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Consider please the situation where an electron is moving to the right with velocity Ve paralel to a horixontal wire in which is found electric current I. For the sake of definitness, let positive charges inside the wire go to right and negative go to left, with velocities of equal modulus for an observer at rest in relation to the wire's reference frame. Let's call this observer A (at rest w.r.t. the wire).

This observer is seeing an electron running paralel to the wire which has this rather simmetrical current.

Classical explanation of situation observed by A:

(1) the wire is neutral

(2) the wire, with current inside, produces a magnetic field which is stationary in space according to A.

(3) the electron has a velocity with respect to this reference frame in which the field is stationary.

(4) Consequently, the electron will experience a magnetic force oriented from the wire to the electron, so that it suffers a repulsion from the wire. (F = q (v X B))

Relativistic explanation of situation observed by A:

(1) the wire is neutral, for the stream of positive charges and the stream of negative charges inside the wire have the same velocities and therefore, are contracted by the same factor yielding a wire with a set of two inhomogeneous local densities of opposite charge and the same magnitude in each place.

(2) the wire, with current inside, produces a magnetic field which is stationary in space according to A.

(3) the electron has a velocity with respect to this reference frame in which the field is stationary. But the electron's electric field is no longer decribed by a spherically simmetrical field. However the electron's field will present simmetry w.r.t the line which crosses perpendicularly the wire and pass through the electron.

(4) the interaction between the electron and the system of charges inside the wire now will be given by solving the problem: Find the resultant electric force between two inhomogeneous charge distributions (but equal in each place and practically superimposed) and a particle which has a sort of spherical field contracted along the direction perpendicular to the wire (perpendicular to its velocity, in fact).

OBS: is seems that this resultant force must be zero. My question is how to conduct this two explanations correctly in order to preserve the internal consistency of both descriptions.

Thank you

DaTario

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