How does the electric field propagates through a wire?

[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

 

[davenn]

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

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.cfmcheers
Dave

 

[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.

 

[Dale]

1. An electric field is generated by a charged particle.

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

2. When a charged particle is submerged in an increasing electric field, it's electric potential energy is also increasing.

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.

 

[jaydnul]

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.cfmcheers
Dave

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.

 

[davenn]

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

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

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.

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

 

[jtbell]

(after all, there is no field inside [the wire]!)

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

 

[jaydnul]

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

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

 

[davenn]

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

yeah I may be wrong as well for a flowing charge ... can't find a reference yet to prove one way or the other

 

[Dale]

when current is flowing there is still an electric field inside the wire, no?

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

 

[jaydnul]

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

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".

 

[davenn]

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

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

can you clarify please

 

[Dale]

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".

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.

 

[jaydnul]

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.

Yes I'm sorry. I realize I'm probably not explaining my question well. I'm going to 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?

 

[Dale]

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

can you clarify please

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

 

[Dale]

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?

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.

 

[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?

 

[Dale]

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.

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

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?

Yes.

 

[jaydnul]

Yes.

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?

 

[Dale]

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?

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.

 

[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?

 

[Dale]

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

 

[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?

 

[Dale]

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

 

[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?

 

[Dale]

If there is only metal present, yes, but that is rarely the case.

By the way, in the previous posts, by voltage or potential I assume we are talking about the scalar potential and specifically in the Lorenz gauge.

 

[jaydnul]

If there is only metal present, yes, but that is rarely the case.

But IN the metal, this is how the voltage is transferred to the different 'non-metal' components, yes?

Edit:

By the way, in the previous posts, by voltage or potential I assume we are talking about the scalar potential and specifically in the Lorenz gauge.

Yea, I assumed we were talking scalar potential.

 

[Dale]

But IN the metal, this is how the voltage is transferred to the different 'non-metal' components, yes?

No. You are forgetting that the retarded potential in Jefimenkos equations includes contributions from everywhere. So if you have both metals and non metals present then the voltage at every point depends on the charge density everywhere (at the retarded time), not just in the metal. So at every point there can be changes in potential which happen due to movement of negative charges in the metal but also changes which happen due to movement of positive charges in the non metals.

That said, I am not sure why you are focused on the electrons specifically. It doesn't matter if the charge carriers are positive or negative.

 

[jaydnul]

No. You are forgetting that the retarded potential in Jefimenkos equations includes contributions from everywhere. So if you have both metals and non metals present then the voltage at every point depends on the charge density everywhere (at the retarded time), not just in the metal. So at every point there can be changes in potential which happen due to movement of negative charges in the metal but also changes which happen due to movement of positive charges in the non metals.

That said, I am not sure why you are focused on the electrons specifically. It doesn't matter if the charge carriers are positive or negative.

Ok cool, you've completely cleared up my confusion on this. Thanks a bunch DaleSpam!

 

[Dale]

Welcome! Glad I could help.