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I'm reading "Practical Electronics for Inventors", Fourth Edition by Paul Scherz and Simon Monk. It describes the method by which batteries generate electron flow as follows: the battery releases a few electrons via a chemical reaction; the free electrons floating in the wire adjacent to the anode are repelled by these additional electrons, so they shove the free electrons adjacent to them and this process continues all the way to end of the wire near the cathode.

Figure 2.6 in section 2.3.1 "The Mechanisms of Voltage" from Practical Electronics for Inventors, Fourth Edition (2016) by Paul Scherz and Simon Monk

The book then says:

It is likely that those electrons farther “down in” the circuit will not feel the same level of repulsive force, since there may be quite a bit of material in the way which absorbs some of the repulsive energy flow emanating from the negative terminal (absorbing via electron-electron collisions, free electron–bond electron interactions, etc.).

(Image source & book quotation: "Practical Electronics for Inventors", Fourth Edition (2016) by Paul Scherz and Simon Monk, published by McGraw-Hill Education (page 11))

The book is essentially describing voltage as the relative capacity to "shove" adjacent electrons and it says the electrons near the cathode feel the least "shove" because throughout the circuit electrons have been colliding with other things.

I understand how this explains resistance when an actual load is placed in a circuit (LED, resistor, etc). But what if you connected the ends of a battery with a wire? Will the free electrons in the wire near the cathode feel the least "shove" because the "shoving force" diminishes due to electrons colliding with the wire walls? Or is this effect marginal in wires, so free electrons near the cathode are equally capable of shoving as the ones near the anode? The reason this confuses me is because one can obviously connect a multimeter across a battery to measure its voltage, but doesn't that imply there's a difference in shove between electrons at the ends despite the lack of a load?

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    \$\begingroup\$ It is important to note that the book simply says "likely" which basically means the author is guessing and doesn't know. In this case it also points towards a mechanical analogy which could just outright be untrue since electrons are more of a quantum thing. This question is also likely better answered by someone on Physics SE. \$\endgroup\$
    – DKNguyen
    Jun 26, 2023 at 1:50
  • \$\begingroup\$ Your question is a about electrochemistry. You're more likely to find an answer in a different stack: chemistry.stackexchange.com/?tags=physical-chemistry \$\endgroup\$ Jun 26, 2023 at 2:09
  • \$\begingroup\$ Ahmed, there are two possible general parts to your question and I'm not sure if you are focused on one, the other, or both. The process of how a battery works as a matter of chemistry is quite interesting and, as it turns out, involves a variety of important details that conspire together. A fuller understanding of that should be left to those with strong chemistry backgrounds and there are recent research additions to this area, by the way. It's not all 'old news.' Another part is about how conductors and semiconductors operate once a potential is set up. Which is your focus? \$\endgroup\$ Jun 26, 2023 at 2:13
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    \$\begingroup\$ Not a chemestry question. definately a physics question. \$\endgroup\$
    – RussellH
    Jun 26, 2023 at 2:32
  • \$\begingroup\$ @RussellH Chemistry is a field of applied physics. Perhaps for the person asking, this link correctly points out a focus on the surface charge arrangement. (It takes a very short time to set them up when powering.) \$\endgroup\$ Jun 26, 2023 at 3:16

2 Answers 2

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After I read back what I said below, I'm not sure I've answered your questions, but I've written it now. Maybe somebody can glean something useful from it.

I always find that these "one or two page" explanations raise more questions than they answer, because there's no way that this is sufficient space to describe all the active processes going on. For that same reason, I cannot possibly describe here everything you need to know in order to understand them, either. I don't understand them, to be honest. I'm going to take you down the rabbit hole a bit, bear with me.

The best analogy to start with, that I can think of is two containers of air at different pressures, connected by a closed tap. Obviously air is more dense in the high pressure vessel, and by opening the tap you allow that imbalance to be corrected, and there will be air flow. This happens because the average force on any individual particle is in a direction towards lower "pressure". From a physics perspective, we would say that the system is tending towards a state of lowest possible potential energy.

There's that word "potential".

A system of charges has similar behaviour. If there exists a region of charges of high density, and also a path available to them to a place where density is lower, the same thing happens. Both fluid and charge systems are always trying to achieve a state where no region in the system has more "pressure" than any other, that the force of repulsion experienced by any particle due to its neighbours is, on average, the same everywhere. Prior to such a state of equilibrium, though, net force on any particle is in the direction it must move in order to reach pressure equilibrium, the state of lowest potential energy.

That's not the whole story though.

what if you connected the ends of a battery with a wire?

If you suddenly applied a potential difference across a wire, then it is not possible for the middle section of the wire to instantly "know" that anything has happened. If we were to believe Ohm's law, uniform current flows immediately, but that's clearly not true. Ohm's law is a useful simplification on the grand scale, but never-the-less untrue. No charge near the centre of the wire would move until the information somehow reaches them that potentials have changed at the ends.

So how does that information get to the middle? In waves. By joining two pieces of metal, you are providing a path between them, through which charge may travel, and if charges on one side happen to be even slightly more densely packed than in the other (an over-simplification, I admit), then there will be a shuffle of charges, a "shoving" from one place to another, to redress this imbalance of charge density. But this shoving doesn't happen all along the wire instantaneously. It travels as a "wave" of potential, charge rarefaction and compression just like a sound wave, which will eventually reach the middle, in the same way disturbing the water at the edge of a pond does not cause molecules in the middle to move until the wave of perturbation gets there.

For this reason, the author's statement "It is likely that those electrons farther “down in” the circuit will not feel the same level of repulsive force" is true, but his justification is somewhat hand-wavy, about energy or something, and doesn't address the most obvious reason, that the "shoving" happens in waves, waves that cannot travel instantly to everywhere in the system.

At a level below Ohm's law, what's happening is that potential ("pressure") waves are travelling back and forth in the whole system, reflecting and delivering energy, doing all the things that waves do. At all points in the system, and at all instants in time, the state of "pressure", or "density", or "potential" is the superposition of all waves present there and then. It sounds complicated, because it is.

If we didn't have the "Lumped Element Model" (LEM), from which we get Ohm's law, and Kirchhoff's laws, the system would be beyond understanding, and we would have no hope of predicting or describing behaviour or designing circuits. The mathematics would be hellish.

The LEM is a description of the average behaviour of charges in a volume large enough to contain a huge number of them, but not so large that these "potential waves" take a long time to traverse it. Happily, in such systems, behaviour "en-masse" of charges is remarkably civilised. The wave superposition I spoke of produces average conditions and behaviour which is highly predictable at scales between, say, microns and metres, without having to consider individual charges, rather like humans having seemingly random behaviour at the individual level, but who together somehow manage to build aeroplanes.

At the level of individual charges, a change in potential, such as that produced when a region of charges of high density is connected to a point where charges are less dense, will produce a ripple, a wave of potential to travel outwards, in all directions. It will do what waves do, travel, reflect and deliver energy to whatever is in their path. Charges will fall down the steepest potential gradient, which is up and down as the waves pass by, but on average they will experience a net force which carries them towards a region of persistently lower potential. This mass migration of charges is what we call current.

The waves of charge compression and rarefaction, like sound waves, travel and interfere and superimpose upon each other, in classical wave-like manner. In huge numbers, this seemingly chaotic soup of oscillating charges exhibits remarkably organised behaviour on average, behaviour which is embodied by the LEM. This permits us to apply very simple principles like Ohm's and Kirchhoff's laws, in terms of potential, resistance and current, instead of having to solve trillions of simultaneous equations of a dynamical system of charges.

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    \$\begingroup\$ I was about to answer with the hydraulic analogy. I'm slightly cautious of your pneumatic analogy, compressibility and all that, but the potential, mass action, waves, are all very good. The pneumatic analogy doesn't have hydraulic's complication of pressure varying with height, that can be a blessing or a curse when trying to propound it. \$\endgroup\$
    – Neil_UK
    Jun 26, 2023 at 9:00
  • \$\begingroup\$ I really appreciate the detailed reply. So in terms of the rippling analogy you gave, when an electron produced by the chemical reaction leaves the anode and enters the wire, is it creating the charge density imbalance which generates those waves (like a rock dropped into a pond generates water waves)? \$\endgroup\$ Jun 26, 2023 at 13:27
  • \$\begingroup\$ @AhmedMalik yes, that is what I am saying, except the electron enters the wire from the battery's negative (cathode). \$\endgroup\$ Jun 26, 2023 at 13:38
  • \$\begingroup\$ @AhmedMalik I should remind you that at the positive end of the battery, there will also be a deficit of charge that "pulls" electrons out of the wire at that end, too, sending waves around the loop in the other direction. The waves are everywhere, in all directions. \$\endgroup\$ Jun 26, 2023 at 13:56
  • \$\begingroup\$ @Neil_UK thank you Neil, that's encouraging. This is a difficult subject to write about, without watering it down too much or getting too complex. If you have a more suitable analogy than gas, that's as easy to describe, I'd appreciate the suggestion. You hit the nail on the head about gravity (height), and that is precisely why I used air. \$\endgroup\$ Jun 26, 2023 at 14:00
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That book simply isn't very good. The mechanical analogy breaks already in the few words the author uses, and his out her vague use of "releases electrons" is a bit of a red flag.

it says the electrons near the cathode feel the least "shove" because throughout the circuit electrons have been colliding with other things.

That book is wrong. There's nothing for us to explain there; the statement isn't true.

In this mechanical model (which honestly raises so many more questions than it answers, so I'm not sure it's a good invention of the author of your book), "the amount of push" would also dictate the amount of current. But that is simply not the case: the current in a circuit is the same at every point.

In a much less complicated model, the elections feel the acceleration that the electric field along the wire exerts on them. And for a wire made if a constant thickness of consistent material, that electric field has a field strength, i.e., how many volts drop over a meter, which is constant along the whole length of the wire.

The acceleration experienced by the electrons is a separate phenomenon to resistance, and the book's approach to subsume then in a single mechanical model hurts your understanding.

I think it's time to find a better book.

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