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Consider an electrically neutral wire carrying a uniform current $I$ driven by a dc battery. It definitely produces a magnetic field at points around the wire which we can calculate using the Biot-Savart law or Ampere's law. I was wondering whether it also produces an electric field. My guess is "No". Though the mobile electrons are moving through the wire, at any instant of time each little piece of the wire remains electrically neutral. There is no unneutralized charge. So it produces no electric field outside. Does it stand to reason?

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  • $\begingroup$ What do you mean by a "neutral wire"? It has a definite meaning in AC power distribution systems. But I'm not sure how you are using it in a battery circuit. $\endgroup$
    – Bob D
    Jul 18, 2022 at 14:01
  • $\begingroup$ I mean that the wire is not charged by rubbing it, by induction etc. $\endgroup$ Jul 18, 2022 at 14:04
  • $\begingroup$ In reality, yes. There are induced surface charges on the outside of the wire. Hence why you get a shock when you touch it. If no E field existed outside of a wire, you would feel no shock. However we mostly model wires as having no net charge density but non zero current density [a positive charge density, and occupying the same space , a sea of moving negative charge]. Even if there was no surface charges then there would still be an E field, but net zero average.I would like to add that a changing curent produces an induced electric field which cannot be ignored when analysing wave behavour $\endgroup$ Jul 18, 2022 at 14:04

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If the wire is at a different electrical potential than surrounding objects, it will have an electric field. The electrons in the wire will position themselves to support this field.

The charge imbalance in situations like this is extremely small (picocoulombs) from a material science or chemical perspective. A coulomb is only about 10^-5 mole of electrons. So, it is common to consider charge to be in balance in these problems.

This is a case where potential is a much more illuminating concept than charge.

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