How can each Coulomb of charge transfer energy

[torxxx]

regards my question is how each coulomb of charge can lose (transfer ) energy when going from a to b when electrons are very slow

the definition of potential difference: is how much each coulomb of the charge loses (transfer ) energy when going from a to b

an example to clarify the question

we have a wire from the beginning to the end of the wire (point a point b ) the potential difference is 1 v so how then coulomb of charge cen go from a to b and transfer that energy when electrons are very slow

energy electricity

 

[Dale]

we have a wire from the beginning to the end of the wire (point a point b ) the potential difference is 1 v so how then coulomb of charge cen go from a to b and transfer that energy when electrons are very slow

You have identified an important point. The electrons move slowly but the energy transfer happens quickly, therefore the electrons are not the thing that transports the energy. In fact, the energy is transported by the fields which “move” at nearly the speed of light. In Poynting’s theorem the energy flux is given by the $E \times B$ term.

What the electrons do is to transfer the energy carried by the field from the field to the matter. This is given my the $E \cdot J$ term in Poynting’s theorem.

So the slow moving electrons don’t carry the energy, but they do transfer the energy from the field to the matter.

 

[sophiecentaur]

regards my question is how each coulomb of charge can lose (transfer ) energy when going from a to b when electrons are very slow

the definition of potential difference: is how much each coulomb of the charge loses (transfer ) energy when going from a to b

an example to clarify the question

we have a wire from the beginning to the end of the wire (point a point b ) the potential difference is 1 v so how then coulomb of charge cen go from a to b and transfer that energy when electrons are very slow

energy electricity

I often use this analogy to show that the speed of electrons is not a factor which limits the rate of Energy transfer. Take a bicycle chain that's moving at probably 1/10 of the linear speed of the cycle over the ground. The links of the chain are the things that are transferring the power from the cyclist's legs to the wheels. The kinetic energy of the links is TINY but the Power is still getting through. The Power is transferred by the tension and the speed of the chain (Force times velocity) and not by the KE (Chain mass times v²/2) per second. Depending on what gear you happen to be in, the Power for a given chain speed can be very different (Tension can be low downhill or high going uphill at the same speed) but the KE is the same.
KE of a chain would be, for a chain mass 0.5kg and a velocity of 1m/s: mv²/2 = 0.25J so power (Energy per second) is 0.25W. A cyclist can put almost 1kW into the system for a short while.
The KE of the links is the same in both cases and, likewise, the KE of electrons can be the same for two entirely different values of Power Transfer.
The proportion of Power transfer for electrons will be even less than for chain links!

 

[torxxx]

You have identified an important point. The electrons move slowly but the energy transfer happens quickly, therefore the electrons are not the thing that transports the energy. In fact, the energy is transported by the fields which “move” at nearly the speed of light. In Poynting’s theorem the energy flux is given by the $E \times B$ term.

What the electrons do is to transfer the energy carried by the field from the field to the matter. This is given my the $E \cdot J$ term in Poynting’s theorem.

So the slow moving electrons don’t carry the energy, but they do transfer the energy from the field to the matter.

can you explain me better with some analogy

 

[Dale]

can you explain me better with some analogy

The analogy given by @sophiecentaur is good. The speed of the chain has little to do with the energy transport.

 

[russ_watters]

The electrons move slowly but the energy transfer happens quickly...

Good explanation and I realize this is just setup, but I want to emphasize to the OP that energy transfer doesn't have a speed, it only has a rate. Changes in the field propagate at a speed (the speed of light), but the energy itself doesn't even have a location in the circuit for the concept fo "speed" to be meaningful.

And even further, for the idealized model that should be used here, the details of the explanation tell us why we can assume steady state/instantaneous effects.

 

[russ_watters]

can you explain me better with some analogy

The chain analogy is good. Another common one is a pipe loaded with ping pong balls of about the same diameter. When you insert a ball into one end, another ball is pushed out the other end. Neither the speed of the individual balls nor the speed that the "signal" (the "feeling" of being pushed) is transmitted has any relevance to the rate at which balls go in one end and out the other.

 

[torxxx]

Good explanation and I realize this is just setup, but I want to emphasize to the OP that energy transfer doesn't have a speed, it only has a rate. Changes in the field propagate at a speed (the speed of light), but the energy itself doesn't even have a location in the circuit for the concept fo "speed" to be meaningful.

And even further, for the idealized model that should be used here, the details of the explanation tell us why we can assume steady state/instantaneous effects.

thanks for the answers but I was rather surprised because I did not teach in school in this way so I'm not quite sure why the professors do not speak at school in such a way as you

 

[russ_watters]

thanks for the answers but I was rather surprised because I did not teach in school in this way so I'm not quite sure why the professors do not speak at school in such a way as you

I'm not a professional teacher (some here are) and I struggled somewhat in school, but I think I have a good understanding of the problem: Teaching and learning are hard because the basic information to be taught is missing the deeper explanation; the "why". For a first pass at electricity, a teacher could write V=IR and P=VI on the blackboard and then dismiss class and most people would pass a quiz on it. But I never accepted that(one of the reasons I struggled) because I always wanted to know "why". The problem is, for introductory subjects, the "why" is very complicated. A good teacher can provide enough (and simple and clear enough) "why" to satisfy that curiosity without going over the students' head or wasting time on material not needed at that level.

It is a difficult balance and in this case you wanted a little more so you came here -- Welcome to PF!

 

[Stavros Kiri]

Changes in the field propagate at a speed (the speed of light), but the energy itself ...

I think that's very crucial! ... (and a common confusion)
[The individual electrons are just detecting those field changes and pass them along to each other via their mutual EM interaction ... (creating thus a chain),
while they are still moving at low speeds.]

 

[slow]

Paragraph by Feynman Lectures on Physics [(Feynman et al., 1964 section 27-5 Examples of energy flow)]

... ask what happens in a piece of resistance wire when it is carrying a current. Since the wire has resistance, there is an electric field along it, driving the current. Because there is a potential drop along the wire, there is also an electric field just outside the wire, parallel to the surface. There is, in addition, a magnetic field which goes around the wire because of the current. The E and B are at right angles; therefore there is a Poynting vector directed radially inward, as shown in the figure. There is a flow of energy into the wire all around. It is, of course, equal to the energy being lost in the wire in the form of heat. So our “crazy” theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside… the theory says that the electrons are really being pushed by an electric field, which has come from some charges very far away, and that the electrons get their energy for generating heat from these fields.

I like to assume that the phrase "crazy theory" is used by Feynman to highlight with a little humor a very serious issue, referring to how strange the behavior of the electromagnetic field looks when compared to what we see in everyday life.

 

[Stavros Kiri]

the definition of potential difference: is how much each coulomb of the charge loses (transfer ) energy when going from a to b

Note also that there is a difference between the concepts of (and distinctions should be made between) 'potential', 'potential difference', 'potential energy' [and '... difference'] of one charge in a field, 'potential energy of a system of charges' (and respective potential [energy] differences), and, finally, 'energy of the [Electical or generally E&M] field'.
Lots of confusion there too and caution is necessary.

 

[Drakkith]

I think that's very crucial! ... (and a common confusion)
[The individual electrons are just detecting those field changes and pass them along to each other via their mutual EM interaction ... (creating thus a chain),
while they are still moving at low speeds.]

I think this touches on a key point. None of the electrons in an electric circuit act individually. The entire behavior of the circuit is a result of trillions of trillions of electrons all interacting with the outside environment and themselves using the electromagnetic field. So an individual electron doesn't transfer X amount of energy, the combined interaction of this huge mass of electrons does.

This becomes more obvious when you realize that the common model of electrons slowly moving through a circuit isn't even accurate. Electrons are whizzing around in the conductors and other components a bit like gas molecules bounce around in the air. It is their net behavior that we're describing when we talk about the velocity of the electrons and other properties. To use air as an analogy once more, each gas molecule might be moving at 1,000 MPH, but their net behavior still leads to a gentle breeze that moves at 2 MPH. The same is true for electrons in a circuit.

 

[sophiecentaur]

but the energy itself doesn't even have a location in the circuit for the concept fo "speed" to be meaningful.

I see what you are trying to say here but the situation of a Pulse of EM waves would be carrying Energy from A to B and there would be a speed associated with 'where the energy was' at any particular time.

 

[Stavros Kiri]

I think this touches on a key point. None of the electrons in an electric circuit act individually. The entire behavior of the circuit is a result of trillions of trillions of electrons all interacting with the outside environment and themselves using the electromagnetic field. So an individual electron doesn't transfer X amount of energy, the combined interaction of this huge mass of electrons does.

I fully agree. [It complies also with the chain analogy.]

This becomes more obvious when you realize that the common model of electrons slowly moving through a circuit isn't even accurate. Electrons are whizzing around in the conductors and other components a bit like gas molecules bounce around in the air. It is their net behavior that we're describing when we talk about the velocity of the electrons and other properties. To use air as an analogy once more, each gas molecule might be moving at 1,000 MPH, but their net behavior still leads to a gentle breeze that moves at 2 MPH. The same is true for electrons in a circuit.

It's a statistical phenomenon of course, but I think there is a difference in the distributions when there is a preferred direction e.g. due to a polarized field (and open both ends [permanent state current], not as e.g. in a gas (in a box) e.g. in gravity ...). Other than that, e.g. free electrons inside a metal conductor are somewhat similar (and velocity-distribution-wise) to gas molecules.

 

[Let'sthink]

There is one more issue in defining potential difference as energy taken by one coulomb of charge. The correct definition should be per unit charge with an understanding that a very infinitesimal charge is to be taken infinitely slowly.

 

[Stavros Kiri]

There is one more issue in defining potential difference as energy taken by one coulomb of charge. The correct definition should be per unit charge with an understanding that a very infinitesimal charge is to be taken infinitely slowly.

For one charge (moving from A to B), or alone the mathematical definition of 'Potential' and 'Potential Difference' (e.g. between A and B). But here it's different (systems of charges and fields). See also post #12 above, for clearing that and more other possible common confusions.

 

[Let'sthink]

"The correct definition should be energy per unit charge with an understanding that a very infinitesimal charge is to be taken infinitely slowly. whatever energy is transferred is to be divided by that small charge and the limit of this process as the small charge tends to zero is the potential difference" is the correct definition of potential difference. a coulomb is a huge charge around 10 ^19 electrons or so.

 

[Stavros Kiri]

"The correct definition should be energy per unit charge with an understanding that a very infinitesimal charge is to be taken infinitely slowly. whatever energy is transferred is to be divided by that small charge and the limit of this process as the small charge tends to zero is the potential difference" is the correct definition of potential difference. a coulomb is a huge charge around 10 ^19 electrons or so.

I see what you're emphasizing at, and I agree. ΔV = Lim_δq→0 [ΔE/δq]
(Or, if we want to be precise and more picky, [and avoid confusion with a derivative]
ΔV_{A, B} = V_B - V_A = Δ[ Lim_δq→0(E_{of δq}/δq) ]_{A, B} , where, in this notation, e.g.
V_A = Lim_δq→0(E_{of δq at A}/δq) ... etc.)
+ the infinitesimally slow moving requirement that you mention.

The expression "per unit [e.g.] charge", for unit purposes, doesn't mean we use e.g. 1Cb for test charge, you're right, I agree!