# Why a moving charge + wire with current in a stationary reference has no electric force?

I've saw the Current in Wire special relativity magnetism question, but the answer did not convince me at all.

My doubt is crystal clear.

I know the electrons move in a very high velocity in all directions and often collide with each other (relaxation time lapse). This move is random and don't change wire linear density. I also know that the velocity of free electrons (drift speed) in the wire is quite slow, but it defines the current. No drift, no current.

Suppose a external positive charge moving in the same speed of electrons (v) to the right.

So it should be possible measure a electric (not magnetic) force on it, because the electron drift in the current direction is denser and are many free electrons that sum up this tiny effect.

If one changes the reference moving together electrons in the wire, I think that is concerning the drift speed and not the real average electron velocity in random directions.

In the stationary reference, except for drift, the average velocity of both electrons and protons approaches 0.

When the reference is changed relative to speed v to the right. First, we suppose that it's the average electron velocity. In that case, the electrons will no longer be stopped but at a mean velocity v to the left. The protons have exactly the same behavior, so both shrink their distances and the wire linear density remains the same.

So, it only makes sense to refer to stopped electrons if we were talking about the drift velocity that is zero when there is no current. The reasoning that walking along with the drift then makes sense. In the new reference, the protons now have a drift to the left and the eletrons be stopped in the referece that uses drift velocity to the right

However, in that case, the the total effect would be supposed to be low, according to some respondents, but it's the only one that make sense.

I'm confused.

In short, why is there no electric force (just magnetic force) acting in a moving charge on the stationary reference?

if drift velocity is enough to explain magnetism, why it does not generate shrink with electron drift in stationary reference and therefore the wire is not neutral anymore.

PS

For instance, this article says literally that magnetism comes from the drift velocity

By the way, it's remarkable that we can measure magnetic forces at all, since the average drift velocity in a household wire is only a snail's pace: v/c is typically only $10^{-13}$, so the Lorentz factor differs from 1 only by about one part in $10^{26}$. We can still measure this effect because the total charge of all the conduction electrons in a meter-long wire is tens of thousands of coulombs; two such charges separated by only a few millimeters would exert enormous electrostatic forces on each other.

• Note that, in general, wires in an electric circuit are charged otherwise energy would not be transferred, i.e., for energy transport, we need both magnetic and electric fields. Still, it is no contradiction (in an idealized problem such as this) to stipulate that, in the rest frame of the wire, the wire is electrically neutral so I'm quite sure what your question goes to. – Alfred Centauri Sep 20 '18 at 0:58
• This article (physics.weber.edu/schroeder/mrr/MRRtalk.html) tells that there is no electrostatic force in stationary reference so there is no electric field, just pure magnetic field. If you change the reference, appears some mixed electric and magnetic field. " .... Shown below is a model of a wire with a current flowing to the right...Therefore there's no electrostatic force on a test charge Q outside the wire.... . Back in the lab frame, we call this force a magnetic force." – Paulo Buchsbaum Sep 20 '18 at 1:24
• See the reason that, in general, wires are charged in an electric circuit here: IN A SIMPLE CIRCUIT, WHERE DOES THE ENERGY FLOW?. And again, it is possible to stipulate, in an idealized case such as at the link you provide, that the wire is uncharged in the rest frame. – Alfred Centauri Sep 20 '18 at 2:50
• I've saw the link but the article proof is a kind of idealized proof in a perfect wire. So there is an equivalence between magnetic field in our reference and electric field in reference together with drift eletrons. In that idealized world, an additional electric field in stationary reference would indicate an energy creation. See also chip-architect.com/physics/… – Paulo Buchsbaum Sep 20 '18 at 3:37