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Pascal DUBOIS

 

Keywords: special relativity; magnetic field; electromagnetic field; electrostatic field; electrostatic interaction; charge; electromagnetic force; Lorentz force; Mach's principle.

 

 

We place ourselves in the weakly relativistic framework (allowing us to neglect the order terms in the progress of the calculation). From the fundamental principle of dynamics, we establish the equation giving the transform of the force applied to a body in motion in a change of Galilean reference frame.

 

Applied to the problem of electrostatic interaction between two moving charges, this equation allows us to obtain the expression for the Lorentz force, which introduces a magnetic field in addition to the electrostatic field.

 

Then, from a geometric approach based on the physical understanding of electrostatic interaction, we show that we can obtain the same result while remaining within the framework of classical mechanics.

 

Taking into account the time shift of the interaction, linked to the distance between the charges, leads to a variation in the rotation of the segment joining them as well as to a variation in their distance, compared to the calculation carried out by reducing to the case where one of the charges is fixed. These variations result in a corrective force to the electrostatic force, which restores the Lorentz force.

 

The relativistic approach gives an equivalent result because the desynchronization of clocks corresponds to a time shift identical to that of the electrostatic interaction. It therefore seems abusive to consider the magnetic field as a consequence of the theory of relativity.

 

Unlike the electrostatic field, the magnetic field does not involve an exchange of energy with the sources. It is a purely vector field, which should be considered as a tool to correct a calculation that does not fully model the interaction of charges with each other as they move.