What causes the potential energy in non-submerged electrons?

[jaydnul]

The water analogy can be used as a rudimentary tool to describe an electronic circuit, but in the case of voltage on a wire, it is exactly analogous. When a voltage on a wire is induced, the power supply or battery is shoving excess charge (which moves to the surface of the conductor) into the copper. Yes there is an electric field running through the wire, but that field is a product of the extra charge on the surface of the conductor. The more charge you shove onto the surface of the wire, the higher the voltage (with a constant reference).

So why isn't voltage explained exactly like this to beginners? Instead of starting with the electric field running through the wire, why not just explain it as electron pressure? Is this just a subjective case where it's more intuitive to only myself?

 

[mfb]

The excess charge is not proportional to anything useful or relevant in the circuit, and it is extremely tiny in most setups.

 

[axmls]

They're not exactly analogous. Pressure is an absolute quantity: the force per unit area. Voltage is relative and only makes physical sense when speaking of a voltage difference.

 

[sophiecentaur]

the electric field running through the wire,

That isn't the way it's taught. Voltage is usually presented as the Energy transferred for a unit charge passing. (1V = 1Joule per Coulomb); hence it corresponds a change of potential energy (a scalar) and no force (a vector) is involved. A field doesn't "run through" anything.
The water analogy always seems totally pointless to me. It merely puts off the problem of acknowledging that is is not complete enough and gives a false sense of 'understanding'. This is a common topic on PF and there is a split between people who want to do it 'properly' and people who think you can get away with it. IMO, those people have just not followed it deeply enough to find the serious flaw.

Is this just a subjective case where it's more intuitive to only myself?

I think that's exactly the problem. The personal model is not a valid one because you have not used the terms in their conventional sense.

 

[jaydnul]

That isn't the way it's taught. Voltage is usually presented as the Energy transferred for a unit charge passing. (1V = 1Joule per Coulomb); hence it corresponds a change of potential energy (a scalar) and no force (a vector) is involved.

Ok, but where does the electron get the extra potential energy? What does the power supply actually do to the charge in the copper wire?

 

[davenn]

Ok, but where does the electron get the extra potential energy?

It comes from the potential difference between the terminals of the power supply, measured in volts

 

[jaydnul]

It comes from the potential difference between the terminals of the power supply, measured in volts

Yes, but how does the power supply bestow this difference in potential, physically? A generator moves the electrons through a magnetic field, which gives them a higher potential energy and pushes them along the wire. But what about the electrons that aren't submerged in the magnetic field? Where do they get the higher potential energy? The only logical conclusion I can come to is that they are being pushed along by their neighboring electrons.

 

[sophiecentaur]

The only logical conclusion I can come to is that they are being pushed along by their neighboring electrons.

In a conceptual sense, that's ok but does it help in any way with 'understanding' and using circuits?
It is true that charges will flow when there is an unbalanced charge. I think it's valid to talk of an 'individual' electron being attracted more in one direction than another so you have to be able to make an explanation in terms of the local forces on all the electrons (and Protons) around the circuit. The problem with approaching electric circuits in this way is that the calculations would become very involved and to what end? Fields (Volts per metre) must exist in a wire and must cause net electron drift. If you want to include this in the understanding of circuit behaviour then the routing and length of the conductors would need to be involved for every circuit you considered. Conventional circuit theory can be hard enough and I suggest that all the extra ideas that your model introduces do not simplify anything - just make it harder. This approach is just not a good way to work out what circuits are doing. There are many papers published that study the details of transfer of power in circuits in this way - but the guys who are doing the theory measurements will still base the design their circuits in the conventional way and will 'understand' what they're doing from the standpoint of the Elelctrical Theory they learned originally.

 

[jaydnul]

The excess charge is not proportional to anything useful or relevant in the circuit, and it is extremely tiny in most setups.

The energy per electron (voltage) is inversely proportional to the distance between electrons $V=k\frac{e}{r}$ (for a 1 dimensional wire with an idealized setup). And the distance between electrons is inversely proportional to the density of electrons (excess charge) on the wire $D_e=\frac{C}{m}$. So the voltage IS directly proportional to the excess charge.

I realize that pressure is the incorrect terminology, but the general idea is that the electrons in a wire are separated by an average distance. As you shorten that average distance, the voltage becomes higher. If two wires at different voltages come into contact, the respective average distances will reach equilibrium until the combined wires are the same voltage (which is now the average of the two separate voltages).

So this extremely tiny excess charge is all you need to get usable voltages in electronics, and all a power supply does is keep the voltages from reaching equillibrium by continually sourcing/sinking charges to keep the electron densities on each lead constant.

Please share your thoughts and also thanks for all the input so far!

 

[mfb]

There are no ideal 1D wires. Your wire would still have a logarithmic divergence, and an actual 3D object has an even worse divergence. That approach does not work. You can use capacitance to find the excess charge.
A related thread.

 

[jaydnul]

Ok, this is one of those things that I thought I had down for a while now and I liked the model because of its simplicity (to me). It's great when something I think I know is proven completely wrong (even something as elementary as this) because it reminds me that nature doesn't care what I like and just is the way it is.

Anyways, thanks for all the help!

 

[jaydnul]

Sorry to post on this thread again but I didn't wan't to start a new one just for supplemental questions.

I think I have it worked out, I just want to make sure it's correct. So the charge density of the electron sea (the charge that moves and makes up the current) in the copper is more or less constant and has no significant correlation to anything in the circuit. However, the density of extra charge on the surface of the wire does vary, and this is what causes the electric field through the wire that gives the electron sea a reason to move (voltage). A power source essentially just provides extra charge to go onto the surface of the wire to create an electric field throughout. Is this correct?

 

[ZapperZ]

Sorry to post on this thread again but I didn't wan't to start a new one just for supplemental questions.

I think I have it worked out, I just want to make sure it's correct. So the charge density of the electron sea (the charge that moves and makes up the current) in the copper is more or less constant and has no significant correlation to anything in the circuit. However, the density of extra charge on the surface of the wire does vary, and this is what causes the electric field through the wire that gives the electron sea a reason to move (voltage). A power source essentially just provides extra charge to go onto the surface of the wire to create an electric field throughout. Is this correct?

What exactly are you basing this on? This is not what the Drude model is, nor is it what is used in the Boltzmann transport model, both of which are extensively used in Solid State physics.

Are you making up your own theory?

Zz.

 

[mfb]

However, the density of extra charge on the surface of the wire does vary

As discussed in the last posts: not in a way that would be useful for circuit analysis in any way.

 

[jaydnul]

So if the extra charge doesn't cause the potential, what does?

What exactly are you basing this on? This is not what the Drude model is, nor is it what is used in the Boltzmann transport model, both of which are extensively used in Solid State physics.

Are you making up your own theory?

Zz.

It's what I took from this text. Not saying it's right, hence the question "is this correct" at the end of the post.

I understand you have to be abrasive with people to deter crackpots, but sometimes it can be unwarranted.

http://www.matterandinteractions.org/Content/Articles/circuit.pdf

On pg.10, last paragraph: "The surface charge density is proportional to the circuit voltage..."

http://www.matterandinteractions.org/Content/Articles/circuit.pdf

Pg. 15, part A:

"Inside a resistive wire 1 meter long connected to a 3 volt battery, the electric field is only 3 volts/meter, which is tiny compared with typical fields encountered in electrostatic phenomena (for example, the breakdown strength of air is about 3 million volts/meter). Therefore, the amount of surface charge on the wires of a typical circuit is extremely small compared to typical electrostatic charges, which is why it requires high-voltage circuits to observe electrostatic effects. However, these small amounts of charge are responsible for driving the current inside the wire"

 

[sophiecentaur]

So if the extra charge doesn't cause the potential, what does?

Consider a different context for potential energy. Would you say it is the strain energy in a spring that 'causes' the potential energy of the mass that you're lifting with the spring or is it your arm muscles? The spring is an intermediate step in the energy transfer and the stretched spring will actually store some of the energy input. If the spring has a very high k, you can ignore this energy. Likewise, the equivalent 'k' for the wire full of electrons is equally high and you may as well ignore it. That 'k' is actually the dielectric constant of the metal, which is virtually infinite.

 

[jaydnul]

Consider a different context for potential energy. Would you say it is the strain energy in a spring that 'causes' the potential energy of the mass that you're lifting with the spring or is it your arm muscles? The spring is an intermediate step in the energy transfer and the stretched spring will actually store some of the energy input. If the spring has a very high k, you can ignore this energy. Likewise, the equivalent 'k' for the wire full of electrons is equally high and you may as well ignore it. That 'k' is actually the dielectric constant of the metal, which is virtually infinite.

So in your analogy, the battery is the arm muscle, and it does work to increase the electric field within the wire. But my problem is still this; the definition of dielectric constant is "a quantity measuring the ability of a substance to store electrical energy in an electric field".

My question is what is the wire doing to "store electrical energy in an electric field"? The links I referred to in previous posts claim that the small amount of excess charge on the surface of the wire IS the cause of this electric field. But mfb says that the excess charge has nothing to do with anything useful.

Hopefully you can see my confusion. Thanks for the help so far!

 

[sophiecentaur]

"a quantity measuring the ability of a substance to store electrical energy in an electric field".

That is a qualitative description. Used in a formula, it is a constant relating charge displacement and applied voltage.
Have you thought of approaching this Mathematically instead of arm waving? I am always wary of the "what's really happening?" approach instead of the "Model to fit the facts" approach. I have no argument at all with mfb's approach. I don't think it clashes with anything I wrote (?). The "excess charge" in a wire, due to the PDs in the circuit is not relevant because the wire is the equivalent of "a very strong spring" which will not stretch.

 

[sophiecentaur]

what is the wire doing to "store electrical energy in an electric field"?

The wire is not storing any energy - that's my point (a very strong spring that will not stretch and cannot store any energy under the conditions of the experiment).

 

[jaydnul]

http://www.matterandinteractions.org/Content/Articles/circuit.pdf

Bruce A. Sherwood and Ruth W. Chabay from Carnegie Mellon University seem to think that the excess charge on the surface of the wire is responsible for the electric field running through the wire. My question is, are they wrong? Or am I not understanding what they are saying.

BTW, I'm not trying to appeal to some other scientific authorities, I'm just genuinely curious about the split in opinion between you guys and these guys.

Maybe there isn't a split and I'm just not getting it...

 

[mfb]

Please don't make multiple posts in a row, if you would like to add something you can edit your post. I merged some of them.

Bruce A. Sherwood and Ruth W. Chabay from Carnegie Mellon University seem to think that the excess charge on the surface of the wire is responsible for the electric field running through the wire.

It is a possible view, but I don't think it is a useful one.

 

[jaydnul]

Please don't make multiple posts in a row, if you would like to add something you can edit your post. I merged some of them.

It is a possible view, but I don't think it is a useful one.

Oh ok, sorry. Probably says that somewhere in the forum rules, it's just been a while.

So it's not supported by evidence?Edit:

You said:

The excess charge is not proportional to anything useful or relevant in the circuit, and it is extremely tiny in most setups.

And Bruce A. Sherwood and Ruth W. Chabay in this http://www.matterandinteractions.org/Content/Articles/circuit.pdf on pg.10, last paragraph said:

"The surface charge density is proportional to the circuit voltage..."

This specific claim can be tested in the lab, and you directly contradict them. So, I'm sorry, but saying...

It is a possible view, but I don't think it is a useful one.

...doesn't really fly in this situation. Now I haven't done, nor do I have the means to do the experiment, which is why I'm asking on PF.

 

[sophiecentaur]

excess charge on the surface of the wire is responsible for the electric field running through the wire.

What do you mean by the word "responsible"? Surely it is the emf at the source end that is "responsible". Logically, that isn't the end of it, of course and you could take the responsibility right the way back to the Big Bang. I can only repeat my previous argument in a slightly different form. The field and the charge situation are both 'just there' because of the existence of an emf somewhere else - which produces a potential difference. Unless you can claim that there is significant difference in the charge density in a wire, when you switch on, then (as in the strong spring), there is no deformation and no storage of energy.
I read this article before and I noted that it was written by 'Educationists", which makes me wonder. I could find just one serious equation in the whole paper and no mathematical proof or evidence of measurements. That's a good reason not to take its message too seriously. It's hardly at a higher level than a chat on PF.
The order of the field / charge thing seems upside down. If you put a conductor in an electric field, charges will flow, to reduce the Potential Energy situation. If you put charges on each end of a wire (briefly) they will flow and eliminate any field that you started off with. To maintain that field, you need to be doing work on moving the charges.
Bottom line is that I don't see where this 'alternative thing' is going.
The reason for the "split in opinion" is, I think, that those guys have not actually tried to apply their ideas to a real situation, needing results. In an arm waving sort of a way, their case is arguable - not complete nonsense ; they want a model that they can present to students (without any health warning which worries me). But they have no quantitative (apparently) evidence or an idea to what degree it applies and no equations. That, to me, is pretty relevant.

 

[jaydnul]

Cool, that's all I was looking for. I'd still like mfb to address my previous post. If the excess charge doesn't proportionally increase/decrease with an increase/decrease in voltage, what is causing the excess charge in the first place?

 

[sophiecentaur]

There will be Capacitance between the wires and components. It isn't surprising that there are - charges detected at the - terminal because Q = CV applies, and so on round the circuit. But that doesn't mean that the charges are the 'cause' of the current. If the circuit has finite resistance then those charges will move due to the Potential Difference.
You may say 'why use an energy rather than a field description of what's happening?' It's because the field based description would involve a total re-write of the circuit equations if the wires were re-routed or shortened just to result in the same answer! That is hardly a good system for circuit analysis and it would be guaranteed to confuse students..

 

[mfb]

So it's not supported by evidence?

I didn't say anything that would suggest this.

It's like trying to understand every single transistor in a computer on an atomic level in order to visit a webpage. You can try (and in principle it is possible), but it won't help you.

"The surface charge density is proportional to the circuit voltage..."

And what is "the circuit voltage" in a circuit of any relevant complexity? Voltage relative to what? In their extremely simple circuit this is true - but even there, the proportionality constant depends on details of the cables and their layout.

If the excess charge doesn't proportionally increase/decrease with an increase/decrease in voltage, what is causing the excess charge in the first place?

Why would anything have to be proportional to be related?

 

[jaydnul]

It's like trying to understand every single transistor in a computer on an atomic level in order to visit a webpage. You can try (and in principle it is possible), but it won't help you.

I'm not looking to do circuit analysis with this information. I see now that my first post would give this impression, but I'm motivated purely by curiosity at this point.

My takeaways
-the wire is not storing energy
-the excess charge is due to the mutual capacitive effects of the circuit components/wires

My question is still this: What physically happens to the electrons in a wire when their potential energy is increased? Voltage is defined as energy per charge, so as voltage increases in a wire (relative to the starting voltage), each charge is getting a greater potential energy. The energy has to come from somewhere, and that somewhere is the power supply. So what does the power supply actually do to the charge in the wire to increase their potential energies?

 

[sophiecentaur]

What physically happens to the electrons in a wire when their potential energy is increased?

I could just as easily ask you what happens, physically, to a stone when it is lifted up. The energy is by virtue of its position (separation from the centre of the Earth). It takes two to tango and it is the relationship between an electron and with all the other charges and fields around that gives it Potential Energy. It is only because the rest of the system is so huge that we talk of the electron as being the one with the energy.

what does the power supply actually do to the charge in the wire

Are you after a 'mechanical' picture of things? We can't allow "pushing" electrons around like little balls, I'm afraid! I do get the feeling that you could accept an idea based on electrons having kinetic energy (but they have no significant amount of that) or a good water flow model (they all let you down). I think it is unreasonable to expect just a mechanical model to be enough. Electricity is a model on its own; is it because it involves both Electricity and Magnetism with orthogonal fields. There are a number of analogies that can be applied but they are only analogies, telling you nothing about what's really happening. Imo, the only analogy that you can rely on is the Mathematical one, which will deliver as long as you obey the rules.
Unsatisfactory perhaps?

 

[Dale]

Personally, I think that KVL and KCL are such simple laws that they don't need further simplification. Analogies to phenomena like pressure and hydraulics are amusing, but the laws governing pipes and fluid flow are much more complicated than the circuit laws.

Why complicate a simple theory?

 

[mfb]

-the wire is not storing energy

A tiny amount due to its capacitance. Completely negligible in most cases.

 

[jaydnul]

I am not asking for a simplification or new way of analyzing circuits! Take this hypothetical situation:

I am given the task of raising the potential difference across a device to the value x. Theoretically I could create a generator; I know that moving charge in a magnetic field will create an emf. The magnetic field causes the electrons to have a higher potential. But I still don't know how the electrons are going to leave the magnetic field and out into more wire (where there is no magnetic field to raise their potential).

Now I'm asking what causes the electrons who aren't submerged in the magnetic field to have a higher potential energy. We've already established that electron on electron interactions don't, as well as excess charge on the surface. So what causes this higher potential in the non-submerged electrons? You said it here:

It takes two to tango and it is the relationship between an electron and with all the other charges and fields around that gives it Potential Energy.

I'm just asking for an extrapolation of this. What charges and what fields?

Edit:
I realize that referencing another forum post is not the most rigorous proof, but the answerer here also seems to think that excess charge on the surface of the metal is responsible for the electric field that pushes the electrons. mfb, please look at this and explain to me why they are also incorrect:

http://physics.stackexchange.com/questions/17741/how-does-electricity-propagate-in-a-conductor

 

[sophiecentaur]

What charges and what fields?

I meant the whole caboodle - charges of the local charged particles and the magnetic and electric fields of the whole system and the way all that is modified by the presence of our electron and what it's doing. It's not useful to take an electron in isolation (in this sort of context).
I looked at that link and it proposes what looks to me like a novel idea without support from references. If you want to clear this up, you should really be reading more mainstream stuff to avoid further confusion.
I don't always quote references when my source is mainly from mainstream textbooks - but that link is not textbook stuff; it's a personal view.

I have just thought of a clincher argument about this. Electrons, in the solid state, are essentially Quantum Particles. They do not behave in a classical way and the whole of this thread has been assuming they do. It is not surprising that trying to describe a QM phenomenon in classical terms doesn't get us far. I think that should let you off the hook when you feel you should be able to explain this sort of situation in this particular way.

 

[jaydnul]

I realize it's a quantum system, but energy is still conserved. At one moment you're saying that the emf in the wire IS induced by local charged particles and the electric and magnetic fields of the whole system, and the next moment you're saying it is an invalid question because the electrons behave quantum mechanically. The reason I am being so persistent is because we have explanations like this for some parts, and then other parts we say that it is an invalid question. I'll illuminate that point by asking one more time in the following fashion (and then I'll stop haha).

Please help me answer the second question:
Q1. Why do the electrons in a wire feel a force when inside a generator?
A: They are moving relative to a magnetic field which induces an emf and raises their potential energy. Edit: Relative to some reference voltage (didn't want to get picked up on that )
Q2: Why do the electrons in a wire feel a force when outside a generator (but connected to the wires that are inside the generator)?
A:?

Do we not know? Is it as simple as that? You said local charged particles and the electric and magnetic fields of the whole system. Great, but those charged particles and electric/magnetic fields must undergo a change from their initial (unconnected wire) state in such a way that corresponds to the change in potential; if no charge moved around, or if no electric field changed in magnitude, nothing would happen in the wire.

BTW, the first link I posted was from a (what I thought) mainstream textbook. Though it looks like it was written by the same people who published that website...

 

[Dale]

I'm just asking for an extrapolation of this. What charges and what fields?

Why would you bring fields into a circuits class? Circuit theory doesn't use the concept of a field at all.

I would teach circuits first, and Maxwell's equations later and I would avoid bringing Maxwell's concepts into a circuits class as much as possible, except to mention that they exist and will be covered in later classes. I don't see the desire to complicate circuit theory nor to teach Maxwell's equations half way.

 

[jaydnul]

Why would you bring fields into a circuits class?

I'm not looking to do circuit analysis with this information. I see now that my first post would give this impression, but I'm motivated purely by curiosity at this point.