Question

For those of you who have a reasonable grasp of relativity and electrodynamics, has anybody ever tried to calculate the electrostatic attraction between two current carrying wires due to the Lorentz contraction of the "electron cloud"?

Answer 1

or "electron sea" or however you wanna think of it... the flow of electrons.

Answer 2

please elaborate, sounds interesting

Answer 3

Are you referring to the length contraction of the electrons due to their velocity relative to the velocity of light?

Answer 4

Imagine I have two long, straight wires running parallel to one another, each carrying current the same current. From the perspective of a stationary proton embedded in wire number 1, the electric field that I see is a superposition of the field generated by the stationary protons and the field generated by the moving electrons in wire number 2, since the electrons in wire number 1 all cancel. Classically the electrons and protons in wire number 2 would cancel each other but because the electrons are flowing in a group, like a cloud, the aggregate structure appears length contracted as per the consequences of special relativity.

Answer 5

@ Dalvoron not the electrons themselves, but the aggregate "cloud" they form as they drift through the wire.

Answer 6

This then increases the apparent number density of the electrons, which creates a net electric field that can be felt by the stationary protons.

Answer 7

Is this roughly what you mean is happening?