Inter-charge forces in relativistic classical electrodynamics: electromagnetic induction in different reference frames

In this paper it is proved by using the Clifford algebra formalism that the standard transformations (ST) of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer ...

In the 1960s, E.M. Purcell presented a basic explanation of the magnetic force experienced by a test charge moving parallel to a stationary current-carrying wire. According to Purcell's derivation, this force results from the difference between the relativistic length contraction of the distance among the stationary positive charges of the wire and the relativistic length contraction of the distance among the negative charges moving in the wire when the charges are observed i...

In a recent Letter [arXiv:1205.0096], Mansuripur considers a magnetic dipole positioned at a fixed location from a point charge. Performing a Lorentz transformation to a laboratory frame where the charge distribution moves he finds that `a net torque acts on the dipole pair'. He then argues that `this torque in the (lab) frame in the absence of a corresponding torque in the (rest) frame is sufficient proof of the inadequacy of the Lorentz (force) law'. In this comment we de...

Although the expressions for energy densities involving electric and magnetic fields are exactly analogous, the connections to forces and electromagnetic potentials are vastly different. For electrostatic situations, the changes in the \textit{electric} energy can be related directly to \textit{electric} forces and to the electrostatic potential. The situation involving magnetic forces and energy changes involves two fundamentally different situations. For charged particles m...

A generalization of the classical electrodynamics for systems in absolute motion is presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate two inertial frames: the privileged frame S and the moving frame S' with velocity v with respect to S. b) The transformation of the fields from S to the moving frame S' is given by H'=a(H - v D) and E'=a(E + v B) where a is a matrix whose el...

It is generally expected from intuition that the electromagnetic force exerted on a charged particle should remain unchanged when observed in different reference frames in uniform translational motion. In the special relativity, this invariance is achieved by invoking the Lorentz transformation of space and time. In this investigation an entirely different interpretation of the invariance of force is presented. We propose a new model of the electromagnetic force given in term...

The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the Lienard-Wiechert potentials. The derivation uses arguments based on Lorentz invariance and a physically transparent expression originally due to J.J.Thomson for the field of a charge that experiences an impulsive acceleration.

In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and papers are only valid under very special circumstances and not satisfactory under a mathematical point of view.

It is well known that electric and magnetic fields may change when they are observed from different frames of reference. For example, the motion of a charged probe particle moving parallel to a current-carrying wire would be described by utilizing different electric or magnetic fields, depending on from which frame of reference the system is observed and described. To describe the situation in all frames by utilizing the theory of relativity, one has to first describe the sit...

The situation of a charged particle passing down the symmetry axis through a magnetic toroid presents a relativity paradox; different inertial frames suggest different forces on the charge and on the toroid due to the unperturbed systems. We review the charge-toroid interaction and suggest that the magnetic Aharonov-Bohm situation is misunderstood because of unfamiliarity with the acceleration fields following from the Darwin Lagrangian, which go unmentioned in recent textboo...