwell and later by H. A. Lorentz, but their expressions disagree. The construction process was the result, in both cases, of analogies rooted in the idea of the ether. Yet, the expression of the force has re...
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A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical electrodynamical theory. Important differences are found and serious errors are found in the traditional treatment of special-relativistic effects in classical electromagnetism. Fields associated with radiation processes are also considered and clas...
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In a brief but brilliant derivation that can be found in Maxwell's Treatise and traced back to his 1861 and 1865 papers, he derives the force on a moving electric charge subject to electromagnetic fields from his mathematical expression of Faraday's law for a moving circuit. Maxwell's derivation in his Treatise of this force, which is usually referred to today as the Lorentz force, is given in detail in the present paper using Maxwell's same procedure but with more modern not...
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The definition of the induced $emf$ as the integral over a closed loop of the Lorentz force acting on a unit positive charge leads immediately to a general law for electromagnetic induction phenomena. The general law is applied to three significant cases: moving bar, Faraday's and Corbino's disc. This last application illustrates the contribution of the drift velocity of the charges to the induced $emf$: the magneto-resistance effect is obtained without using microscopic mode...
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