Understanding Voltage: Explaining Potential & Potential Energy in Circuits

[Cyrus]

Im having trouble grapshing this concept. Can anyone please explain what voltage across two points means. Does it mean that one point is at a higher potential energy than the other point? Does it mean that the charges present are closer to the point a, and thus produce a stronger net force when a charged body is placed at point a, than at point b? I am trying to see how you get a potential inside a wire. I know you need a battery, but what does that mean in terms of the charges inside the wire?

U(potential) = 1/4pi epsilon * q q0 / r^2.

and V = 1/4pi epsilon * q /r^2

How does the definition of potential and potential energy relate to a circuit. Let's juse use a simple one, a battery and a light bulb or a resistor or something. How do these equations apply, more imporantly what is the MEANING of it?

I don't see how we can talk about voltage in a wire to begin with. The book does cases of voltage where charge is not moving and is treated as points or a continuous distribution. In a wire, the charge is moving around the circuit.

 

[spacetime]

Voltage across two points means the difference in electric potential of the two points. You don't need to include charges in the definition of voltage or potential. It becomes very difficult to include charges and every time do calculations with them and that is why these concepts of voltage and fields are very important. Sometimes the charge distribution may not be known at all.

The equations you have written are not correct but they aren't even needed to define voltage across a wire.

 

[ehild]

See thread
"Differences b/w Voltage,EMF,Potential diff. "

 

[Cyrus]

oop should be 1/r I am sorry for the typo.

 

[Cyrus]

I read that thread before but its not what I am asking ehild. I will ask this question again in a different way.

I understand what electric potential means when we have some charges, be it point charges or a distribution along a ring or a line or what ever other shape. But in the examples in my text, if its a line of charge, the potential is found radially outward from the line. If it is a series of points, the potential is found by asking what does it take to move all the charges from infinitely far away to their position due to their interactions.

But what of a wire? The electrons in the wire are the distribution of charges that is of concern now. But they are not infinitely far away, and I cannot bring them to a certain position and hold them there to calculate the potential energy. The electrons are moving, it has current. So how does electric potential energy apply here? Since potential is a derivative of potential energy, i don't see how i can use it too, since I am having trouble using potential energy.

 

[ehild]

I read that thread before but its not what I am asking ehild. I will ask this question again in a different way.

I understand what electric potential means when we have some charges, be it point charges or a distribution along a ring or a line or what ever other shape. But in the examples in my text, if its a line of charge, the potential is found radially outward from the line.

The potential is a scalar function. It has no sense that the "potential is found radially outward from the wire".

If it is a series of points, the potential is found by asking what does it take to move all the charges from infinitely far away to their position due to their interactions.

You do not use the term "potential" in the same meaning as it is used in Electricity.

Charged bodies interact with each other. That is true. Sometimes one side of this interaction can be ignored. Using the term "field' and "potential" is a method of approximation. It is applied when there is a fixed charge distribution, fixed in the sense that it is not influenced by the motion of the test charge. We even might know the field or the potential without knowing anything about the distribution of those charges which produced that field.
Later you will learn that electric and magnetic fields do exist without charges.
Light wave, for example, has both electric and magnetic field intensity without charges present.

When you calculate the work done by producing a given distribution of charges it is the potential energy of that configuration, not the potential of the field produced by those charges. The potential at a point of an electric field is the work done on unit positive charge by that field when that test charge moves from that place to an other where the potential is taken zero
(you can chose the place of zero potential anywhere).

But what of a wire? The electrons in the wire are the distribution of charges that is of concern now.

Entirely wrong. The distribution of charges IS NOT the same as the distribution of electrons. The wire that carries current is not charged. It has equal amount of positive and negative charges, ions and electrons.

When we speak about the electric field in some material we ignore its atomic structure. We do not need to know the exact position of atoms and electrons to construct a hair drier or a television set... All we have to know is the average electric field in the material body in question: average for a volume which is big compared to the size of an atom but still small compared to the dimensions of the body; and average for time period long compared to the periods of atomic motions. When a piece of wire is connected to the terminals of a battery we know that current would flow which carries electrons away from the negative pole of the battery toward the positive pole without causing any charge redistribution in the wire.

But they are not infinitely far away, and I cannot bring them to a certain position and hold them there to calculate the potential energy. The electrons are moving, it has current. So how does electric potential energy apply here? Since potential is a derivative of potential energy, i don't see how i can use it too, since I am having trouble using potential energy.

You mix potential energy and potential again. You do not need the potential energy of the own electrons of the wire. You need the macroscopic potential or the electric field inside the wire. And the potential is not "the derivative of potential energy". It is the electric field intensity that is the negative derivative of the electric potential - more correctly: the electric field intensity is the negative gradient of the potential. When you have a wire of length L connected to a battery and you measure a voltage Vo across the terminals of the battery than the intensity of the electric field is Vo/L inside the wire, and the potential at any point is xVo/L+(U-) where x is the length of wire between the negative terminal and the point chosen and UA- is the potential of the negative terminal.

ehild

 

[Cyrus]

Hmm, I thought about it some more. So please help me out ehild. I know that if the potential in a circuit is different at two points, then the potential energy is also different. That means one point is at a higher potential energy than the other point is. This means that the charge that can move, namely the electrons, will move to lower potential energy if possible. This is possible since it is in a conducting wire which is free to let charge move through it.

I have read that the potential is analogous to, h, the height for potential energy in gravity. But in the case of gravity, i can SEE a change in potential energy. I can see that the brick is higher than it used to be.

So what can I SEE in the wires of the circuit?

I know that in the case of point charges, potential energy increases as you bring the charges together, (if they are like sign), becasue they want to repell more strongly. Now let's say that I HOLD these charges so they can't move.

There is a potential associated with different points along the radial line that connects these two charges. And it will be different at different points, or zero, or the same depending on how it is set up. If you look at the picture I attached, you can see that there is different potential at A and at B. Let's say that I put a charge at point A, there is more potential over there, becuase it is CLOSER to the one charged body, than at point B. So we would expect the charge to move from A to B. Here I can SEE what the potential means. It means there is MORE Charge close to point A than to point B. So there will be stronger forces at A to move a charge when placed at point A.

The same reasoning holds true for a single point charge. Or other similary bodies for that matter.


But in the case of a circuit, the charge is NOT held fixed. So I cannot apply this same reasioning to SEE what the difference in potential results in physically. The amount of current is the same everywhere, so obviously, the current is moving.

Do you se my question now?

See something must CAUSE the potential difference, and it cannot be the electrons in the pieces of wire. As you pointed out, the wire is overall neutral. Even though charge moves through it, exactly as much elctrons move through it as there are positive ions, so it remains overall neutral.

I suspect the battery has to be the only way to look at it.

It seems like the potential in the case of the circuit is an entirely different beast than the charged body problems.

 

[ehild]

I know that if the potential in a circuit is different at two points, then the potential energy is also different. That means one point is at a higher potential energy than the other point is.

This is entirely out of sense, Cyrus. Stop mixing potential with potential energy. The potential belongs to a field, it is a function of place. The potential energy belongs to a body or to an arrangement of bodies. A point-like charged body has some potential energy at a place in an electric field, equal to the product of its charge and the potential at that point. A body with mass also has potential energy in gravitational field which is the product of its mass and the gravitational potential at that point. A couple of bodies can have interaction energy - kind of potential energy- as a whole.

This means that the charge that can move, namely the electrons, will move to lower potential energy if possible. This is possible since it is in a conducting wire which is free to let charge move through it.

Yes, bodies starting from rest tend to move to places where they have lower potential energy. If you just drop a stone it moves downward, but you can throw it upward and then it moves upward for a while.

I have read that the potential is analogous to, h, the height for potential energy in gravity. But in the case of gravity, i can SEE a change in potential energy. I can see that the brick is higher than it used to be.

Yes, it is analogous, but rather to hg .

So what can I SEE in the wires of the circuit?

You can see if you connect a voltmeter to those two points. The pointer deflects towards the positive voltages or it reads positive value if you connect the terminal marked with "-" to the point of lower potential and you connect the "+" terminal to the point with higher potential.

But in the case of a circuit, the charge is NOT held fixed. So I cannot apply this same reasioning to SEE what the difference in potential results in physically. The amount of current is the same everywhere, so obviously, the current is moving.

Cyrus, the wire is not an empty place with some fixed electrons. And the potential is not the potential energy of the charge distribution. Have you learned about capacitors? Certainly, you have. And you also had to learn that the energy of a charged capacitor is 0.5*Q^2/C , while the potential difference between the two plates is Q/C. You see, how different thing is the potential energy of a charge distribution - the energy of the capacitor is kind of potential energy - than the potential of the electric field, belonging to the same charge distribution.


You might want to consider the real electric field inside a metal. You have point charges: ions and electrons, the ions vibrating around their equilibrium positions in a random way, the electrons whirling around with speed of a couple of hundreds m/s, randomly again, so the electric field is like white noise, both in time and in place, what would the sense in investigating it?
Electricity can work with averages only.

Do you se my question now?

I have seen your question several times already...

See something must CAUSE the potential difference, and it cannot be the electrons in the pieces of wire. As you pointed out, the wire is overall neutral. Even though charge moves through it, exactly as much elctrons move through it as there are positive ions, so it remains overall neutral.

I suspect the battery has to be the only way to look at it.

I think I have said the same. The drift of electrons towards the positive pole of the battery is a consequence of the electric field caused by the charges which have been accumulated on the electrodes of the battery.

It seems like the potential in the case of the circuit is an entirely different beast than the charged body problems.

It is not different, only you should understand the difference between the energy of the charge distribution and the potential in the field caused by a steady, not moving charge distribution. Do not forget, that there is no potential if the forces are time dependent. (There are defined some functions in electrodynamics called scalar and vector potential but they are really
"entirely different beasts".)

ehild

 

[russ_watters]

If you want to hold onto the potential=potential energy analogy, consider that a plane in motion doesn't lose its potential energy if its in motion. Potential, like potential energy, exists independent of the motion. But that's as far as I'll take it: ehild is right to try to get you to separate the two.

 

[Cyrus]

And the potential is not the potential energy of the charge distribution.

. I realize that, its not what I am trying to say. I know that potential is not the same thing as potential energy. What I am saying is that if there is a potential at a point, and I put a charge there, then it will have a certain potential energy at that point. Likewise for some other point, point B for example. So there is a difference in potential energy, and it will fall to the lower potential energy.

You can see if you connect a voltmeter to those two points. The pointer deflects towards the positive voltages or it reads positive value if you connect the terminal marked with "-" to the point of lower potential and you connect the "+" terminal to the point with higher potential.

That still does not explain what I see. I have seen the voltmeter produce a voltage across two points, but that does not explain why.

You see, you stated that potential is a function of distance. I agree with you in the case of point charges or some charge distribution on an object in empty space.

But what of the wires in a circuit. If I have a circuit with a batter to a resistor back to the other side of the battery, for example. The wire from the battery to the resistor is an equipotential. So the potential is the same everywhere on that wire. The same is true for the other wire, but it is at a different potential.

You can easily see in the first picture from my last post, that the potential was related to its location from the static charges. The closer you got, the greater the potential became. but this was for STATIC charges.

In that any of the wires there is no static charge, they have motion around the loop, as you pointed out. So I can't use this relationship between potential and being close to charge for a wire in a circuit to deduce why the potential is bigger or smaller.

Im sorry to keep asking you ehild. But I don't think were on the same page. Maybe I am not asking my question clearly, because you insist on the difference between potential and potential energy, but that's not what I am asking. I understand that they are different, but I am saying that they are related. Thanks for putting up with me thus far

 

[ehild]

.

In that any of the wires there is no static charge, they have motion around the loop, as you pointed out. So I can't use this relationship between potential and being close to charge for a wire in a circuit to deduce why the potential is bigger or smaller.

There is static charge on the electrodes of the battery. If you connect a long wire with high enough resistance to the battery so as it do not get flat in an instant and you can measure potential difference between the negative terminal and subsequent points along the wire you would find that the potential is the higher the closer you get to the positive pole of the battery. Try. You will see that a wire which carries current is not "equipotential".

 

[Cyrus]

Its not equipotential? I thought that because it is a conductor, the charge will move into the wire our out of the wire until it is at exactly the same potential as the battery, since it is a conductor. Wont the charge rush for an instant but then stop once its an equipotential with the battery?


Let me ask my question from a different angle. We have a circuit with a resistor and a battery. The potential is going to be different at each wire. And my volt meter will verify this. This means there is a difference in Energy between the two points. Energy can take two forms, kinetic or potential. The kinetic HAS to be the same, if it were not, the current would be different in each wire, and there would be charge pile up. This only leaves potential energy. So how does this potential energy manifest itself? The mobile charges cannot be spaced closer together as the move, because this would make the density of the wire change, and it would no longer be neutral. So spacing cannot be the reason for potential. So what is going on?

 

[ehild]

Its not equipotential? I thought that because it is a conductor, the charge will move into the wire our out of the wire until it is at exactly the same potential as the battery, since it is a conductor. Wont the charge rush for an instant but then stop once its an equipotential with the battery?

The potential inside a metal and on a metal surface is the same in the static case when there is no current. The potential difference between the ends of a wire when it carries current is the product of the current I and the resistance of the wire, R. U=R*I this is the famous Ohm's law, you might have learned about it already. We usually neglect the resistance of the wireing in a circuit as the resistance of the wires should be much lower than that of the resistors and other devices in order to minimize losses. That makes the product R*I so small that a piece of wire in the circuit can be considered as equipotential.

Let me ask my question from a different angle. We have a circuit with a resistor and a battery. The potential is going to be different at each wire. And my volt meter will verify this. This means there is a difference in Energy between the two points.

You speak about energy again. The energy of what? "there is a difference in Energy between the two points." this sentense has no sense. A point can not have energy.

Energy can take two forms, kinetic or potential. The kinetic HAS to be the same, if it were not, the current would be different in each wire, and there would be charge pile up. This only leaves potential energy. So how does this potential energy manifest itself?

Well, if you speak about the energy of the electrons in the field of the battery, yes, the electrons have greater potential energy if they are closer (along the wire) to the negative pole of the source. The higher potential energy manifest itself in nothing but higher potential energy. It is the potential difference that manifest itself in current flow in a conductor. It is the same as in water flow. Water in a river flows downward, from higher potential to lower. A drop of water has higher potential energy up along the stream than somewere down. Do you see any difference between those water drops just because of their potential energy?

The mobile charges cannot be spaced closer together as the move, because this would make the density of the wire change, and it would no longer be neutral. So spacing cannot be the reason for potential. So what is going on?

The electric field inside the wire is established by the battery and not by the electrons in the wire. Do not stick to that picture of fixed charges. Spacing between the charge carriers making up the current is not "the reason for potential". Think of the stream of water again. Are the molecules of the water closer to each other upstream than downstream? The density of water stays the same along the flow of water and so is the density of electrons in the wire. Also it has no sense to speak about "reason of potential". You can assign an arbitrary potential value to any point, it is only the potential difference that has meaning. The "reason" of potential differences in an electric circuit is the battery or other type of source, the charges produced at the poles of the source by electrochemical reactions or by light, or by temperature differences. What is the reason of different potential energy of water drops along a stream of water? That they are at different height. What is the reason of being at different height? Has this question sense?

I think you should do some experiments using a battery, a torch bulb, a voltmeter, and some wires to connect them, in order to see what happens in the real word...

ehild

 

[Cyrus]

It is the same as in water flow. Water in a river flows downward, from higher potential to lower. A drop of water has higher potential energy up along the stream than somewere down. Do you see any difference between those water drops just because of their potential energy?

yes, I see that one drop is higher than the other drop.