# Homework Help: Electric Potential/Capacitor Misconceptions

1. Oct 1, 2006

### Noesis

I am having some trouble conceptualizing some of the central ideas involving capacitors and potential differences.

First off...a question about electric potential. Electric potential simply refers to the potential energy per unit charge (like a field of potential), and always refers to a source of a field (some charge distribution) and points away from it.

Is that right?

Now, if that assumption about electric potential is right...then when we are looking at a battery with two terminals, one with higher potential (+) than the other terminal (-), are these just two points that have different potentials coming from the same source of charge?

Which would be some electrochemical stuff inside the battery itself? If anybody knows as well...what the hell is this electrochemical stuff and how does it produce such an orderly potential difference?

What I mean by orderly is that since a field and thus potential is directed radially from a charge...how can there be a potential difference between two terminals which basically both exist on the same surface?

Now...besides all of those questions on just batteries....when we connect a parallel plate capacitor to a battery's terminals...how is the charge brought to the capacitor?

I imagine that the electrons just start moving from the terminal with less potential, negative terminal, to one of the plates...which then induces electrons to leave that plate and go to the positive terminal..but I don't quite understand what the hell it means when the terminals are at different potentials so I am not sure if that is right.

And lastly...when all of the charge is distributed...why in the world would the plates have the same potential difference as the battery terminals?

Potential difference should be between a source of charge and where respective test charges would be...so how does that fit into a parallel plate model?

Sorry about the barrage of questions...I just have a general misunderstanding in the entire realm. Any clarity on ANY of the questions is greatly appreciated.

Thanks guys.

2. Oct 2, 2006

### andrevdh

A battery is an electrical source that can create an electrical potential difference between its two terminals. It achieves this by separating electrical charges and accumulating them at its terminals. The energy of this process comes from eletrochemical processes. Basically chemical energy is sacrificied to push electrical charges into the terminals and into the circuit. See it as a sort of charge pump that supplies the electric charge with energy (via the generated electric field that propagates through the circuit). For example in the dry cell we find that the central carbon electrode is surrounded by two different pastes. The inner paste draws electrons off the carbon terminal (+). The outer paste then delivers electrons to the outer zinc electrode (-). This process is driven by the difference in electronegativity of the two types of atoms/molecules in the paste and electrodes.

The electric potential difference tells us the amount of electric energy that a unit electric charge deposits in the circuit when it flows between the two points. Like a stream of water being pumped up into a reservoir the electric charge gains energy when pumped into the high potential terminal. (Energy is an abstract concept, but makes it easy to talk about things in a general context without going into too much detail.) As the charge flows through the circuit it deposits its energy in the components in it and thereby doing all sorts of work. The charge arrives at the low potential terminal with all its energy expended, unless the battery is shorted. In which case the energy is deposited back into the battery itself which causes it to overheat and exaust it supply of charge.

When a capacitor resides in the circuit we find that the battery start to push the positive charge around the circuit towards the low potential terminal.The positive charge accumulates on the plate closest to it but it cannot cross the gap. The electric field can cross the gap and push positive charge off the other plate though. As more electic charge accumulates on the plates we find that the battery needs to push harder to force more charge onto the plates. This process stores energy in the capacitor (like compressing a spring does). The capacitor now starts to oppose the flow of current from the battery since its own electric field works agains that of the battery and when the electric potential difference over the capacitor is equal to that of the battery the flow stops.

Last edited: Oct 2, 2006
3. Oct 2, 2006

### Noesis

Thank you andrevdh...I will definitely be reading that through and trying to figure this out.

I'm just a bit confused in your last paragraph, you say the battery starts to push the positive charge towards the low potential terminal...I thought the electrons, or negative charge, were the ones who would be moving?

I thought they'd flow out of the negative terminal...and go through the wire to the plate like that.

That part lost me.

Thanks again.

4. Oct 2, 2006

### Hootenanny

Staff Emeritus
I think it was just a slip of the tounge (or perhaps fingers) by andrevdh; I'm sure he meant negative charge. Everything else is correct though

5. Oct 2, 2006

### Integral

Staff Emeritus
http://hilaroad.com/camp/projects/lemon/lemon_battery.html" [Broken] you can make at home.

Last edited by a moderator: May 2, 2017
6. Oct 2, 2006

### Noesis

Hmm...going to have to go buy some lemons soon.

Now as I'm going over this...I am definitely starting to understand things a bit more..but am still having questions popping up all over the place.

I'll try to separate them and put key stuff in bold for coherence and so t's not a giant block of text:

Direction of charge flow

Now I do not as of now totally understand how a battery works in terms of the electrochemical reactions, and that's fine, I understand that it somehow sets up a potential difference.

Now a question I had was, is this potential difference taken with the convention that the source charge distribution is a positive one?

I mean, field lines by convention are always taken to generate radially outward of a positive charge, and radially inward for a negative charge, which is only the direction of a force for a positive charge.

So now..if the potential difference marked by + and - at the terminals, indicates that the potential is higher at the + terminal than the - terminal...is this going by the positive source convention?

Because if it is...then the lower potential for a positive charge, the - terminal, would actually be a higher potential for a negative charge. So the electrons would actually flow from the positive terminal outwards to the plates. They would flow towards the higher potential for positive charges.

Is this actually correct or is there some blatant flaw in my thinking?

Equivalent potential difference across terminals and plates

Now, if all things go as they should, we should have the same potential difference across the plates as there are between the terminals.

Now, a potential difference is always caused by some electric field, so the entire idea is that the electric field from all of the charge buildup on one of the plates on the capacitor is going to equal the field that produces the potential differences in the terminals, and thus the fields negate causing both the plate and the terminal to have the same potential and no reason for charges to move anymore: equilibrium.

Now if the terminal has the same field as the plate, the only way for the potential difference between the two plates to be the same as the difference between the terminals would be if the plates have the same distance between them as the terminals do.

If they don't...they cannot have the same potential difference.

Am I on the right track or doomed to eternal physics stupidity?

Problem with induction from one plate to the other

If the plates are separated by a distance d, then of course the electric field drops off by that distance squared.

Now if there is a certain charge -Q on one of the plates, it should induce an equal magnitude but opposite charge Q on the second plate.

It would do this of course through the electric field it produces.

But now this field is dropping off by the distance d squared...so it cannot quite induce an equal charge on the other side. It would be off by some constant proportonial to the distance....so what gives?

What's the problem with my reasoning?

7. Oct 3, 2006

### andrevdh

The zinc chloride dry cell functions by pumping electrons from the carbon electrode in the middle of the paste to the outer zinc electrode. It does this via the $Zn^{++}$ ions in the paste. It is a string of chemical reactions allowing one another to occur as soon as electrons start moving in and out of the terminals. Each electron that is pushed onto the zinc terminal is therefore the result of some chemical process occurring. This means that the electrons are supplied with a certain amount of energy as they are released. The chemical processes can therefore push just a certain amount onto the terminal before they start "backing up". That is the potential of the cell can build up only to a certain level depending on the "strength" of these processes. As the cell deteriorates we find that the rate at which it can supply electrons drop.

Last edited: Oct 3, 2006
8. Oct 3, 2006

### andrevdh

Yes. Confusion will arise especially when you mix the workings of a battery and that of current flow in a circuit. Historically physics developed along the lines of positive current flow (conventional current flow), although we all know that it is actually the electrons that flows in metallic conductors. Inside of the cell we find that both types of charges are in motion - positive ions, negative ions and electrons.

When raising an object in a gravitational field we say that its gravitational potential energy increases. Similarly when pushing a positive charge up towards a positively charged plate we conclude that its electrical potential energy is raised - it is located at a higher potential. If we assume for the moment that the battery separates positive charge inside of it and pushes it towards the higher potential terminal (+) we find that the motion of positive charge is up against the field in the battery. So the cell needs to do work to push the positive charge towards the higher potential terminal of the cell. This energy comes from chemical reactions that progress towards more stable compounds forming inside of the cell.

Outside of the cell we find that the positive charge moves in the opposite direction - from the high potential terminal to the low potential terminal. This releases the accumulated energy that was given to it by the cell as the positive charge moves back to the low potential terminal. Analogous to the mass being released and falling down to the ground again.

If we consider the motion of electrons in the circuit we find that they migrate in the opposite direction of the positive charge, that is from the low potential terminal (-) to the high potential terminal (+) in the circuit.

Last edited: Oct 3, 2006
9. Oct 4, 2006

### Noesis

Thank you Andrevdh, that definitely does clear some stuff up.

I do understand the 'migration' of the charges now and how the potential difference is set up by the cell.

These questions still puzzle me:

Equivalent potential difference across terminals and plates

Now, if all things go as they should, we should have the same potential difference across the plates as there are between the terminals.

Now, a potential difference is always caused by some electric field, so the entire idea is that the electric field from all of the charge buildup on one of the plates on the capacitor is going to equal the field that produces the potential differences in the terminals, and thus the fields negate causing both the plate and the terminal to have the same potential and no reason for charges to move anymore: equilibrium.

Now if the terminal has the same field as the plate, the only way for the potential difference between the two plates to be the same as the difference between the terminals would be if the plates have the same distance between them as the terminals do.

If they don't...they cannot have the same potential difference.

Am I on the right track or doomed to eternal physics stupidity?

Problem with induction from one plate to the other

If the plates are separated by a distance d, then of course the electric field drops off by that distance squared.

Now if there is a certain charge -Q on one of the plates, it should induce an equal magnitude but opposite charge Q on the second plate.

It would do this of course through the electric field it produces.

But now this field is dropping off by the distance d squared...so it cannot quite induce an equal charge on the other side. It would be off by some constant proportonial to the distance....so what gives?

What's the problem with my reasoning?

And a new question:

Uniform field inside capacitor and zero field outside

Let's say we have two parallel plates in a capacitor configuration, with of course charge Q on one plate and charge -Q on the other.

Now the idea is that the field will be uniform on the inside because both electric fields from charge Q and charge -Q will superpose and add up.

Although the strength of one field will start to die off as distance increases, the strength of the second field gets stronger by that same amount as you get closer to it.

Is this argument for field uniformity right?

Now what I don't understand is the zero field that should be outside of a capacitor.

In order to have a zero field, it means we must have an electric field of equal magnitude but opposite direction superposing.

On the outside of any of the parallel plates, the only opposing field will come from the other plate, and this field has to cross over a distance d that separates the two plates...meaning it is going to be weaker once it actually gets to the other plate than what the field is there.

So I don't understand how we can have a zero field outside the plates if the field that should cancel it is not strong enough to fully cancel it.

Thanks in advance guys...I'm trying to totally understand this and one question just leads to another. I hope to expose all of the mistakes in my thinking and learn the truth of how it actually works. That or just give myself a really large headache...either/or.

10. Oct 5, 2006

### andrevdh

We say that a electric field exist at a point in space if a (positive) test charge can experience a force at that particular point. A positive test charge will be repelled by the positive plate and attracted by the negative plate. So we conclude that the electric field lines stretches from the positive plate towards the negative plate inside of the capacitor. Outside we find a different situation though. In this region you can see that the capacitor and the battery opposes each other perfectly at each point in the circuit. So no resulting field exist in the circuit outside of the battery and the capacitor.

Between the plates of the capacitor we find that when there is a decrease in the amount that a positive test charge is repelled by the positive plate the negative plate increases the attraction by the exact same amount thereby keeping the field uniform in between the two plates.

Last edited: Oct 5, 2006
11. Oct 6, 2006

### andrevdh

As far as the remark about the potential difference between the plates and terminals and the electric field of each goes envisage this situation:

To raise the potential energy of a 1 kg brick by the same amount on the moon than that on the earth you would need to raise the brick to a much higher height.

So you see that the electric potential difference tell us about the combined effect of the strength of the field and how far the charge have been moved in the field. The strength of the field is tied much closer to the charge distribution than the actual distance. You can also see it another way - if the plates were distanced further away the capacitor would still be charged up to the same potential by the battery. It is a question of stored energy and not so much strength of field that does the trick. When the charge flows around a circuit from one terminal to the other (with just a resistor say) it is the energy that is expended, irrespective of the size of the resistor. Inside of the resistor we would find a different electric field gradient depending on the size of the resistor.

You should also not think that the distance between the terminals of a battery has anything to do with the potential between its terminals - think of 1.5 V batteries, they come in all shapes and sizes and remember dynamite comes in small packages!

In spite of all the misconceptions that you currently display I still think that your way of thinking will be very valuable to the scientific community. So I do hope that you intend joining them someday. I do think that you have one of the essential requirements for becomming a great scientist.

Last edited: Oct 6, 2006