# Where energy is going?

When we make plates of charged capacitor farther apart,energy density of capacitor suppose to diminish.Where this energy is going and could we tell thet we conserve this energy in some other form?

## Answers and Replies

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Redbelly98
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Assuming you mean the stored energy (not energy divided by the capacitor's volume) in the capacitor, then as the plates are moved farther apart:

• The energy stored will increase if the charge Q is held fixed, and
• decrease if the voltage V is held fixed.

If V is held constant, say by connecting the capacitor to a battery, then the energy goes back into the battery (as the charge flows between the capacitor and the battery.)

Hope that helps.

As I know there is two basic ways to increase energy in a capacitor.
1)Increase charge on the plates.
2)Reduce distance between plates.
It looks logical beacause both ways make charges on plates attract each
other stronger and therefore have more potential energy.
In example that I gave capacitor isn connected to anything elese.
I cant understand as you say how moving plates farther apart could increase energy of
the system.I thought it should diminish.

It looks logical beacause both ways make charges on plates attract each
other stronger and therefore have more potential energy.
They attract each other more strongly, but have less distance to travel before they meet each other. Move them apart, and they attract each other less strongly, but can do work as they move back to their original distance. The plates would have maximum potential energy if separated by infinite distance. As they approach zero distance, their potential energy approaches minimum.

As with gravitation, the potential energy between attracting charges is zero at infinity, and negative at all finite distances (proportional to q1*q2/r). You are usually interested in differences in potential energy, which is what confuses a lot of people.

1) In this case where is energy going when we make plates of capacitor closer to each other?Energy should diminish in this case?

2) Currently, they are trying to create high energy density capacitors for electric car such as Eestor.
Is it possible to make large unipolar capacitor which would discharge to the Earth?It could have ground of variable lenghth and be discharged through electric motor.Could you calculate how great energy density would it have if distance between capacitor (ground) and the Earth is 40 cm (15 inches)?Big distance between plates should meen big potential energy?What polarity such unipolar capacitor better to have taking in account that Earth have 200.000 V of negative potential?

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Currently, they are trying to create high energy density capacitors for electric car such as Eestor.
Is it possible to make large unipolar capacitor which would discharge to the Earth?It could have ground of variable lenghth and be discharged through electric motor.Could you calculate how great energy density would it have if distance between capacitor (ground) and the Earth is 40 cm (15 inches)?Big distance between plates should meen big potential energy?What polarity such unipolar capacitor better to have taking in account that Earth have 200.000 V of negative potential?
That's a crazy sounding idea that actually makes some sense. Capacitance is inversely proportional to dielectric thickness, maximum voltage is proportional to dielectric thickness, and energy is proportional to capacitance and the square of voltage. Thus, energy storage capacity is proportional to the distance between the plates.

Air gap capacitors start off rather low, though. The dielectric constant will be far, far lower than it is for things like barium titanate, and there's limits to how highly charged you can make an object before it starts ionizing the air around it, so it would be a lot larger than a conventional supercapacitor, and dealing with the high voltage is certainly inconvenient. You would also need a good contact with the ground to discharge through, so the unipolar idea is useless for ground or air vehicles. Think bigger, and maybe it starts to work for some purposes.

A giant vacuum capacitor as a storage device is an interesting variation. There's still limits on how strongly charged you can make things before they start spraying electrons into the vacuum or tearing themselves apart, but no mass would be required for dielectrics, only for the plates. Perhaps on spacecraft, where vacuum and space are readily available, but mass is at a premium...a couple large aluminized balloons as the plates.

A vacuum capacitor formed from a 100 m sphere inside a 200 m sphere charged to 10 MV/m would have a total charge of 1 GV, and store http://www.wolframalpha.com/input/?...m.*Meters.dflt--&a=UnitClash_*V.*Volts.dflt-- = 11 GJ (enough to supply 1 MW for about 16 minutes, or 350 W for a year), for what would be rather large, but could be rather little mass. You've got to deal with 1 GV to use it, though.

1) In this case where is energy going when we make plates of capacitor closer to each other?Energy should diminish in this case?
If the charge on the plates is constant, the energy's being removed as mechanical work.

capacitors fascinate me as I get the feeling that the math to deal with them has been simplified. Gauss flux law and Maxwells polarization delt with the permittivity of dielectric and the charge potential.

a half wave bridge rectifier of capacitors will increase the voltage potential to greater than the capacitance value for each capacitor. the equations for EM and electrostatic flux are very similar so the dielectric can be thought of as the R value and gives rise to the potential. It makes me wonder if you could vary the dielectric conductivity in a capacitor circuit you should be able to increase the voltage potential and then reduce to match the charge draw, a kind of dielectric controlled cascade effect. could be wayyyy off to.

and there's limits to how highly charged you can make an object before it starts ionizing the air around it,
I didnt remark that high voltage lines which have voltage up to 100.000 V would ionize lot of air around.At least I didnt smell lot of ozone near such lines.But agree that in conventional design there could be some looses through air ionisation and charge penetration.Why unipolar design seems interesting to me is because its greater safety.In case if something went wrong and dielectric breakdown occurd it will just discharg to the Earth instead of creating explosion.But nothing prevents you to create casing for such big capacitor made of Barium Titanate for better capacitance.
Also, if we charge giant unipolar capacitor positively, will it still arching to the air?I know that oxygen
more like to attract a negative charge carriers such as electrons.
If the charge on the plates is constant, the energy's being removed as mechanical work.
So in which form will be converted part of energy from capacitor?In the heat?

One more question.There exist so-called negative ion generators which produce only negative oxygen ions and virtually no positive.Where they constantly take electrons from to donate them to oxygen atoms?From body of generator itself?Some of those generators seem to be portable,they work from batteries.I thought that in any electrical circuit charges could only circulate but not to change their quantity.If ion generator constantly loosing electrons why it doesnt ionize positively itself?

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The dissipation seems to depend on how you separate them (the character of the process - an example would be the difference between a quasistatic and non-quasistatic process). Changing the electric field content of the capacitor is likely to generate a magnetic field; there may also be a momentary conventional current. If removal is done by springs (or anything spring-like), then some of the energy will go into the state of the spring. There is also the possibility of heat dissipation, etc...

I didnt remark that high voltage lines which have voltage up to 100.000 V would ionize lot of air around.At least I didnt smell lot of ozone near such lines.
Corona discharge is an issue and a non-zero source of losses for high voltage systems. You would have to be dangerously close to smell the ozone, but sometimes you can hear a buzzing sound from the discharge. (from connections at insulating posts, etc, not from a transformer)

But agree that in conventional design there could be some looses through air ionisation and charge penetration.Why unipolar design seems interesting to me is because its greater safety.In case if something went wrong and dielectric breakdown occurd it will just discharg to the Earth instead of creating explosion.But nothing prevents you to create casing for such big capacitor made of Barium Titanate for better capacitance.
Have you ever seen damage caused by a particularly strong lightning bolt? Don't be so sure it won't make a bang...

If the charge on the plates is constant, the energy's being removed as mechanical work.
So in which form will be converted part of energy from capacitor?In the heat?
The question was answered in the portion you quoted...as mechanical work, force exerted on the plates as they move. How it ultimately ends up depends on what's done with that mechanical work.

One more question.There exist so-called negative ion generators which produce only negative oxygen ions and virtually no positive.Where they constantly take electrons from to donate them to oxygen atoms?From body of generator itself?Some of those generators seem to be portable,they work from batteries.I thought that in any electrical circuit charges could only circulate but not to change their quantity.If ion generator constantly loosing electrons why it doesnt ionize positively itself?
It will. Ion generators without an earth ground won't generate many ions unless they emit ions of both charges.

It will. Ion generators without an earth ground won't generate many ions unless they emit ions of both charges.
Do you want to tell that negative ion generators are sucking electrons from the Earth? Could you detail it?

Have you ever seen damage caused by a particularly strong lightning bolt? Don't be so sure it won't make a bang...
When lightning is striking in Lightning rod it is usually not damaged itself at least it is not blow in thousand pieces.When lightning is striking in the Earth what could happen is usually some molten ground.To happen big explosion you need to have some material which would expand because of lightning heating.Thin air is not very dangerous in this sense.

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Do you want to tell that negative ion generators are sucking electrons from the Earth? Could you detail it?
That is essentially what happens with those that are grounded, yes. What detail is needed?

When lightning is striking in Lightning rod it is usually not damaged itself at least it is not blow in thousand pieces.When lightning is striking in the Earth what could happen is usually some molten ground.To happen big explosion you need to have some material which would expand because of lightning heating.Thin air is not very dangerous in this sense.
Dangerous enough that it can break windows and cause other damage, and you'll have to store far more energy than is released in any lightning bolt.

That is essentially what happens with those that are grounded, yes. What detail is needed?
How much is there spare electrons in the ground? Ion generators are particularly interesteng because they may provide posibility to create MHD generator with low temparature air pre-ionization
instead of heating fuel mixture to extreme temperatures.How great persentage of air molecules could be theoretically ionized in some given volume of air?For example if we use some electrostatics for ionizing and will pass air through some dense nanofilter under very high voltage?

Another question: what takes more energy - to ionize negatively an oxygen molecule or later (for nature) convert it back to neutral oxygen? How negative oxygen ions created by lightning or whatefalls are converted back to neutral oxygen in nature?

How much is there spare electrons in the ground?
You're sitting on an entire planet of protons and electrons. Pulling a few electrons out to make a few negative ions doesn't make any significant difference in the net charge of the planet.

Ion generators are particularly interesteng because they may provide posibility to create MHD generator with low temparature air pre-ionization
instead of heating fuel mixture to extreme temperatures.How great persentage of air molecules could be theoretically ionized in some given volume of air?For example if we use some electrostatics for ionizing and will pass air through some dense nanofilter under very high voltage?
What do you plan to use to force the air through the generator? That's typically done with the temperature and volume changes created by burning fuel...

Efficiently running a MHD generator requires highly ionized (or otherwise conductive) working fluid, and electrically ionizing air to a high degree is not particularly efficient.

Another question: what takes more energy - to ionize negatively an oxygen molecule or later (for nature) convert it back to neutral oxygen? How negative oxygen ions created by lightning or whatefalls are converted back to neutral oxygen in nature?
Neutral atoms are the lowest energy state. If there's a positively charged atom around, energy will be released as the extra electron on the negative one moves to the positively charged one...the same amount of energy it took to move it the other direction initially, assuming perfect efficiency in doing so.

Pulling a few electrons out to make a few negative ions doesn't make any significant difference in the net charge of the planet.
I thought it takes lots of energy to stripe electrons from neutral molecules of such substances as silicon dioxide which constitute major part of the Earth crust.Wonderfully that negative ion generators consume such low energy.
What do you plan to use to force the air through the generator? That's typically done with the temperature and volume changes created by burning fuel...
Yes,oxydized air shoud burn with fuel altogether and created plasma will fly past magnetic field.
I think conductivity of such plasma should be good because of inheritent charge.

Small correction, the net charge of the planet is changed by exactly the same amount regardless of its size, but the charge is spread across such an enormous object that there's no significant change in the electrical field at any one point. It also has a non-zero charge to begin with, and the few electrons you pull away to make ions won't make any difference there.

I thought it takes lots of energy to stripe electrons from neutral molecules of such substances as silicon dioxide which constitute major part of the Earth crust.
Electrons are rather easily pulled from silicon dioxide, simple contact with materials like wool will do it. The issue is conductivity, though, and if Earth were a dry glass sphere, it would not make a very effective ground. It isn't, and while it's not a particularly good conductor, it's good enough to quickly distribute a small change in charge across an enormous area.

Wonderfully that negative ion generators consume such low energy.
For what they do, they consume enormous amounts of energy.

You seem to be under the impression that ion generators do far more than they actually do. They don't produce many ions. They mostly convert electrical power into heat, and the ones that actually work also pump a handful (an obscure technical term meaning "not very many") of electrons (from the ground or from their own mass) into the air, where they latch onto oxygen molecules until they encounter something that'll take the excess electron (the case of an ungrounded ion generator will serve).

Yes,oxydized air shoud burn with fuel altogether and created plasma will fly past magnetic field.
I think conductivity of such plasma should be good because of inheritent charge.
If you're using combustion to force the gases through the MHD generator and the gases are already ionized plasma, where does the ion generator fit in?

where does the ion generator fit in?
Air should pass through ionizator filter and after that get to combustion camera through
intake valve already being ionized.It would be similar to usual engine but you need to replace usual air filter with grounded ionization filter.But probably it would not work out because as you said it cant create lot of ions at low energy price.I thought before that number of ions produced doesnt
depend largely on amount of energy spend but rather on contact area.I thought you need just create very high voltage and it will ionize unlimited amount of ions purely electrostatically.
Electrons are rather easily pulled from silicon dioxide, simple contact with materials like wool will do it.
Are you sure that metalic ground of ionizer works exaclly like wool?
where they latch onto oxygen molecules until they encounter something that'll take the excess electron (the case of an ungrounded ion generator will serve).
I dint unerstand this expression.Do you meen that action of ion generator will stop at certain point if its ungrounded?

Air should pass through ionizator filter and after that get to combustion camera through
intake valve already being ionized.It would be similar to usual engine but you need to replace usual air filter with grounded ionization filter.But probably it would not work out because as you said it cant create lot of ions at low energy price.
I'm not sure what you hope to gain by producing ions, no matter how cheaply you do so. The gas will be much more thoroughly ionized by the combustion process. It's like grabbing occasional pieces of coal going into the combustion chamber, carefully warming them with a lighter, and tossing them back into the stream of coal. I don't know what you're trying to accomplish.

I thought before that number of ions produced doesnt
depend largely on amount of energy spend but rather on contact area.I thought you need just create very high voltage and it will ionize unlimited amount of ions purely electrostatically.
Nope. You have to charge a negative electrode strongly enough that electrons on that electrode are at a lower energy state attached to a negatively charged oxygen atom or flying away alone through the air than they are remaining on the electrode. The current is very small for consumer ion generators, but there must be a current, through a circuit including the ionized air and the ground or case of the device. The vast majority of the power used will be wasted in the circuitry generating and holding that high voltage.

Are you sure that metalic ground of ionizer works exaclly like wool?
...I'm quite sure it doesn't work anything like wool.

I dint unerstand this expression.Do you meen that action of ion generator will stop at certain point if its ungrounded?
At some point it'll be unable to generate negative ions faster than they neutralize against its positively-charged case, yes. If they are prevented from reaching the ion generator, it will eventually accumulate such a strong positive charge that it can no longer produce negative ions.

The gas will be much more thoroughly ionized by the combustion process.
To make it sufficiently ionized in MHD generator you need to heat it up to 10.000°C.And at just a bit smaller temperatures this plasma is already useless.Not talking that any material tends to melt at such temperatures.Usually they use sodium additives and efficiency of MHD is still low in classical process.If you would be able to make 90% of air ionized and after burn it with fuel there would be excess amount of electrons that will make those gases very conductive and at usual combustion temperatures - 2000-2500°C.I think that if idea of cold ionization would be completely useless they would not experiment with electron beams:http://ieeexplore.ieee.org/Xplore/l...553806.pdf?arnumber=553806&authDecision=-203"

I get back to my idea of big unipolar capacitor.If we will charge it positively e.g. with shortage of electrons,could there be some sonditions under which dielectric breakdown with Earth could occur?I mean solid body cant discharge to the Earth itself?We could draw electrons from the ground to capacitor through the motor and gradually neutralise its charge.Whould it be not safer?

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To make it sufficiently ionized in MHD generator you need to heat it up to 10.000°C.And at just a bit smaller temperatures this plasma is already useless.Not talking that any material tends to melt at such temperatures.Usually they use sodium additives and efficiency of MHD is still low in classical process.If you would be able to make 90% of air ionized and after burn it with fuel there would be excess amount of electrons that will make those gases very conductive and at usual combustion temperatures - 2000-2500°C.
The household negative ion generators and battery powered gadgets don't ionize more than a few molecules per million, far less than 9 out of 10. Ionizing air at atmospheric pressure to the degree you're talking about requires something more like an electric arc.

I think that if idea of cold ionization would be completely useless they would not experiment with electron beams:http://ieeexplore.ieee.org/Xplore/l...553806.pdf?arnumber=553806&authDecision=-203"
That's a completely different system from what you described, using ionization of noble gases in a closed cycle with some external heat source. I only have access to the abstract, but it's probably intended to be coupled with an RTG or nuclear reactor.

I get back to my idea of big unipolar capacitor.If we will charge it positively e.g. with shortage of electrons,could there be some sonditions under which dielectric breakdown with Earth could occur?I mean solid body cant discharge to the Earth itself?We could draw electrons from the ground to capacitor through the motor and gradually neutralise its charge.Whould it be not safer?
Lightning seems to be a rather clear and obvious counterexample to the idea that things can't discharge to Earth.

Safer than what? It would be somewhat less safe than a storm cloud about to produce a particularly strong lightning bolt (being more conductive, and thus more able to dump all its charge into an arc to ground), and about the same size or larger (or constructed in large numbers) to store a useful amount of energy.

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and thus more able to dump all its charge into an arc to ground
Positive charges in the clouds are rather in gaseous form while positive molecules in capacitor
are still bonded with some covalent bonds.Do they need to vaporize first to arc to the ground?
Ionizing air at atmospheric pressure to the degree you're talking about requires something more like an electric arc.
Then it still may works.Corona discharge do not consume too much energy.What about some electrostatic material with high surface area?I dont know,but usual car catalysts are able to eliminate 90% of polutants due to their high surface area honeycomb structure.What if we make such ionizer for air made of some material which like to donate electrons (such as fur).
Electrons are rather easily pulled from silicon dioxide, simple contact with materials like wool will do it.
I thought that wool is rather positively charged,it prone to donate electrons,not to accept them.
And silicon dioxide (I guess) is rather triboelectricaly neutral.What is different from pure silicon or silicon rubber.
http://en.wikipedia.org/wiki/Triboelectric_effect" [Broken]

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Positive charges in the clouds are rather in gaseous form while positive molecules in capacitor
are still bonded with some covalent bonds.Do they need to vaporize first to arc to the ground?
No, they don't. They're surrounded by air and the ground has plenty of electrons to contribute to an arc. The atoms of the positively charged plate don't have to go anywhere. (though a good number of them will go everywhere when the discharge occurs)

Then it still may works.Corona discharge do not consume too much energy.What about some electrostatic material with high surface area?I dont know,but usual car catalysts are able to eliminate 90% of polutants due to their high surface area honeycomb structure.What if we make such ionizer for air made of some material which like to donate electrons (such as fur).
Corona discharge can consume quite a bit of power, and isn't going to ionize 90% of the air. Fur isn't going to help here.

I thought that wool is rather positively charged,it prone to donate electrons,not to accept them.
And silicon dioxide (I guess) is rather triboelectricaly neutral.What is different from pure silicon or silicon rubber.
http://en.wikipedia.org/wiki/Triboelectric_effect" [Broken]
I don't understand what you're thinking or trying to say. You just linked to a page that shows glass and quartz as further toward the positive end of the triboelectric series than wool. Why do you guess it's neutral?

Silicon dioxide is a compound of silicon and oxygen...quartz/silica is pure silicon dioxide, glass is mostly silicon dioxide. Silicon is an element, and silicone is a compound of silicon with hydrogen and oxygen...the three have very different properties.

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Silicon dioxide is a compound of silicon and oxygen...quartz/silica is pure silicon dioxide, glass is mostly silicon dioxide. Silicon is an element, and silicone is a compound of silicon with hydrogen and oxygen...the three have very different properties.
Thanks for enlightening me.If I no make mistake and quartz is basicaly a silicon dioxide than it may work.Although quartz and fur (wool) are quite close on the triboelectric ladder,so the effect will be not very strong.
They're surrounded by air and the ground has plenty of electrons to contribute to an arc.
Oh,so you mean that Earth electrons may arc to capacitor rather than backwards?I dont know if it may lead to a big explosion.Although I never going to make experiment myself.
Fur isn't going to help here.
Do you know if oxyden could get charge just on contact with some material?The link that I provided you places air at the positive end of triboelectric series,although I think there is either some mistake or they mean some dust in air rather than oxygen.I thought that oxygen shoud be the most negatively charged.
Also I know there exist some piezoelectric ion generators.Possibly they do not use electric power.
Why you such sure that we cant create high surface contact area for oxygen?

a half wave bridge rectifier of capacitors will increase the voltage potential to greater than the capacitance value for each capacitor. the equations for EM and electrostatic flux are very similar so the dielectric can be thought of as the R value and gives rise to the potential. It makes me wonder if you could vary the dielectric conductivity in a capacitor circuit you should be able to increase the voltage potential and then reduce to match the charge draw, a kind of dielectric controlled cascade effect. could be wayyyy off to.
Could you explain what did you exactly mean?Are you talking about increasing energy density of capacitors?Or something else?