# How does the electric field propagates through a wire?

1. Sep 17, 2015

### jaydnul

A recent thread of mine eventually evolved into this question, but did not start off that way. I think the initial post was poorly worded and didn't ask the same question that the thread eventually became about, so I figured I'd post a new thread to directly address it.

First let me start by stating a few things, and please correct me if I'm wrong.

1. An electric field is generated by a charged particle.
2. When a charged particle is submerged in an increasing electric field, it's electric potential energy is also increasing.
3. An electric field is present inside a wire when there is current flowing.
4. (Redux of statement 1.) The electric field inside the wire is generated by an arrangement of charged particles.

Now my question is about statement 4. In my previous thread, it was said that the excess charge on the wire was not responsible for the electric field within the wire. It was also said that electron-electron interactions were rare and were also not responsible (i.e. the electrons are not pushing themselves along the wire like a train).

Assuming my statements are correct, what charges are creating the electric field within the wire?

Thanks

2. Sep 17, 2015

### davenn

you are coming from a false premise on where the electric field is

have a read of this and see how it changes your views

http://www.physicsclassroom.com/Class/estatics/u8l4d.cfm

cheers
Dave

3. Sep 17, 2015

### rumborak

It's also worth pointing out that the wire itself carries little to none of the energy (after all, there is no field inside!). I would suggest reading the Wikipedia article about the Poynting vector.

4. Sep 17, 2015

### Staff: Mentor

When you say "generated" are you thinking "associated with" as in Maxwell's equations, or are you thinking "caused by" as in Jefimenkos equations?

This isn't true. The relationship between the field is more complicated than that, and the potential energy of a particle will be the opposite of the potential is the charge is negative.

Last edited: Sep 17, 2015
5. Sep 17, 2015

### jaydnul

So I understand that it's 0 at equilibrium, but when current is flowing there is still an electric field inside the wire, no?

Tell me if this correct: The electrons are attracted to the negative battery terminal and repelled by the positive battery terminal, that's why there is current.

6. Sep 17, 2015

### davenn

no, that's incorrect, the electric field is on the surface and out from the surface of the conductor

that's back to front
like charges repel, different charges attract

7. Sep 17, 2015

### Staff: Mentor

This would be true in an electrostatic situation, but charges in motion through a wire is not an electrostatic situation.

8. Sep 17, 2015

### jaydnul

Haha oops, what I meant. But is that correct?

Last edited: Sep 17, 2015
9. Sep 17, 2015

### davenn

yeah I may be wrong as well for a flowing charge ... cant find a reference yet to prove one way or the other

10. Sep 17, 2015

### Staff: Mentor

Yes. In a conductor $J=\sigma E$

11. Sep 17, 2015

### jaydnul

Thank you for referencing Jefimenkos equations. I had never heard of them before and they are really interesting.

On the other hand, I don't think that question matters here. The electric field is there because of a charged particle, and whether it is "associated with" or "caused by" is semantics. What I'm after is the location of the charged particles that the electric field is "associated with"/"caused by".

12. Sep 17, 2015

### davenn

This annoying the hell out of me LOL
I am taught that when there is a current ( flow of charge) the electric (EM) field is moving on the outside of the conductor and in the dielectric around it

13. Sep 17, 2015

### Staff: Mentor

I'm sorry, but if you don't answer that question then I don't know how to translate the English into the math in order to answer. It is purely semantic, of course, but communication is about semantics. I am trying to understand what question you are actually asking.

14. Sep 17, 2015

### jaydnul

Yes I'm sorry. I realize I'm probably not explaining my question well. I'm gonna try to ask in segments and await confirmation so I can pinpoint exactly where I'm confused (or not explaining properly).

Lets say the electric field in a wire is caused by charged particles (Jefimenko). Do those charged particles have a physical location in the 3 dimensional volume of the wire?

15. Sep 17, 2015

### Staff: Mentor

The equation I posted is the continuum form of Ohm's law. It is the defining equation for Ohmic materials.
https://en.m.wikipedia.org/wiki/Ohm's_law

You may be thinking of the skin effect.
https://en.m.wikipedia.org/wiki/Skin_effect

16. Sep 17, 2015

### Staff: Mentor

You have to include time also, particularly for AC circuits, and the battery, even for DC.

So using Jefimenko's equations, the easiest way to think about it is in terms of the scalar and vector potentials.
https://en.m.wikipedia.org/wiki/Jefimenko's_equations#Origin_from_retarded_potentials

The potential at a given point in space and time is caused by charges and currents at all other points in space at the retarded time.

17. Sep 17, 2015

### jaydnul

I understand this, and I realize now that we are not on the same page, which is my fault. Let me reiterate what you just said.

The potential at a point and time in the wire is caused by the charges at all other points in the wire at the retarded time. Now my question is, when the potential at that point changes, that means the the charges at the other points moved from those points at the retarded time, yes?

Last edited: Sep 18, 2015
18. Sep 18, 2015

### Staff: Mentor

Yes, but including all points in the wires and the battery.

Yes.

19. Sep 18, 2015

### jaydnul

Ok, now I'm wondering about the manner in which those charges move. The electrons at the end of the wire will move when the wire is connected to the terminals of the battery at the retarded time. But how does the charge towards the middle of a long wire feel a force? Are they being pushed along by their neighboring electrons?

20. Sep 18, 2015

### Staff: Mentor

Neither Jefimenko's equations nor Maxwell's equations cover the motion of the charges in response to the imposed fields. For that you need some description of the electromagnetic behavior of the material. Microscopically all you need is the Lorentz force law, but macroscopically you usually use things like Ohm's law and constitutive equations.

Last edited: Sep 19, 2015
21. Sep 18, 2015

### jaydnul

$F=q[E+(vBsin\theta)]$ tells me that the charge I'm looking at in the wire will feel a force when submerged in an electric and/or magnetic field. Are those fields being caused by other electrons in the electron sea of the metal?

22. Sep 19, 2015

### Staff: Mentor

They are caused by all of the electrons and protons in the wire and all of the other electrical components.

23. Sep 19, 2015

### jaydnul

Ok. So in order for an electron in the wire to be at a higher potential, other negative charges must get closer to it AND/OR other positive charges must get further away, yes?

24. Sep 19, 2015

### Staff: Mentor

Almost. You have the right idea, but a higher potential is near positive charges and far from negative charges.

25. Sep 19, 2015

### jaydnul

Oh yea, good point. Last question (then I'll stop haha):

Since electrons are the mobile charge carriers in a metal, a change in voltage means a chance in electron density, yea?