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When I connect a battery across the two ends of a copper wire, the electric field set up in the wire will follow the direction of the wire, no matter how weirdly the wire is bent. How does this happen? Why does the electric field not shoot out from any point on the wire?

I am thinking that something similar happens to magnetic field, and it gets concentrated through materials like iron in the core of a transformer. I don't know the reason for that either.

Assuming that the wire has a uniform resistance per unit length, please answer this question, with reference to distributed element models (and not lumped element models).

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Note: I know that one should not connect terminals of a battery with a copper wire directly, it can cause the battery to burn. The visual is only a creative representation of my question.

Vincent Thacker
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VedantBang
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    A conducting wire actually expels the electric field, which exists only outside the wire (we say that the wire has an equipotential surface). Rather obviously, current flows through conductors but not insulators. You need to clarify what you are asking. – Guy Inchbald Jul 23 '21 at 07:40
  • No I'm asking about a real wire, one with resistance. So the potential keeps dropping along the wire. In such a wire, it is the electric field, which causes electrons to move along, right? – VedantBang Jul 23 '21 at 07:54
  • OK. But there is still an external field, it's more a case of the conducting wire distorting the field. It's not so much the field shooting out, as the resistance allowing some of the field in. From Ohm's law, V=IR, you can calculate the field potential drop per unit length of wire. – Guy Inchbald Jul 23 '21 at 10:06
  • Okay so, non ideal conductors allow some electric field into themselves. Is it related to how different magnetic materials allow different amount of magnetic fields into themselves? Referring to this as an example. – VedantBang Jul 23 '21 at 11:38
  • No, it is rather different. The electric analogue to magnetic permeability is dielectric permittivity, which is not the same as conductivity. – Guy Inchbald Jul 23 '21 at 16:44

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That's a very good question. The process of starting a current in a wire is actually quite complex. Quite a lot happens before the circuit is complete: as you move the wire towards the first battery terminal it encounters the dipole-like electric field between the two terminals. Charges flow in the wire to maintain it at an equipotential, and this results in a distribution of charge around the outside surface of the wire, cancelling within the wire the $\mathbf{E}$ from the battery. The end result of this process is that the dipole-like field exists between the other terminal and the far end of the wire. (Of course we are assumuing that it is always possible for an electrostatic charge configuration to make the wire an equipotential, regardless of the complexity of the path it follows. I don't know of anyone who has addressed that question, although the fact that current will continue to flow as long as there is field within the conductor makes it plausible. But can that be made into a sceptic-proof argument?)

Then as the wire approaches then second terminal the same process continues, maintaining the wire as an equipotential. Finally, when contact is made, a voltage step travels at the speed of light round the circuit initiating the current flow. The voltage step weakens as it travels in proportion to the resistance it encounters, and there is probably some transient oscillatory behaviour before the DC situation is established.

I don't know of a detailed integrated account of this process backed by calculation or modelling, elementary though it is. It's just assumed. The problem is that it depends in detail on the specific geometry, and that makes analytic calculation possible only for unrealistic simplified models.

CWPP
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  • Thank you, this seems viable to me. Is this analogous to the way ferromagnetic materials pull magnetic field inside their bodies? (I hope 'body' is the right term) I have seen diagrams where initially straight magnetic field lines flow in a concentrated manner through a piece of iron. – VedantBang Jul 23 '21 at 12:33
  • @VedantBang I think it's not very closely analogous to trhe ferromagnetic case, because the 'expulsion of the field' is caused by a current flow. The ferromagnetic example is more closely analogous to the distribution of current in a non-homogeneous conductor, or the distribution of current in a lump of material with unsymmetrical shape. – CWPP Jul 23 '21 at 13:00