# Question on Voltage and Charge Carriers

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I've got myself turned around apparently. I thought voltage was the potential difference between oppositely charged poles - that voltage is a measure of the difference in charge carriers. I'm envisioning ionized clouds of opposite charge and I thought that the amount of voltage between the two would depend on the amount of the difference in charge between the two - that the amount of voltage would depend on the number of charge carriers.

But somewhere in that bit up there I'm apparently off. Because you can have high voltage with only a small amount of charge carriers, or a small voltage with a high quantity of charge carriers. I'm not getting that at all and it's making my intuition cry.

And I've been through the water pipe analogies, and I actually do get the "pressure" concept. But with water pipes I can see where 'pressure' comes from and I can imagine a pint of water under 200 lbs of pressure. But I cannot "see" where voltage is coming from, and I cannot imagine a trickle of current from a thousand volts of 'pressure'. (please note, I'm not talking about resistance and insulating materials that restrict the flow of charge carriers, rather I'm assuming a perfect conductor).

Can anyone see where I'm going conceptually wrong here?

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Voltage is a measure of 'Electric Potential' which is just as you stated a potential based on the quantity of any two charges, not necessarily a +/- pair, at a set distance(when regarded as a static potential.) I think the issue you may be having is in your frame of reference where you are trying to apply the concept to the externalized system as opposed to internalizing it. The voltage measured is that potential created internally and between the two charges separated by the dielectric and/or whatnot; think in terms of a charged capacitor. Also note that as a battery is drained voltage drops proportionately until the potential becomes too low for the battery to be of any use. I am expecting a few replies in this thread

Edited by Xittenn
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Potential difference is the amount of energy per unit charge. So a small number of carriers with a lot of potential energy can have a large V. Pushing a few charges very close together will give you a large potential energy.

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Ok, much thanks for the replies.

It looks like I need to now grasp "energy per unit charge". I've seen that repeated in the book I'm using and I need to understand that much better.

What is an example of a small number of charge carriers with a lot of potential energy?

Also, am I supposed to assume that only the difference in charges allows for "carriers"? (Surely that must be since energy is only expended until the two "poles" are electrically neutral - or there is no longer a difference in charges). If that's true, then it would seem that two massively charged poles, one positive and one negative, with only one charge carrier difference, then you would have an extremely low voltage because of the ridiculously small difference, even though both poles are heavily charged. Is that a true statement?

So a small number of carriers with a lot of potential energy can have a large V.

So, how do charge carriers get this potential energy in order to have that large V? I'm probably asking the same question again, but it does sound different to me.

Edited by ParanoiA
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Also, am I supposed to assume that only the difference in charges allows for "carriers"? (Surely that must be since energy is only expended until the two "poles" are electrically neutral - or there is no longer a difference in charges). If that's true, then it would seem that two massively charged poles, one positive and one negative, with only one charge carrier difference, then you would have an extremely low voltage because of the ridiculously small difference, even though both poles are heavily charged. Is that a true statement?

I'm not sure what you mean by a difference in charges allowing for carriers. Charge carriers in basic electronics applications are typically electrons, but when you move the electrons around, the areas they have vacated will have a positive charge. If you started with a neutral system, the net charge is zero.

So, how do charge carriers get this potential energy in order to have that large V? I'm probably asking the same question again, but it does sound different to me.

Lots of ways. You can do it mechanically by rubbing certain materials together, like a balloon on your head, or shuffling your feet on a carpet on a dry day. You can do it chemically, like in a battery.

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I can't speak much to the mechanical generation of electric potential, but I can the chemical:

In a battery there are two different cells, each containing some chemical dissolved (sometimes more like suspended) in a strong electrolyte solution. The chemicals in one cell have this inherent tendency to donate electrons to the chemicals in the other cell. It's all relative though, substance "A" may donate electrons to substance "B" but receive electrons from substance "C". This is called an oxidation/reduction potential. Normally, if you were to mix these chemicals you would just get a pretty energetic reaction. In the battery, they cannot mix, and the electrons are forced through the wire.

So in short, the potential is generated by "redirecting" an oxidation/reduction potential through a wire.

Wikipedia: Electrochemical Cell

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Ok, much thanks for the replies.

It looks like I need to now grasp "energy per unit charge". I've seen that repeated in the book I'm using and I need to understand that much better.

What is an example of a small number of charge carriers with a lot of potential energy?

Also, am I supposed to assume that only the difference in charges allows for "carriers"? (Surely that must be since energy is only expended until the two "poles" are electrically neutral - or there is no longer a difference in charges). If that's true, then it would seem that two massively charged poles, one positive and one negative, with only one charge carrier difference, then you would have an extremely low voltage because of the ridiculously small difference, even though both poles are heavily charged. Is that a true statement?

Consider if you had a giant capacitor as big as your car, and one as small as your finger. If you put the same amount of charge difference in each, the potential difference will be much smaller in the larger capacitor since the charges aren't as "crammed together". Or consider if you had a set of negative charges and a set of positive charges, one cm from each other or ten cm from each other. The ones with the larger separation have more energy per unit charge, and in fact you could get energy by moving them together from the 10 cm point to the 1 cm point.

More generally, integrate the force as you move a charge against an electric field and you get the energy that charge can release when it is allowed to return. A stronger electric field over a longer distance will give you more energy per unit charge.

So, how do charge carriers get this potential energy in order to have that large V? I'm probably asking the same question again, but it does sound different to me.

Move charges against the electric field, and you increase the potential energy. If you move a significant number of charges against the field you also make the field stronger, and so increase the energy per unit charge (voltage) as well.

---

In particle physics, it is convenient to measure energy as electron-volts, the amount of energy you get by dropping an electron across 1 volt differential. Joules too relate to electricity, E = Volts * Coulombs, And watts (Joule/s) too can be related to electricity:

Two additional unit conversions for watt can be found using the above equation and Ohm's Law.Where ohm (Ω) is the SI derived unit of electrical resistance.

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I'm not sure what you mean by a difference in charges allowing for carriers. Charge carriers in basic electronics applications are typically electrons, but when you move the electrons around, the areas they have vacated will have a positive charge. If you started with a neutral system, the net charge is zero.

Yeah, I'm probably not using the terminology correctly. Engineers speak of electrons and holes, the latter referring to an electron shortage causing a positively charged atom. With that in mind, my statement "the difference in charges allowing for carriers" was trying to look at the difference between two oppositely charged poles in terms of how many electrons would actually move until the poles cancel each other out or one of them becomes neutral.

For instance, just to keep the numbers simple, if pole A has an excess of say 10 electrons, and pole B has an excess of 10 protons (or really a shortage of 10 electrons), then I was wondering if that means there are no charge carriers. Since each pole cancels each other out, I should not see any electron movement.

But, if Pole A has an excess of 20 electrons, while pole B has an excess of 10 protons, then I was thinking I would then see electron movement until Pole B is neutral, or 10 electrons, or 10 charge carriers.

This net "difference in charges" is what I've been envisioning as the source of potential difference. I also see problems with it of course, because if the size of that charge difference between two poles or substances drives the voltage level, then it would seem impossible to have a high voltage, yet very little difference and therefore very little electron movement - it's self contradictory. Apparently that's because this is not how it works, no matter how nice it fits in my head.

Lots of ways. You can do it mechanically by rubbing certain materials together, like a balloon on your head, or shuffling your feet on a carpet on a dry day. You can do it chemically, like in a battery.

Funny, because that's exactly the example that got me all screwed up. I was reading about shuffling your feet on the carpet to generate thousands of volts, yet the book states "although the voltage seems deadly in terms of numbers (thousands), there are not that many coulombs of charge that can accumulate on an object the size of your body."

Well crap, if there aren't that many coulombs of charge that can accumulate, then how did we achieve thousands of volts of potential? In this example, it's a little easier to accept not being killed because the voltage is not sustained, unlike a battery or household source. But I'm still not making the right connection between charge and voltage.

Consider if you had a giant capacitor as big as your car, and one as small as your finger. If you put the same amount of charge difference in each, the potential difference will be much smaller in the larger capacitor since the charges aren't as "crammed together". Or consider if you had a set of negative charges and a set of positive charges, one cm from each other or ten cm from each other. The ones with the larger separation have more energy per unit charge, and in fact you could get energy by moving them together from the 10 cm point to the 1 cm point.

More generally, integrate the force as you move a charge against an electric field and you get the energy that charge can release when it is allowed to return. A stronger electric field over a longer distance will give you more energy per unit charge.

Hmm, I like the way you're explaining this but I can't say I'm getting it. The separation creating more energy per unit charge is not untuitive. I need to chew on all this some more...

Edited by ParanoiA
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Hmm, I like the way you're explaining this but I can't say I'm getting it. The separation creating more energy per unit charge is not untuitive. I need to chew on all this some more...

Would it be intuitive if the charges were replaced with planet-sized masses? The same masses at different distances would have different gravitational potential (greater for larger distance). Or, if you arrange to keep the force nearly constant, if the distance changes? Raise an object 1 m against gravity, and it has some potential energy, raise it 2 m against gravity and it has twice the potential energy, despite being the same mass. When you have charges there's a slight difference because you have to account for whether the charge is positive or negative which changes the direction "up" (against the field) would be. But distance only counts when it's along or against a field, which gets complicated if charges are moving. If you have moving charges you probably want to ignore what portion of the voltage is due to distance and what portion due to field strength, and just think of it as potential energy difference between two places, per unit charge.

In metals, you probably want to consider electron flow like this:

http://en.wikipedia.org/wiki/Drift_velocity#Numerical_example

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The gravity analogy really helps. But electric field strength decreases as the distance between charges increases, so it's weird to think of potential energy increasing as the field strength decreases in response to the increased distance between charges.

Then, of course, I have to wonder about maximum distance. If two charged particles are a mile apart, their electric fields won't affect each other. As you move them closer together, as some point, eventually, their electric fields will mingle. And instead of a gradual increase in energy as you move them together, it would seem you would run into the maximum energy potential all of the sudden - from nothing to maximum in one discrete step - and then as you keep moving them together the potential energy would gradually drop.

Say it ain't so man.

I was googling the electric field stuff and ran across this page...

The strength of the electric field is dependent upon how charged the object creating the field is and upon the distance of separation from the charged object.

http://www.physicsclassroom.com/class/estatics/u8l4b.cfm

That fits with what you've been describing. Am I correct to at least assume that quantity of charge carriers determines how charged the object creating the field is?

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Be careful not to confuse force and energy. If you move things that attract each other farther apart, as a general rule the force between them decreases and the potential energy increases. But consider what happens if you drop the objects, so that they fall together. Then, work can be done by allowing them to move closer together, and they get closer together. Thus the potential energy at a distance is the the sum of the energy released when bringing them closer plus the potential energy they have at the nearer distance. Even though the force gets stronger, the potential energy decreases, as the objects move closer together. But again, for a lot of electrical stuff worrying about force and distance will just confuse you and you'd be better off just worrying about the voltage difference. (incidentally, voltage is always a difference, just like potential energy. There is no one absolute voltage, though the voltage difference to a grounded cable comes close.)

Am I correct to at least assume that quantity of charge carriers determines how charged the object creating the field is?

I'd say no. There's no reason you can't have your charge carriers carry two charges each, eg magnesium ions. Better measure your charges in coulombs or in multiples of e. But charge is conserved, so if you take a given amount of charge from an item it will be lacking that much charge.

As for the (maximum) field strength, it depends on the charge density, much like a dense planet will have a stronger surface gravity than a less dense planet (if you prefer, you can think of that as being able to get closer).

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If I may? I made a really horrible drawring; forgive any presumptions or errors on my part.

1) There is a potential E between any two electrons at distance r

2) If you halve this distance you double this stored potential

3) A cloud of electrons occupying a volume will have, at a point of reference, a measurable voltage(E)

4) If you were to halve the electrons in this cloud but the remaining were to occupy the same volume of space you would halve the potential

5) If the volume containing this half quantity were then halved you would have the same potential as in 3)

6) If you connected 3) and 4) by wire you would have the difference between the two potentials

Now the clouds in 6) would be affected by each other also and measurably at a proper distance. The two clouds would effectively repel just like a pith-ball thingy and there would be an incurred stored potential that would increase continuously as they approached one another. Note the difference between the potential given by connecting the two clouds by wire and that of bringing the two clouds together.

Edited by Xittenn
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But again, for a lot of electrical stuff worrying about force and distance will just confuse you and you'd be better off just worrying about the voltage difference. (incidentally, voltage is always a difference, just like potential energy. There is no one absolute voltage, though the voltage difference to a grounded cable comes close.)

Yeah, I don't have any plans to obsess over force and distance as I evolve through this review, that's for sure. It's extremely confusing and I'm a little disappointed that I can't grasp it more immediately. At this point, if I can just "see" potential difference and understand the basics at the particle level, then I can move on and feel fairly comfortable about it.

I'd say no. There's no reason you can't have your charge carriers carry two charges each, eg magnesium ions. Better measure your charges in coulombs or in multiples of e. But charge is conserved, so if you take a given amount of charge from an item it will be lacking that much charge.

Ah, there's another bit of confusion for me. When I'm thinking charge carriers, I'm thinking electrons. When one mentions ions, I'm actually thinking of a charged atom containing charge carriers. Since only electrons are moving in a given electric current, I wouldn't have thought of considering the whole of the atom as the charge carrier.

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The gravity analogy really helps. But electric field strength decreases as the distance between charges increases, so it's weird to think of potential energy increasing as the field strength decreases in response to the increased distance between charges.

Then, of course, I have to wonder about maximum distance. If two charged particles are a mile apart, their electric fields won't affect each other. As you move them closer together, as some point, eventually, their electric fields will mingle. And instead of a gradual increase in energy as you move them together, it would seem you would run into the maximum energy potential all of the sudden - from nothing to maximum in one discrete step - and then as you keep moving them together the potential energy would gradually drop.

Say it ain't so man.

It ain't so. The fields don't make discrete jumps. Even a mile apart there would be a force (and thus potential energy) but it's so small one would never notice, since it would be swamped by other effects.

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It ain't so. The fields don't make discrete jumps. Even a mile apart there would be a force (and thus potential energy) but it's so small one would never notice, since it would be swamped by other effects.

Is he referring to some threshold of voltage needed to overcome the initial resistance within the conducting medium, maybe?

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Yeah, I don't have any plans to obsess over force and distance as I evolve through this review, that's for sure. It's extremely confusing and I'm a little disappointed that I can't grasp it more immediately. At this point, if I can just "see" potential difference and understand the basics at the particle level, then I can move on and feel fairly comfortable about it.

It might help if for the water pipe analogy you consider the difference in potential energy rather than in pressure. For example with water pipes you could use a high pressure to pump a higher volume at a lower pressure (like a transformer), and then you realize that what you should be keeping track of is potential energy and not the force or pressure.

Ah, there's another bit of confusion for me. When I'm thinking charge carriers, I'm thinking electrons. When one mentions ions, I'm actually thinking of a charged atom containing charge carriers. Since only electrons are moving in a given electric current, I wouldn't have thought of considering the whole of the atom as the charge carrier.

Whole atoms can and do move around, for example in an ionic solution, which is also how batteries and electrolysis work. In a metal, charge moves as a sea of electrons, like water in a ginormously huge pipe. In a vacuum, the electrons can get emitted by a filament and then move around through space as free particles. In air, charge moves as a plasma with atoms getting stripped of their electrons. In semiconductors the material can be doped to have free electrons or missing electrons (aka "holes") and I'm not too sure of the details but charge flows very much better from the direction of free electrons to the area of lacking electrons. In the gap between the two plates of a capacitor, the flow of electricity doesn't involve the movement of charge carriers past the gap at all, but rather the current is a change in the electric field. In a Van der Graff generator, there are charges being carried along on macroscopic strips of metal (though it also involves more standard electrical flow), and I think that is similar to how the currents powering earth's magnetic field work. I think that if you make an electric field strong enough you'll get a flow of new particle/antiparticle pairs in opposite directions. Anyhow, I hope that clears it up for you.

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Oh crap, I think I might actually be getting this now.

Electric potential = PE/Q. The volt = Joule/Coulomb of charge. The volt is the unit of measure for electric potential.

An electric field will be in the direction of a negative charge as that's the direction a positive charge would be impelled when exposed to the field. A positive charge will gain potential energy as you move it against the field toward the source because it requires work to move it this way and the amount of work it takes is the potential energy - it does not require work for that charge to move in the same direction as the field, but of course it would lose its potential energy (although energy must be conserved...I'll need to revisit that later, it's already starting to bother me)

So, electric potential is based on location within the field, not the amount of charge - potential energy will be the product of the electric potential and the actual charge. Electric potential is a rate of how many joules per unit of charge in a given spot in the field. If I place a 2 coulomb charged object in a location within a field with an electric potential of 24 Joules/Coulomb, then that object has 48 Joules of potential energy at that location. That's 48 Joules that can do work in the direction of the field when "released" (and should have taken 48 Joules of work to get to that location in the field).

I hope that's close. I have to quit for the night, and I'm not near there, but I think I have a better handle on some of this.

Edited by ParanoiA
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An electric field will be in the direction of a negative charge as that's the direction a positive charge would be impelled when exposed to the field. A positive charge will gain potential energy as you move it against the field toward the source because it requires work to move it this way and the amount of work it takes is the potential energy - it does not require work for that charge to move in the same direction as the field, but of course it would lose its potential energy (although energy must be conserved...I'll need to revisit that later, it's already starting to bother me)

Yes indeed. As it loses its potential energy, it'll gain kinetic energy, since it's now moving faster. So, if I have two opposite charges a distance apart, and I let them go, they'll accelerate toward each other. The kinetic energy they have when they collide is equal to the potential energy they gave up while moving toward each other.

So, electric potential is based on location within the field, not the amount of charge - potential energy will be the product of the electric potential and the actual charge. Electric potential is a rate of how many joules per unit of charge in a given spot in the field. If I place a 2 coulomb charged object in a location within a field with an electric potential of 24 Joules/Coulomb, then that object has 48 Joules of potential energy at that location. That's 48 Joules that can do work in the direction of the field when "released" (and should have taken 48 Joules of work to get to that location in the field).

Yes!

(At least, I think, since it's been a year now since I did this in class.)

Of course, if you have a field caused by a positive charge, and you place a positive charge in it, the potential will change signs, out of convention.

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I've got myself turned around apparently. I thought voltage was the potential difference between oppositely charged poles - that voltage is a measure of the difference in charge carriers. I'm envisioning ionized clouds of opposite charge and I thought that the amount of voltage between the two would depend on the amount of the difference in charge between the two - that the amount of voltage would depend on the number of charge carriers.

But somewhere in that bit up there I'm apparently off. Because you can have high voltage with only a small amount of charge carriers, or a small voltage with a high quantity of charge carriers. I'm not getting that at all and it's making my intuition cry.

And I've been through the water pipe analogies, and I actually do get the "pressure" concept. But with water pipes I can see where 'pressure' comes from and I can imagine a pint of water under 200 lbs of pressure. But I cannot "see" where voltage is coming from, and I cannot imagine a trickle of current from a thousand volts of 'pressure'. (please note, I'm not talking about resistance and insulating materials that restrict the flow of charge carriers, rather I'm assuming a perfect conductor).

Can anyone see where I'm going conceptually wrong here?

Start with the electric field from a static arrangement of xharges.. A point charge creates a spherically symmetric electric field that drops off like 1/r^2. The field due to an arrangement of point charges

is the vector sum of the fields due to the individual chsarges.

A electrostatic field is a conservative field. Therefore it is the gradient of some scalar field, called the potential. The voltage, aka potential difference, between two points in space is the difference between the values of the potential function at those two points.

So, voltage depends on both the amount of charge ane the spatial arrangement of that charge.

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Yes indeed. As it loses its potential energy, it'll gain kinetic energy, since it's now moving faster. So, if I have two opposite charges a distance apart, and I let them go, they'll accelerate toward each other. The kinetic energy they have when they collide is equal to the potential energy they gave up while moving toward each other.

Cool, thanks for the confirmation.

So, looking at electric potential, I notice that so far the rate has been arbitrarily assigned for a spot in the field. The example I used was a mirror image really of what I've read; just assuming that a certain spot contains a given electric potential, J/C and then reasoning out what's going on, doin' the math. That was great.

But how is that rate created? The field strength? It seems intuitive now that field strength would determine how many Joules of work would be required to move a single unit of charge toward the source or the high energy potential. Seems it would be that way for all field forces.

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Cool, thanks for the confirmation.

But how is that rate created? The field strength? It seems intuitive now that field strength would determine how many Joules of work would be required to move a single unit of charge toward the source or the high energy potential. Seems it would be that way for all field forces.

All force fields define the work expended to move an object between two points along a given path.

But only fields that arise from a potential, conservative fields, are such that then points alone determine the work; i.e. the work is path-independent and is 0 for all closed paths.

Not all fields are potential fields. The electrostatic field is a potential field.

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Fair enough, but is the first part correct about electric fields? The strength of the field determining the work required to move the charge to the high energy potential? Little steps...

The other thing that's bothering me now is the movement of positive charge in metals. I see now that the electrochemical solution in battery cells are doing the work to push the ions to the high energy potential (Mr Skeptic mentioned this too) and so when we provide a conductive path, positive charge moves to the low energy potential doing work on the circuit in the process.

But we can't move ions in metals, and we can't move protons either (which would change the substance in the process I'm guessing even if it were possible) - so how are we moving a positive charge?

Just one of many follow up thorns that arrest my progress...

Edited by ParanoiA
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As far as I know, we only move electrons in metals. You can, however, consider a flow of negative charges going one direction to be equivalent to positive charges going the other direction, for basic circuit analysis at least.

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As far as I know, we only move electrons in metals. You can, however, consider a flow of negative charges going one direction to be equivalent to positive charges going the other direction, for basic circuit analysis at least.

And we certainly do, that's for sure. But since I'm refreshing my knowledge on a subject I have never applied, and haven't even looked at for about 12 years, I'm determined this time to really grasp how the particles are moving. I took these things for granted before, assumed this and that for convencience, and I'm not satisfied with that anymore.

At this point, I feel like I can "see" the potential energy when we push charge against the field toward the source, but so far I only get this when I think of "charge" as positive and negative units - now I need to understand it in terms of electron movement.

For instance, if I touch a positively charged conductive object to a neutrally charged conductive material (let's just stick with metals), conceptually I can think of that positive charge equally distributing itself across the surface of these materials. But, positive charges don't move in metal, instead the electrons in the neutral object will be attracted to the positively charged object and they will move to provide the equal distribution (since they repel and would like to be farther apart from each other and were just granted a whole new wing to move into). The end result is the same, but the actual movement is different from the concept of positive charges moving around.

So, in thinking of an electric field, we are always directed away from a positive source and toward a negative source - and since it would not require work to move an electron toward the positive source (opposites attract) then it would seem to require moving positive charge toward the positive source to create potential energy that can be used to do work on a circuit.

Unlike the simpler electrostatic example using conductive materials, I'm not seeing how to readjust the electric field concept to realize how it works in terms of electron movement, or what's actually moving around.

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So, in thinking of an electric field, we are always directed away from a positive source and toward a negative source - and since it would not require work to move an electron toward the positive source (opposites attract) then it would seem to require moving positive charge toward the positive source to create potential energy that can be used to do work on a circuit.

Unlike the simpler electrostatic example using conductive materials, I'm not seeing how to readjust the electric field concept to realize how it works in terms of electron movement, or what's actually moving around.

I'm not sure I get what you're aiming at here. Could you elaborate?

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