# Redistribution of charge in a capacitor

Hmmm, but if we go along with this 'no charge is stored' idea then doesn't it follow that there can never be any device that stores charge? I mean, the universe is electrically neutral overall, isn't it? Any build up of charge in any location is going to be caused by a loss of charge somewhere else. Since charge is conserved in the universe there's only ever going to be 'separated' charge hanging around. If this is the case we, shouldn't we give up using the phrase 'stored charge' all together? What would be gained by this? In addition, you've stated several times that there's no conservation of charge in a capacitor. But if the total charge is always zero, that's still a conserved quantity right?

Also, how can the charge transfer take place in zero time? Any collection of particles is going to take some time to move one location to another. They're going to have to start moving, travel some distance and then stop. I'm not sure how these particles can fail to radiate energy when they do this, but maybe this is a failing in my understanding of electrodynamics.

Like I say, it's all a bit too non-physical for my taste. We end up with these two capacitors with exactly zero resistance separated by zero distance or something. It doesn't sound much like the situation posited in the OP.

MalachiK,

Hmmm, but if we go along with this 'no charge is stored' idea then doesn't it follow that there can never be any device that stores charge?
I said that caps do not store a net charge. You cannot expect to take x coulombs from one cap and give it to another.

I mean, the universe is electrically neutral overall, isn't it?
I don't know.

Any build up of charge in any location is going to be caused by a loss of charge somewhere else.
Not if free charge carriers already exist somewhere.

Since charge is conserved in the universe there's only ever going to be 'separated' charge hanging around.
You have no basis to extrapolate from a cap to the universe.

If this is the case we, shouldn't we give up using the phrase 'stored charge' all together? What would be gained by this? In addition, you've stated several times that there's no conservation of charge in a capacitor. But if the total charge is always zero, that's still a conserved quantity right?
Charge is equally separated and conserved within a cap A. But you cannot give net charge away to cap B, because cap A has no net charge to give away. If you try to work problems that way, you will fail. Work those problems on an energy basis. Then you will never go wrong.

Also, how can the charge transfer take place in zero time? Any collection of particles is going to take some time to move one location to another. They're going to have to start moving, travel some distance and then stop. I'm not sure how these particles can fail to radiate energy when they do this, but maybe this is a failing in my understanding of electrodynamics.
You are trying to explain mathematical infinitesimals and infinities by a real world model. I showed what happens when the resistance is finite. You can make the resistance as small as you want, until the physical model can no longer support the values of current and velocity of the charge carriers.

Like I say, it's all a bit too non-physical for my taste. We end up with these two capacitors with exactly zero resistance separated by zero distance or something. It doesn't sound much like the situation posited in the OP.
The OP did not specify a resistance or say that any resistance was in effect. Therefore, it does seem to match what the OP asked.

Ratch

But clearly the question is a real world question. It says that there's this capacitor that's connected to another capacitor. Whyfore this assumption that the question concerns some utterly non-physical idealisation?

To take your free charge example... wouldn't removing some of these free charges and putting them some place else represent a net reduction in charge in the original location? Isn't that what happens when we charge a capacitor? We have the delocalised electrons in the metal of one plate moved around to the other plate. I don't understand how this is different. What if I get some charge from some other place and put it on one of the capacitor plates? Does it store charge then? Or is that plate now just storing separated charge in concert with wherever I got the charge from? I honestly don't understand how this thinking makes anything clearer.

Anyway, the only way to do a complete analysis from the point of view of energy transfer would be to take into account all of the energy losses. I don't see how you can invoke energy conservation and they ignore the losses that must take place when we have a non uniform current flowing between two points. But each time I suggest a reason why there might be additional energy losses to account for you propose some reasons that I don't understand to say that they don't happen.

I'm not saying your solution is wrong within the limitations that it sets itself - I just don't think that it's valid to ignore radiative losses. Maybe I'm too hung up on this 'real world model', but if we stop thinking about charge carriers moving around then we're not talking about two capacitors that have been connected together anymore - we're talking about some mathematical novelty that hasn't got anything to do with the reality of how this system behaves.

In any event, it's given me something to think about.

ehild
Homework Helper
Electric charges can be separated, and it is possible to give one plate of a capacitor some charge Q while the other plate stays neutral or has some charge different from -Q, although capacitors in electric circuits usually have equal and opposite charges on the plates.

The model of connecting a charged and an uncharged capacitor with zero resistance wire would mean infinitely great current flowing for infinitely short time. It does not happen in real life. The wire has resistance, and it has got also inductance. The capacitors and the wires connecting them make a loop. The current flowing in the loop changes in time, causing a varying magnetic field around. Varying magnetic field causes changing electric field, it causes magnetic field... the electric energy of the capacitors radiates away.

The real situation is quite complex, and the system can loose energy in different ways. If the resistance of the wire dominates, the lost energy transforms to heat, warming up the wire. The inductance of the wire makes a resonant circuit with the capacitors and the stored energy would oscillate between the inductor and the capacitors, and at the same time dissipating on the resistor. If the resistance is very small, radiation would be the energy-dissipating process.

ehild

Malachik,

But clearly the question is a real world question. It says that there's this capacitor that's connected to another capacitor. Whyfore this assumption that the question concerns some utterly non-physical idealisation?
It is real world if a finite resistance is assumed. It is an idealization if no resistance is assumed.

To take your free charge example... wouldn't removing some of these free charges and putting them some place else represent a net reduction in charge in the original location?
Where else? Outside the capacitor? What location? The capacitor?

Isn't that what happens when we charge a capacitor?
You don't charge a capacitor, you energize it.

We have the delocalised electrons in the metal of one plate moved around to the other plate.
You add some amount of electrons to one plate and remove the same amount from the other plate. They are not necessary the same electrons.

I don't understand how this is different.
Different from what?

What if I get some charge from some other place and put it on one of the capacitor plates? Does it store charge then? Or is that plate now just storing separated charge in concert with wherever I got the charge from? I honestly don't understand how this thinking makes anything clearer.
That is what I have been trying to tell you. You can't do that. Whatever voltage you use to put coulombs on one plate will remove the same number of coulombs from the opposite plate. Net charge is zero, remember? You can't have 4 coulombs on one plate and 2 coulombs on the opposite plate. Or how about 4 coulombs on each plate? How would you do that?

Anyway, the only way to do a complete analysis from the point of view of energy transfer would be to take into account all of the energy losses.
Which I did with the resistor.

I don't see how you can invoke energy conservation and they ignore the losses that must take place when we have a non uniform current flowing between two points. But each time I suggest a reason why there might be additional energy losses to account for you propose some reasons that I don't understand to say that they don't happen.
You are going beyond the scope of the problem if you suggest any significant loses occur from things other than resistive elements.

I'm not saying your solution is wrong within the limitations that it sets itself - I just don't think that it's valid to ignore radiative losses. Maybe I'm too hung up on this 'real world model', but if we stop thinking about charge carriers moving around then we're not talking about two capacitors that have been connected together anymore - we're talking about some mathematical novelty that hasn't got anything to do with the reality of how this system behaves.
The problem definition sets the limits. Ignore radiation unless you are given more info from the problem. No one said charge carriers don't move. But their quantity stays in balance. For instance, the amount of charge that exits from one plate of a capacitor is match by the same amount of charge that enters the opposite plate.

Ratch

ehild,

Electric charges can be separated, and it is possible to give one plate of a capacitor some charge Q while the other plate stays neutral or has some charge different from -Q, although capacitors in electric circuits usually have equal and opposite charges on the plates.
How would you put different amounts of charge of the plates of a cap? Inductive methods, perhaps?

Ratch

... it is possible to give one plate of a capacitor some charge Q while the other plate stays neutral or has some charge different from -Q, although capacitors in electric circuits usually have equal and opposite charges on the plates.
ehild
That's what's been bothering me. I mean, a capacitor doesn't have to be a sealed unit. I can just get two plates that I've independantly charged up with different amounts of +ve and -ve charge (opposite charges in each metal plate) and put them next to each other. BAM! I've got a capacitor with a different charge on each plate. That works, right?

This whole infinite current in infintesimal time is all too clever for me. I'm quite simple and infinites make my head hurt!

ehild
Homework Helper
That's what's been bothering me. I mean, a capacitor doesn't have to be a sealed unit. I can just get two plates that I've independantly charged up with different amounts of +ve and -ve charge (opposite charges in each metal plate) and put them next to each other. BAM! I've got a capacitor with a different charge on each plate. That works, right?
It is right. Even a single metal sphere is a capacitor and you can give charge to a metal sphere... Just rub a comb and touch to it.

This whole infinite current in infintesimal time is all too clever for me. I'm quite simple and infinites make my head hurt!
It makes my head hurt, too. That is why I would include the resistance of the connecting wire. With that, everything is simple and all right.

ehild

MalachiK,

That's what's been bothering me. I mean, a capacitor doesn't have to be a sealed unit. I can just get two plates that I've independantly charged up with different amounts of +ve and -ve charge (opposite charges in each metal plate) and put them next to each other. BAM! I've got a capacitor with a different charge on each plate. That works, right?
What are you going to use for positive charges? Protons?

Ratch

ehild
Homework Helper
You can make a glass rod positively charged by rubbing it with cats fur. You touch it to a metal plate: That will be positively charged, too, as some electrons of the metal go over to the glass.

ehild

ehild,

You can make a glass rod positively charged by rubbing it with cats fur.
Correct, by the absence of electrons, not by any positive charges.

Ratch

ehild
Homework Helper
Absence of electrons leaves positively charged particles behind. Yes, because of the excess protons.
Positively charged particles are made in ion guns. Positively charged alpha particles can arise in radioactive decay. There is a material testing method using positrons, also positively charged particles.
There are both positively and negatively charged particles in the world, and they can be isolated.

ehild

ehild,

Absence of electrons leaves positively charged particles behind. Yes, because of the excess protons.
Yes, but the protons are locked into the ionic core of the molecule and cannot move like the electrons can. They certainly do not move in capacitors.

Positively charged alpha particles can arise in radioactive decay.
Yes.

There is a material testing method using positrons, also positively charged particles
A positron is a antimater particle. How are they made and controlled?

There are both positively and negatively charged particles in the world, and they can be isolated.
Yes, ions in electrochemistry and holes in p-type semiconductor. But not in capacitors.

Ratch

ehild
Homework Helper
See http://en.wikipedia.org/wiki/Positron_emission .

Well, what do you think, can an isolated capacitor have net positive charge? You have two metal plates and remove electrons from both of them. Is it possible?

I think you mix "charge" with charged particle. Charge is a property. Anything can have some charge, positive or negative.

The charged particles - electron, proton, positron, ions, - all carry some charge, integer multiple of the elementary charge. In different materials, different particles are the main charge carriers. In metals or semiconductors the main charge carriers are free electrons. In fluids and gases, the charge carriers are mainly ions. But there is ionic conductions also in solids, and ionic conduction is the main conduction process in insulators like glass or in ionic crystals.

ehild

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ehild,

Well, what do you think, can an isolated capacitor have net positive charge? You have two metal plates and remove electrons from both of them. Is it possible?
According to the link you gave, it would have to be a radioactive capacitor. But even if you could do it by some electrostatic induction method of taking away electrons, the sea of electrons present in metallic conductors would rush in and neutralize your efforts. That is why holes only exist in semiconductors. It is certainly not practical for a working circuit.

Ratch

ehild,
According to the link you gave, it would have to be a radioactive capacitor.
Ratch
So? Why not paint one of the plates with potassium-40? Everyone should have a hobby.