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When a steady current flows through a wire, there is usually charges on the surface of the wire. These surface charges have an nonuniform distribution so that the electric field inside the wire is uniform and parallel to the wire.

But… If I understand correctly due to the nonuniform surface charge distribution there should be tangential electrical field on the surface of the wire, which is directed same as the current. If so, why don’t surface charge move in same direction as free charges in the bulk of conductor. In other words, what force makes the charges on the wire surface be stationary?

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  • $\begingroup$ Why do you think this being true?"there is usually charges on the surface of the wire." $\endgroup$
    – trula
    Commented Aug 8 at 10:07
  • $\begingroup$ @trula that is part of standard physics explanation of how wires actually work. See the huge debate that Veritasium kicked off with the "energy does not flow in wires" video. $\endgroup$
    – naturallyInconsistent
    Commented Aug 8 at 10:11
  • $\begingroup$ > "why don’t surface charge move in same direction as free charges in the bulk of conductor." I think that is an approximation. Maybe they do move, but the surface is pretty thin and has high resistance, unlike the wire inside, so in usual DC conduction, surface current is considered negligible. $\endgroup$
    – Ján Lalinský
    Commented Aug 8 at 13:44

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The entire wire feels a constant $\vec E=\rho\vec J$ field, and the constant $\vec J$ flow of current means that every bit of the surface charge that flowed tangentially to the next bit of the wire, is also being replaced by the charge that is coming from the back that flows into it. This steady state of affairs means that the non-uniform surface charge is easily kept there, and does not diminish away, at least until the power supply or battery stops supplying either of voltage or current.

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  • $\begingroup$ so, your idea is that the surface charges actually flow too as bulk charges, but the distribution is constant. Right? If it is the case, then I find a phrase “stationary surface charges”, which I came across in the internet several times, to be quite confusing. It is distribution of the surface charges that stationary, not surface charges themselves. $\endgroup$
    – Alexandr
    Commented Aug 8 at 10:28
  • $\begingroup$ Yes, but "distribution of the surface charges" is a mouthful. $\endgroup$
    – naturallyInconsistent
    Commented Aug 8 at 10:35
  • $\begingroup$ P.S. In textbook Physics for Scientists and Engineers by Randall D. Knight there is the following text: "Note that the surface charges are not the moving charges of the current. Further, the current—the moving charges—is inside the wire, not on the surface. " What do you think about that? $\endgroup$
    – Alexandr
    Commented Aug 8 at 13:37
  • $\begingroup$ That is not a big disagreement. The surface current flow is not a big contributor. In fact, the magnetic field produced by the the general current flow tends to bind the current into the centre of the wire (in the DC case; only in the high frequency AC case is skin effect important) and so the contribution due to the surface current flow is necessarily not big $\endgroup$
    – naturallyInconsistent
    Commented Aug 8 at 14:55
  • $\begingroup$ Frankly speaking, I thought the same. Thank you again! $\endgroup$
    – Alexandr
    Commented Aug 8 at 15:29

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