## Interaction between charges in motion

In order to explain the relativistic nature of magnetism, a book shows an example of linear procession of charges: positive charges in one direction and negative charges in the opposite one. It says that this is equivalent in the reality to a not charged current carrying wire. In a metallic wire only electrons should have moved but it prefer a this simmetric model in order to simplify the discussion. Then It says that a charge at rest at a specific distance from the wire is not affected by any force because electric field in null.
Why, if we assume the not simmetric model (in which only electrons move), the electric field is still null?
I know that we have assumed that the wire is not charged, but in respect to the charge at rest only electrons move in this alternative model, then only negative electric density should go up, due to relativistic contraction
I know (of course) that my perspective is wrong, because a charged current carrying wire does not attract a charge at rest, but I don't know where is my mistake
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 If I move at a speed v relative to that wire, electrons and protons going opposite ways, And I use Lorentz velocity addition rules. And I get my relative speeds of the 2 line charges and then I use length contraction, One of the line charges will now be more dense and I will get a net charge and an E field. And a charged current carrying wire will attract a charge at rest, it has an E field F=qE. But if the wire just had a B field then it would not attract the charge, it would need to be moving.

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