# A question about an electron’s movement in a DC circuit

Tiger
I have been thinking of the nature of the electric current , or the motion of electrons in a copper cable of a closed DC circuit. Recently I learned the speed of electron is very slow in the copper cable and in a AC circuit the FREE ELECTRONS are in fact moving back and forth. But in a DC circuit, if enough long time is given, will a specific electron finally move though the cable and power source and come to the point it started motion? That is my question. Thanks for enlighten me.

Delta2

## Answers and Replies

Homework Helper
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In QM all electrons are indistinguishable, so there's no experiment that could identify one electron over another. Fundamentally, therefore, it makes no sense to talk about specific electrons.

Tiger
Thanks. Perok. Okay let's talk about all the electrons in the copper wire in a DC circuit. Are they moving in the circuit one loop after another loop? I want to understand how they move in a DC circuit. Electric current speed is light speed that is for sure. I learned electrons are moving in the wire, slowly. That's where my question came from. Thank again.

Homework Helper
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Thanks. Perok. Okay let's talk about all the electrons in the copper wire in a DC circuit. Are they moving in the circuit one loop after another loop? I want to understand how they move in a DC circuit. Electric current speed is light speed that is for sure. I learned electrons are moving in the wire, slowly. That's where my question came from. Thank again.
Explaining a DC circuit in QM terms won't be simple. It's more straightforward to explain it in terms of classical EM theory.

https://control.com/textbook/dc-electricity/electrical-current/

sophiecentaur and vanhees71
mitochan
Hi. Drift velocity of electrons are average velocity of electrons relating to EM energy transmission. For 1 A current in 1mm diameter copper wire it is order of mm/s.
You may know free electrons move in metal like molecules in gas. Its speed of standard deviation around average zero in room temperature is 60 km/s >> mm/s. One particular electron could frequently reach the end of wire and bounce back as gas molecules bounces at container wall in long time of 1000 s = 1m circuit wire length / 1 mm/s .

Tiger

Below is from the link Perok sent. It says clearly electron is moving in the DC circuit. Very good. My quetions is, what is the speed, roughly? The moving speed of electrons, with negative charge.

If the poles of a voltage source are joined by a conductor, the free electrons within that conductor will drift toward the positive pole (electrons having a negative charge, opposite charges attracting one another). For each electron reaching the positive pole, an electron exits the negative pole of the source to replenish the total number of electrons in the flow. If the source of this voltage is continually replenished by chemical energy, mechanical energy, or some other form of energy, the free electrons will continually loop around this circular path. We call this unbroken path an electric circuit. The drifting motion of electrons in a circuit has the same average rate of flow (current) at all points in that circuit, because there is only one pathway for the current.

Delta2
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Below is from the link Perok sent. It says clearly electron is moving in the DC circuit. Very good. My quetions is, what is the speed, roughly? The moving speed of electrons, with negative charge.

If the poles of a voltage source are joined by a conductor, the free electrons within that conductor will drift toward the positive pole (electrons having a negative charge, opposite charges attracting one another). For each electron reaching the positive pole, an electron exits the negative pole of the source to replenish the total number of electrons in the flow. If the source of this voltage is continually replenished by chemical energy, mechanical energy, or some other form of energy, the free electrons will continually loop around this circular path. We call this unbroken path an electric circuit. The drifting motion of electrons in a circuit has the same average rate of flow (current) at all points in that circuit, because there is only one pathway for the current.
https://wtamu.edu/~cbaird/sq/2014/02/19/what-is-the-speed-of-electricity/

Staff Emeritus
In QM all electrons are indistinguishable, so there's no experiment that could identify one electron over another. Fundamentally, therefore, it makes no sense to talk about specific electrons.
It is not just QM. For decades energy financial analysts have been demanding to know the origin of the electrons coming out of a customer plug. They want to assign a value to each one and do a proper debit/credit analysis just like they do with other commodities.

My angst is that the minds of those analysis were poisoned at an early age by someone using the water analogy to teach electricity. That bell can not be un-rung.

dRic2, nasu, nsaspook and 3 others
Mentor
just like they do with other commodities.
To be fair... indistinguishability (within the parameters set by the contract definition) IS a foundational assumption of the commodities exchanges.

Vanadium 50, vanhees71 and PeroK
Staff Emeritus
To be fair... indistinguishability (within the parameters set by the contract definition) IS a foundational assumption of the commodities exchanges.
Ah yes. Commodity was a poor choice of words. They want to treat them as mass produced products like automobiles with VIN numbers.

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It is not just QM. For decades energy financial analysts have been demanding to know the origin of the electrons coming out of a customer plug. They want to assign a value to each one and do a proper debit/credit analysis just like they do with other commodities.

My angst is that the minds of those analysis were poisoned at an early age by someone using the water analogy to teach electricity. That bell can not be un-rung.
Well, the horrible thing is that the "water analogy" to teach electricity is now strongly supported by some physics didactic people with the pressure as the analog for the electrostatic potential :-(.

sophiecentaur, nsaspook, etotheipi and 1 other person
Staff Emeritus
Well, the horrible thing is that the "water analogy" to teach electricity is now strongly supported by some physics didactic people with the pressure as the analog for the electrostatic potential :-(.
Horrible yes. It wouldn't be so bad if they remembered power as pressure*flow, but in reality too many students come away with the mental image of a bucket full of energy and electrons as little capsules full of energy. Curiosity about time needed for the electrons to get to the far end of the wire is a clue to that mental model.

Homework Helper
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Horrible yes. It wouldn't be so bad if they remembered power as pressure*flow, but in reality too many students come away with the mental image of a bucket full of energy and electrons as little capsules full of energy. Curiosity about time needed for the electrons to get to the far end of the wire is a clue to that mental model.

View attachment 275098

Can we set @Tiger on the right track here?

Delta2
Well, the horrible thing is that the "water analogy" to teach electricity is now strongly supported by some physics didactic people with the pressure as the analog for the electrostatic potential :-(.

Old analogy joke.
1st year electrical apprentice: "Now tell me again, how does that voltage and current stuff work?"

Electrical instructor: "It's simple. Just think of it like water."

Meanwhile, over at the plumbers apprentice school:

1st year plumbing apprentice: "Now tell me again, how does that pressure and flow stuff work?"

Plumbing instructor: "It's simple. Just think of it like electricity."

vanhees71, nasu and PeroK
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Electric current speed is light speed that is for sure.

No it isn't

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The electron speed in household currents is tiny (of the order of millimetres per second). Nevertheless it's true that it's the speed of light (or almost the speed of light to be precise) with which the electromagnetic signal propagates which sets the electrons into motion in the wire.

Correspondingly also the energy transport is mostly electromagnetic field energy and not the mechanical energy of the electrons. The most simple example is a coaxial cable. Just calculate the electric and magnetic fields and then the Poynting vector!

A thorough discussion of the DC case can be found in

A. Sommerfeld, Lectures on Theoretical Physics, vol. 3 (electrodynamics).

PeroK
Tiger
Thanks guys for all the discussion. I understand now the drifting velocity is the actual motion speed of electrons in a copper wire in a DC circuit. Water flow analogy is not right. Misleading. Now I am thinking a lithium battery circuit as below. So when power source is ON, electrons start moving from cathode to anode via power source and Lithium-ion are moving from cathode to anode through intercalate. As the conclusion we get from previous discussion, the actual electron's moving speed is slow . I am now looking at below Lithium batter charging process. Can I say the reason we need wait hours to do the charging is because we need to wait those electrons to arrive anode （via power source) and lithium-ions to reach anode ( via Electrolyte )?

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The total current is of course not that small, because you have a huge number of electrons (and in this case also positive ions) around. You can easily make the current (i.e., the amount of charge going through the wire per unit time) very large and shorten the time for charging your Li battery. The only trouble is that this may destroy it, and that's why we rather charge our cell phones with lower currents to prolong the lifetime of the battery.

Tiger
Thanks. Vanhees71. So when I increase the power source voltage, there will be bigger electromagnetic field in the wire so it can push more electrons moving per unit time - a bigger current as a result. In that case should I say when voltage is not big, only a certain percentage of electrons in the wire can be pushed moving forward and the rest will stay. When voltage increase the percentage increase. Is that correct?

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No, all the conduction electrons move. The most simple classical model for the current is the Drude model. Though not entirely correct, because the right theory to describe the electrons in the conductor is quantum theory, it nevertheless gives a qualitatively correct picture.

The idea is that the metal consists of a lattice of positively charged ions and the conduction electrons moving more or less freely in this lattice. Now the lattice vibrates due to thermal motion and also the lattice is not perfect and all this effectively leads to friction for the conduction electrons. If you now put a voltage along the wire you have an electric field along the wire, which we can consider as constant. Then the equation of motion for a conduction electron is ##m \vec{a}=\vec{F}=-e \vec{E}-m \gamma \vec{v}##. Here ##(-e)## is the charge of an electron, ##m## the mass of the electron, and ##\gamma## the friction coefficient of the electron moving through the wire.

After some short time the flow of the electrons comes to a stationary state, i.e., the velocity of the electron gets just as large that the friction force compensates the electric force and the electrons then move with constant velocity, i.e., the acceleration ##\vec{a}=0##. This implies that
$$e \vec{E}=-m \gamma \vec{v} \; \Rightarrow\; \vec{v}=-e \vec{E}/(m \gamma).$$
Now you have a conduction-electron density ##n## in the metal, and the current density vector
$$\vec{j}=-n e \vec{v},$$
where ##|\vec{j}|## describes the number of electrons going through the cross section of the wire per unit area and per unit time. The direction tells you where the electrons move, and of course for a wire that's along the wire. From the above equation you now get
$$\vec{j}=-n e \vec{v}=\frac{n e^2}{m \gamma} \vec{E}=\sigma \vec{E}.$$
Here ##\sigma## is the electric conductivity of the material the wire is made of, and what we've derive here is just Ohm's Law in "local form".

To see how it is related to the more famliar Ohm's Law for DC circuit theory, we just note that the total current is ##i=A|\vec{j}|##, where ##A## is the cross-sectional area of the wire, and ##|\vec{E}|=U/L##, where ##U## is the voltage and ##L## the length of the wire. Plugging this into Ohm's law in local form we get
$$i=\frac{\sigma A}{L} U \stackrel{!}{=}\frac{U}{R},$$
where ##R## is the resistance of the wire. From this we get
$$R=\frac{L}{\sigma A}.$$
Often one uses the specific resistance ##\rho_{\Omega}=1/\sigma##. Then the formula reads
$$R=\frac{\rho L}{A}.$$
This makes intuitively sense: The longer the wire the longer the electrons need to move and the more friction they suffer. That's why the resistance becomes bigger the longer the wire is. On the other hand the larger the cross sectional area is the more electrons can move per unit area and time through the cross section, which is why the resistance gets smaller the larger the cross section of the wire is.

hutchphd and etotheipi
abcd112358
Horrible yes. It wouldn't be so bad if they remembered power as pressure*flow, but in reality too many students come away with the mental image of a bucket full of energy and electrons as little capsules full of energy. Curiosity about time needed for the electrons to get to the far end of the wire is a clue to that mental model.

View attachment 275098
What modle would you prefere techers to show young students, when first trying to make the abstract thing that is electricity a bit more available?
I know that some people have huge problems getting rid of wrong concepts later on, but when students learn about electricity in say 7th grade not giving them any mental image isn't the way to go either, in my oppinion.

Merlin3189
Tiger
Hi, Vanhees71. Thanks for your answer. A bit difficult for me to understand exactly. Can you simplify and tell me what is the difference between the 2 scenarios. A - Everything same but low voltage B everything same but high voltage. I mean in the charging circuit as the diagram. What is the difference in terms of the motion of the electrons, and the lithium-ions as well. Their actual drifting velocity is different?

Staff Emeritus
What modle would you prefere techers to show young students, when first trying to make the abstract thing that is electricity a bit more available?
I know that some people have huge problems getting rid of wrong concepts later on, but when students learn about electricity in say 7th grade not giving them any mental image isn't the way to go either, in my opinion.
Great question. It has been discussed some on other threads. I prefer to give several days thought and drafts before answering.

In short, I think physics and circuits should be taught in separate courses at different times and different paths. Circuit analysis (CA) is a trade craft. CA skills are not needed by everyone. CA is not very helpful as an first step to understand conduction or electrostatics/electrodynamics.

But in part, I am driven by experiences on PF. Many of the most confused questions posted on PF come from those who are attempting self teaching. The world could use an electricity study guide that targets those people.

abcd112358 and vanhees71
snorkack
Note that while electrons may be indistinguishable, Li nuclei are not. Li-6 cations have practically the same chemical properties as Li-7 cations, but are very distinguishable. So if you run a Li battery where part of the electrolyte consists of Li-6 and a part of electrolyte of Li-7, can you measure precisely where the division between Li-6 and Li-7 goes inside the battery, and how it moves with battery´ s state of charge?

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Hi, Vanhees71. Thanks for your answer. A bit difficult for me to understand exactly. Can you simplify and tell me what is the difference between the 2 scenarios. A - Everything same but low voltage B everything same but high voltage. I mean in the charging circuit as the diagram. What is the difference in terms of the motion of the electrons, and the lithium-ions as well. Their actual drifting velocity is different?
I talked only about the wire and the electrons in it, not about the ions. For electrolytes of course you have both ions and electrons in the solution moving. The qualitative theory a la Drude is not so much different. No matter whether the voltage is low or high all these charge carriers move but the higher the voltage the larger the drift velocities get and thus also the larger the current gets.

Gold Member
But in part, I am driven by experiences on PF. Many of the most confused questions posted on PF come from those who are attempting self teaching. The world could use an electricity study guide that targets those people.
I have to question the motives of the PF contributors who 'claim' to be teaching themselves. One can only 'teach' from a position of better knowledge than the 'student'. The term "teaching oneself" is a misnomer. The required process is actually "learning for oneself".

In many cases of attempted autodidacts, it's because they expect that their own path through a topic will be less demanding than if they follow a well structured course. I realize that personal tuition is not always available but without well curated information by a better informed source, there's always a massive risk of wasted time and effort following blind alleys in the process.

PF has a lot of input from people who want to learn Physics using Q and A, which is essentially on their terms. and it is very inefficient. There are dozens of textbooks (cheap when bought second hand) that will do the job and using two or three books is even better. The chapter and paragraph structures of most of them are very much the same and they all will suffer from not putting the information in exactly the same way that a student might wish. That's part of the necessary grind of learning any subject, though.

Vanadium 50, hutchphd, vanhees71 and 1 other person
What modle would you prefere techers to show young students, when first trying to make the abstract thing that is electricity a bit more available?
I know that some people have huge problems getting rid of wrong concepts later on, but when students learn about electricity in say 7th grade not giving them any mental image isn't the way to go either, in my oppinion.

How about something novel, use the correct physics concepts. Kids are amazing in their ability to assimilate absolutely new information as an article of faith.
https://www.abc.net.au/science/articles/2014/02/05/3937083.htm

nasu and sophiecentaur
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I think the main problem to teach DC (and even more AC) theory is indeed that you first need to understand the field concept to get an adequate picture. There's no way to understand even a simple DC circuit without the field concept, and using the hydro analogy which doesn't work, because the equations are already not the same, and there's no way to give the right picture of energy transport, as is nicely stated on the quoted webpage, and I think the suggested didactic concept is very promising.

What's, however, also not a good idea is to leave out vectors. You can't treat the electromagnetic field without at least a heuristic notion of vectors, and it's not so difficult since of course also children have an idea of direction and quantities that are only complete if you tell, in addition to their "magnitude", also a direction, like moving something around: To know where a car is you need to tell where you started and how far in which direction you drive. From this you get to the idea of velocity and acceleration as vectors too and so on.

The main obstacle is that you can't use vector calculus, but I think if you add the heuristic idea of vectors to the concept promoted in the webpage you have a good chance to teach (at least DC) circuits way better than with the hydro analogy.

To argue that indeed it's not the electrons transporting the electromagnetic energy along a wire is easy, once you derives that the drift velocity is very very slow (about 1mm/s). If this were true, turning on the light, would take a very long time, while in reality it's (almost) instantaneous.

Gold Member
How about something novel, use the correct physics concepts. Kids are amazing in their ability to assimilate absolutely new information as an article of faith.
https://www.abc.net.au/science/articles/2014/02/05/3937083.htm
It may make some people feel awkward but the concept, based on flow of charge (a continuum) was absolutely fine for me, at school in the early 60s.
We were told (and accepted) that we need go no deeper YET. Totally fine. The apparent problems come from the direction of the teachers and not the students.
Young people can happily deal with the weirdness of games so why not with Physics? We should give them credit for their abilities.

nsaspook
Gold Member
I think the main problem to teach DC (and even more AC) theory is indeed that you first need to understand the field concept to get an adequate picture.
I have to agree with you basically BUT you are looking at this from the point of view of someone who already knows the whole (or most of the) picture. Imo it would be a disaster to try to teach the subject in this way. Far too many balls in the air at once for a newbie.
I do hate the water analogy but it is only at the other extreme to your 'full treatment all at once".

And you have to ask yourself what you actually mean by the word "adequate". Water is "adequate' for many purposes but "adequate" would need QM or better for some others.

You can't do it all in one pass and V=IR is a pretty good formula that you can learn and it works for a vast number of problems.

Merlin3189
Tiger
I talked only about the wire and the electrons in it, not about the ions. For electrolytes of course you have both ions and electrons in the solution moving. The qualitative theory a la Drude is not so much different. No matter whether the voltage is low or high all these charge carriers move but the higher the voltage the larger the drift velocities get and thus also the larger the current gets.
Thanks. Vanhees71. I got the poit now. The higher the voltage, the faster the electrons move. Thank you

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I have to agree with you basically BUT you are looking at this from the point of view of someone who already knows the whole (or most of the) picture. Imo it would be a disaster to try to teach the subject in this way. Far too many balls in the air at once for a newbie.
I do hate the water analogy but it is only at the other extreme to your 'full treatment all at once".

And you have to ask yourself what you actually mean by the word "adequate". Water is "adequate' for many purposes but "adequate" would need QM or better for some others.

You can't do it all in one pass and V=IR is a pretty good formula that you can learn and it works for a vast number of problems.
Hm, but I find the way proposed in the above quoted website okish. It's of course not full Maxwell theory, which is out of reach at 7-10th grade, but at least it proposes to use a qualitative field picture rather than the water analogy (note that you can't do fulfledged hydrodynamics in high school either, it's even more complicated than Maxwell's equations since it's nonlinear). I think it's pretty intuitive to discuss that there's an electric field along the wire and conduction electrons moving quasifree (with friction) driven by this field to overcome the friction (in the stationary case), i.e., the naive Drude model. I'm not sure, whether it's treatable for AC (in the quasistationary limit) at high school, where you have a quasifree particle with friction with a sinusoidal driving force. Perhaps it's just feasible in the last grades, where they have some calculus at hand (but of course not complex exponential functions, which make the calculation simpler than the use of trig. functions needed for a purely real calculation).

Homework Helper
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It seems to me that part of the problem is the attempt to provide facile explanations in the first place. It is far worse to give a woefully incomplete and therefore necessarily incorrect explanation to a student: they will assume a depth of knowledge that is unwarranted and it may in fact stifle, for those so imbued, the urgent need to know. This requires discipline from both student and teacher.
Teaching half-truths without relentlessly identifying them as such is therefore to be avoided as a reckless enterprise. Education is demanding. In my (limited) experience the systems that have traditionally been best with this disciplined approach have been those associated with the military. Their production of technically competent people from often educationally deficient backgrounds is remarkable.

anorlunda
Gold Member
“Half truths” is a perjurative term. You may have forgotten how used kids are to being given and making good use of limited information. I’m sure we had a much more pragmatic than purist attitude to learning when at school.
My memories of teaching are that many of the “Yes sir but what does that really mean” questions were more used to disrupt the lesson when things were getting hard.

vanhees71