What makes the charge gradients within a cloud?

[Edison Bias]

Hi!

It has been explained to me in another thread of mine that there actually can be lightning/thunder within a cloud.

My question now is how there can be such high charge gradients within a cloud that this can happen and of what types of ions and electrons there is and how they have emerged.

Because it's for sure not gravity, or?

As the amateur I am I will try a explanation of my own: a cloud consist of water vapor, this vapor has then become ionized by photons from the sun but if hydrogen are free ions and oxygen free ions, there should be a "big bang", right? And this still not explains the obvious gradients in space.

Edison

 

[Simon Bridge]

Things to think about: real life is messy...
You can have molecular ions, and objects like dust and water droplets can become charged.
Photoionization (sunlight) is not the only way that objects can become charged in Nature.
Objects can become charged by friction or interaction with ions carried in the air: ie by wind.
Similarly, wind can separate out charges in a region just by blowing through it, and different clouds may carry different potentials depending on their histories.
It may be that the potential difference is between a region carrying a large net negative charge and another region carrying a smaller net negative charge, with a static discharge (lighting) occurring as these regions approach.

 

[Edison Bias]

Things to think about: real life is messy...

No simple answers here, then :)

You can have molecular ions, and objects like dust and water droplets can become charged.

Interesting.

Photoionization (sunlight) is not the only way that objects can become charged in Nature.

The only way I could think of with my limited knowledge.

Objects can become charged by friction or interaction with ions carried in the air: ie by wind.

Friction brings me back to how a balloon may be charged by rubbing a plastic stick on it, it then attaches to ones hair :)

Similarly, wind can separate out charges in a region just by blowing through it, and different clouds may carry different potentials depending on their histories.

Interesting.

It may be that the potential difference is between a region carrying a large net negative charge and another region carrying a smaller net negative charge, with a static discharge (lighting) occurring as these regions approach.

This approach of thinking was educational, a potential difference can then consist between two regions of only electrons but with different number of electrons, right? But why not? Potential is defined by number of charge and here we only have a difference in number of charge. At the same time, why and how is there a difference in charges? As I have read the above one answer may be the wind and when the wind slows down, these regions approaches with lighting as the result.

But getting back to what you have said, ionization by sunlight is not the only way objects can become charged, friction is also important. But I still don't see how there can be so much free charges (weather they are molecules or electrons). Maybe two water molecules rubbing against each other can strip electrons so that there are water molecules of positive charge along with electrons of negative charge just by, as you have told me, friction? And wind makes these charges move away or toward each other which finally, when they are close, makes lightning? It's hard to see though.

Thanks Simon for your answer, it educated me!

Edison

 

[davenn]

This approach of thinking was educational, a potential difference can then consist between two regions of only electrons but with different number of electrons, right?

yes, one region is just more positive than the other
remember it's primarily the movement of electrons and positive ions ... electrons are being stripped off atoms resulting in charge separation

As I have read the above one answer may be the wind and when the wind slows down, these regions approaches with lighting as the result.

not quite see previous comment and the following ones I make

But I still don't see how there can be so much free charges (weather they are molecules or electrons). Maybe two water molecules rubbing against each other can strip electrons so that there are water molecules of positive charge along with electrons of negative charge just by, as you have told me, friction?

yes ... consider we are talking about zillions ( uncountable numbers) of atoms being stripped of electrons
you commented on the rubbing of a balloon experiment not really big sparks being formed
take that a step further, when you rub you feet across a carpet and go to touch a doorknob etc you can produce a 5mm spark ~ 10,000 - 50,000 Volts
another step further, a Van de Graff generator, a major electron stripping operation. a few million volts and much larger sparks

now to a thunder storm cell say 20km wide and 12,000 metres high (15 miles and ~ 38,000 ft) more electrons being stripped from atoms than you could ever imagine by the friction of water droplets, ice crystals and full sized hail stones all being carried by huge updraughts within the storm cell
10's to 100's of millions of volts and huge charge build ups resulting in 10's of 1000's of amps in a single lightning bolt.

And wind makes these charges move away or toward each other which finally, when they are close, makes lightning? It's hard to see though.

no, not quite the way you stated it
there is that charge separation with in the cloud(s), by the process I described, producing the inter and intra cloud discharges
there is also a buildup of separation of charge between the ground and the base of the clouds resulting in huge potential differences

When that potential difference ... the value of the electric field ... that is formed between the cloud base and the ground builds and finally reaches the breakdown voltage of the air gap insulation, a lightning charge will occur
Dave

 

[Edison Bias]

Thank you Dave very much for trying to explain this to me, yet I am mainly interested in lightning within a cloud and I still not really se it happening. Friction seem more important than I ever could have thought. Nice example with the walking on a carpet and touching a handle, gave me a clue of what it's all about. But charge separation within a cloud, why and how? If two water droplets, ice chrystals or full sized hail stones are rubbed together, why should the ions and the electrons get separated? Because they need to get separated, at least for a while, so that a high potential difference can be built up, right? Otherwise they just separate and recombine, I think. So somehow these electrons and ions get separated over a considerable time and then, suddenly, they crash into each other (breakdown voltage). Because even if there are "zillions" of atoms being stripped of electrons, they need to reside somewhere for a huge potential difference to occur. If the atomes are stripped of electrons all the time, the may also recombine all the time. There thus seems to be some kind of accumulation of charge which then discharges at some convenient opportunity, which is not fully defined.

Edison

 

[davenn]

yet I am mainly interested in lightning within a cloud and I still not really se it happening. Friction seem more important than I ever could have thought. Nice example with the walking on a carpet and touching a handle, gave me a clue of what it's all about. But charge separation within a cloud, why and how?

it's all in the response I gave ... here it is again

now to a thunder storm cell say 20km wide and 12,000 metres high (15 miles and ~ 38,000 ft) more electrons being stripped from atoms than you could ever imagine by the friction of water droplets, ice crystals and full sized hail stones all being carried by huge updraughts within the storm cell
10's to 100's of millions of volts and huge charge build ups resulting in 10's of 1000's of amps in a single lightning bolt.

So somehow these electrons and ions get separated over a considerable time and then, suddenly, they crash into each other (breakdown voltage).

no

as the electrons are stripped from atoms that is a charge separation. The positive ions ( atoms with less than their usual # of electrons) get moved away from the negative charges ... this results in an electric potential (and electric field) building up over a distance ( the gap between them) as with the cloud to ground strikes.
when the electric field exceeds the breakdown voltage of the gap, a lightning discharge occurs. There is no difference to this occurring be it with /between areas of the cloud and between the cloud and ground.Dave

 

[davenn]

here's a few pictorial examples ...

http://icons-ak.wxug.com/i/severe/lightning_explainer.png

cheers
Dave

 

[Edison Bias]

Once again I thank you Dave for trying to explain this to me. However I fail totally in understanding charge separation. Your kindly provided pictures looks nice and gives me more understanding generally but specifically, the charge separation with focus on staying separated and accumulate remains an enigma to me. Because where does the ions and electrons go? Why not just recombine? Why build up a huge potential difference and then discharge, I don't get it.

I expect no answer to this, you have put down enough time and effort into helping me, thanks.

Edison

 

[davenn]

the charge separation with focus on staying separated and accumulate remains an enigma to me. Because where does the ions and electrons go?

my previous comments and the images clearly show where they go

Why not just recombine?

recombine with what, they have become greatly separated over many kilometres as shown in the images ... between clouds and ground or between different regions in the clouds

Why build up a huge potential difference and then discharge, I don't get it.

I'm not sure how to be clearer ... the build up of the potential difference continues UNTIL the electric field reaches the breakdown voltage for that particular sized gap. Then the discharge occurs causing a recombination of the + and - charges and then the process repeats over and over until the storm dies out.
The charge separation can only occur when there is good updraught within the storm cell. As the updraught strength diminishes, so does the charge separation
Dave

 

[Edison Bias]

The charge separation can only occur when there is good updraught within the storm cell. As the updraught strength diminishes, so does the charge separation

I think this is the explanation I was looking for. Because how can charges of equal sign otherwise accumulate? It is even hard to understand how rubbing your feet on a carpet can strip and accumulate electrons within your body and then just discharge when you touch a doorknob of metal which even only may be sitting in a wooden door, that is the electric discharge does not even have to have a low ohmic path to the ground. It even feels like the discharge happens because the doorknob is made of metal without other considerations. As if metal itself accepts a bundle of electrons or even crave for it ;)

Edison

 

[davenn]

Because how can charges of equal sign otherwise accumulate?

that's indeed how they separate

It is even hard to understand how rubbing your feet on a carpet can strip and accumulate electrons within your body and then just discharge when you touch a doorknob of metal which even only may be sitting in a wooden door, that is the electric discharge does not even have to have a low ohmic path to the ground.

it doesn't need a path to ground ... it just needs a path to a place where the charge amount is different ... there is no grounds in the cloud are there ?

It even feels like the discharge happens because the doorknob is made of metal without other considerations. As if metal itself accepts a bundle of electrons or even crave for it ;)

it works better with metal as it is a good conductor. remember your body can collect that charge then discharge it to another object eg remember you can charge yourself up and then zap the person standing beside you, but neither of your bodies are made of metal.
Don't go there ! it's an inanimate object, has no feelings Dave

 

[Dotini]

Possibly useful table copied from a reference.

http://www.nap.edu/read/898/chapter/11#127

 

[NascentOxygen]

You can often see lightning flashes within the turbulent black cloud billowing from the vent of an erupting volcano.

 

[davenn]

You can often see lightning flashes within the turbulent black cloud billowing from the vent of an erupting volcano.

yup, indeed, and the process of charge separation is just the same
instead of cool wet materials in a cloud it's hot dry materials in the ash plume
D

 

[Edison Bias]

it doesn't need a path to ground ... it just needs a path to a place where the charge amount is different ... there is no grounds in the cloud are there ?
Dave

Hi Dave!

This was a real good explanation, thanks!

By the way, I didn't really mean "crave", my english is not so good :)

Edison

 

[Edison Bias]

Okey, Dave.

Maybe I should quit now but I am qurious, do I dare ask the question of charge accumulation? I think I understand charge separation in the aspect of stripping and friction, but I do not understand how charges with the repelling equal sign can accumulate. Let's again consider the simple situation of me walking on a carpet stripping electrons from it, why would I collect electrons at all? Is it because I'm positively charged to begin with, or? If I'm not positively charged to begin with, why would the electrons enter my body and stay there (until I touch something with a less/higher amount of electrons)? I really don't grasp this accumulation part.

Edison

 

[davenn]

but I do not understand how charges with the repelling equal sign can accumulate. Let's again consider the simple situation of me walking on a carpet stripping electrons from it, why would I collect electrons at all?

I'm not sure I can answer that overly well ...
@Dale @mfb can you help please ?

My first thought would be is that the forces separating the charges is stronger than the repelling force between like charges

Is it because I'm positively charged to begin with, or?

You are likely to be at or close to neutrally charged ( equal numbers of positive and negative charges)

some reading up of electrostatic charges may help ...

a couple on the Van de Graff generator...
https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/applications-of-electrostatics-138/van-de-graff-generators-496-6320/

http://www2.physics.ox.ac.uk/accelerate/resources/demonstrations/van-de-graaff-generator

a couple on general electrostatics ...

http://phun.physics.virginia.edu/topics/electrostatics.html

http://sardarsinghsir.com/XI-XII/XII-BC/I-v1.1-BC-Part-I-Electrostatics.pdfreading all those will keep you busy for a while
Dave

 

[mfb]

The triboelectric effect (charge separation by contact) is complicated, and not always intuitive - you can get some charge separation even if you rub two identical materials.

 

[Dotini]

You are likely to be at or close to neutrally charged ( equal numbers of positive and negative charges)

I think it is fairly well agreed upon that the surface of the Earth is negatively charged. It seems to me that a person standing barefoot in intimate contact with Earth is going to acquire the same charge as the Earth. Agreed?

 

[Tazerfish]

The triboelectric effect (charge separation by contact) is complicated, and not always intuitive -you can get some charge separation even if you rub two identical materials.

Would you further elaborate on that ? I am quite confused how this would be possible.
The wikipedia article is full off "citation needed" and it didn't really explain why charge separation between the same materials might work.
It said, that some materials have other "chemical potentials" and so some charge is more likely to accumulate there.
However if both substances are identical then there really shoudn't be any charge seperation.(When you base your assumption on only that idea)

And has there been any consensus of what the "dominant" process is in charge genertaion in a cloud ?

Speculation alert : I had an idea for a charge separation process.
Maybe because the droplets are often supercooled(i have no source for that) they will freeze a little upon contact with an snowflake or ball of hail, which might push out ions at different speeds causing some to be captured more in the ice than others.
To be honest I have no clue about this ...

 

[mfb]

I have read that in an article years ago, and the reason was not well understood at that time. Identical materials don't have to have completely identical properties, you still have things like temperature, strain and so on that can differ.

 

[Dotini]

I do not understand how charges with the repelling equal sign can accumulate.

Negatively charges particles may attract if enough positive charges lie in between.

• 
  
  

 

[mfb]

But then the positive particles are quickly going to the negative charges, neutralizing them.
The accumulation needs a different drive.

 

[Dotini]

But then the positive particles are quickly going to the negative charges, neutralizing them.
The accumulation needs a different drive.

Experiments have shown a balance is achieved and an order develops.
- Ise N, Okubo T. “Ordered” distribution of electrically charged solutes in dilute solutions. Acc Chem Res. 1980;13:303.
- Ise N, Okubo T. Ordered structure in diluted solutions of highly charged polymer latices as studied by microscopy. Chem. Phys. 1983;78:536.
- http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3859271/

 

[davenn]

I think it is fairly well agreed upon that the surface of the Earth is negatively charged. It seems to me that a person standing barefoot in intimate contact with Earth is going to acquire the same charge as the Earth. Agreed?

irrelevant ... as we weren't talking about barefooted standing on the Earth

we were talking about walking across a carpet and accumulating charge

 

[Edison Bias]

You're right Tazerfish, it says nothing about charge separation between two identical materials. It does however say something about "chemical potentials" and while being kind of vague sounds like a good explanation for charge separation. Then it goes on with saying that two materials are charged even more if rubbed together. I think I have noticed that in practice but the reason is kind of vague.

Thinking aloud: When an electron is, by simple touch, stripped (due to differencies in chemical potentials, let's say) from the carpet and enters my body, I get negatively charged. This creates an electromagnetic force that counteracts more electron stripping, right? So why will there be more stripping of electrons if my feet rubbes the carpet harder? Finally, why do the electrons stick to me or in other words, why not recombine with the positively charged "capet"?

The carpet is sitting there awaiting each step and it now has a slightly positive charge (which attracts electrons, obs) but the electrons refuse to recombine and stays in my body until I touch something that has an enormous larger difference in charge amount and the material can even reside on an totally insulating material like a metal handle on a wooden door.

Davenn has however kindly explained the fact that there is no need for a low ohmic path (to ground) to create a spark, only difference in charge amount. But still, what makes these potentials? How can there be accumulation of charge in materials?

"I'm negative, I want to be more negative", it does not compute :)

Edison

 

[Tazerfish]

When an electron is, by simple touch, stripped (due to differencies in chemical potentials, let's say) from the carpet and enters my body, I get negatively charged. This creates an electromagnetic force that counteracts more electron stripping, right?

That is correct.

why not recombine with the positively charged "capet

You seem to assume that charges will always equalize themselves if they have somewhere to go.
That is wrong.Think about the "depletion layer" in diodes.
Because the doped semiconductors have different "chemical potentials"(which is probably the wrong term here) they will cause small layers of charges to "equalize" the "chemical potential". In other words, the system would reach equillibrium when the work done against the electric field of the charges is the same as the work done by the difference in chemical potential. So a charge would neither gain nor loose energy by going from one point to another.
That equillibrium exists when there are two small layers of charges, not when everything is neutral.
There likely are a few other examples from electrochemistry as well, but I don't know much about that.
One example would be batteries(or rather one part of them).
If you just put certain metals into water they will become solved ions(the surplus electrons remain on the metal).
Although they are now charged they have a lower potential energy. This continues until there is a certain voltage between the metal and the solution.
Then we again have equillibrium and no further charge flows.
What I found very strange is that these voltages are on the order of a few Volts. How can triboelectricity generate such huge voltages ?
Why doesn't the charging continue until some point, at which the energy difference due to the voltage is equal to the energy difference due to the chemical potential and the charging stops ?

Speculation alert 2: I might know the answer:
Lets look at this like a capacitor where the plates (almost) touch. Charges move from one side of the capacitor to the other, because of the difference in chemical potential.That stops when a certain pretty low voltage is reached.
Now imagine the capacitor to be pulled apart.No charge flows because when the voltage increases enough for charges to "want" to flow back the separation is already too great.The voltages you would get when the capacitor is pulled apart a large distance could be pretty big.
Subsequently, if you brought them back together the voltage would be pretty low again and charge would feel no incentive to flow back and neutralize.
Speculation end.

but the electrons refuse to recombine and stays in my body until I touch something that has an enormous larger difference in charge amount and the material can even reside on an totally insulating material like a metal handle on a wooden door.

It is not about the difference in charge, but about the voltage.And while there is a high voltage between you and the carpet no charge will flow, mainly because the carpet is a horrible conductor and the reason i explained in the "speculation section" of this post.
You have to have a object that conducts well and is either connected to ground or has a relevant capacitance.
If you charged yourself and touched an insulated hanging metal lamp, you would get shocked and charges would flow onto the lamp until your potential was roughly equal. Nonetheless you haven't lost all your charge and some of your charge is now on the lamp.You could possibly still shock people by touching them and so could the lamp.
Ps : I have to do something about the way i write comments, because i feel like a spammer.
PPS:When i say potential i am usually talking about erergy per charge (something very similar to voltage) and not chemical potential

 

[davenn]

It is not about the difference in charge, but about the voltage.

it is about the difference in charge ... that is what gives rise to a voltage potential difference and electric field

 

[Tazerfish]

it is about the difference in charge ... that is what gives rise to a voltage potential difference and electric field

What I was trying to get across is, there is no direct connection between the amount of charge difference and wether discharge will occur.
I magine you have one object that has a lot of positive charge, but is big and a small object with a small amount of positive charge.
They may have the same electrial potential and so there would not be any voltage between them, although there is a high amount of charge difference.
It also is about how the charges are distributed!You cannot predict how much charge will flow just by knowing the difference in charge.
Wouldn't you agree on that ? ;:I

 

[Edison Bias]

I really do not know so much about physics but I find it interesting. That being said I would like to make a comment anyway:

What I was trying to get across is, there is no direct connection between the amount of charge difference and wether discharge will occur.

Yes there is, from what I have been taught. The amount of charge difference gives potential difference and when this potential difference exceeds the dielectric strength of the medium, a discharge will happen. Moreover, potential is directly related to charge amount, nothing else. You probably know the definition (which I only think goes):

[tex]Work=qU=\int_{-\infty}^{r}\frac{qQ}{4\pi \epsilon r^2}dr=[-\frac{qQ}{4\pi \epsilon r}]_{-\infty}^{r}=-\frac{qQ}{4\pi \epsilon r}[/tex]

Which gives U as proportional to Q (epsilon is usually for vacuum but I think the formula is more useable if the actual medium is considered)

I magine you have one object that has a lot of positive charge, but is big and a small object with a small amount of positive charge.

Here you will automatically have a potential difference, the number of positive charges will have to be exactly the same for zero potential difference, it has nothing to do with size, I think.

They may have the same electrial potential and so there would not be any voltage between them, although there is a high amount of charge difference.

Following my reasoning, this is false.

It also is about how the charges are distributed!You cannot predict how much charge will flow just by knowing the difference in charge.

This is interesting, I really don't know but I suspect it doesn't matter. However, a current (flow of charge) will flow due to the difference in amount of charge (if they not just differ in sign) and that current is depended on the potential difference as well as the resistivity between the two objects. Another aspect of this interesting thought is how there can be charge gradients (in clouds ;) ).

Finally, on the bus today I thought "why is there a discharge when I touch the metal handle and not when I touch the door? Davenn has taught me that the key reason for discharge is difference in amount of charge, okey I think I get that, but the door handle and the wooden door itself should have the same potential (amount of charge), right? Because he has also taught me that a low ohmic path to ground is of no importance. So why no discharge by touching the wooden door? Something is wrong here.

Edison
PS
Wait a minute, what does r mean in "my" formula above? Potential is inversely proportional to r (if you solve the integral) this means that two objects with the exact same amount of charge (Q) can have different potential if they are at different r and r can not be distance between Q's, right? The formula (The Electromagnetic Force) comes from distances between Q's but when it comes to potential, r has to mean something else (because a single Q has potential). So r means, what?

I guess r means hight but hight over what I don't know. Anyway say it's hight, then if two objects has the same Q and one resides in 2r, the one at 2r will have half the potential, can this really be true? Does hight at all affect voltage?

 

[Tazerfish]

We obviously have an misunderstanding here:

Moreover, potential is directly related to charge amount, nothing else.

That is simply incorrect! The potential IS determined by the distribution.
In your formula, you calculate the energy necessary to bring two charges together from infinity to a distance r.
So if you just take ## U=\frac{W}{Q} ## where U is the potential of your upper formula you get something like this:
## U= \frac{-Q}{4 \pi \epsilon r} ##
So the potential of at the distance r away from a charged point is U.
So assume we have a conductive sphere with some charge on it. Because of Gauss' law we can treat the charged sphere as a point charge at the center of the sphere as long as we are outside it.So you realize the potential of the sphere is exactly what we have worked out for U above.
Here r is the radius of the sphere and not the separation of two charges.
As you can clearly see the potential is NOT independant of the radius.
The distribution does matter.
PS: r is not height.
It makes intuitive sense:
If you put the charges closer together you have to do more work.And since Potential is Work per charge the potential must be higher just like the work.

 

[davenn]

What I was trying to get across is, there is no direct connection between the amount of charge difference and wether discharge will occur.

yes there is
increasing the charge difference = increasing the potential = increasing the electric field, between 2 points
that is what determines whether there will be a discharge. Those 3 things have to occur till the electric field
rises to a point where the breakdown voltage of the gap is reached ... then the discharge occurs
the larger the gap the higher the potential difference / electric field needs to be for discharge to happenD

 

[Tazerfish]

Finally, on the bus today I thought "why is there a discharge when I touch the metal handle and not when I touch the door?

Daves explanation was very close to correct. As he has mentioned charges are the cause for any potential and voltage.
But if you only think about the charges you don't get the bigger picture.
So let's quickly forget everything we know and I will try to concisely tell you why the door doesn't shock you.

For it to shock you, you need charge to flow from your body and into or through the other object.
So first of all, the door is a terrible conductor so it doesn't provide a path to the ground.
Neither does the handle, so why can it shock you ? 2 Reasons:
1.Some charges can flow onto the the handle, without directly flowing away.It essentialy acts like a capacitor.
Charges cannot easily flow into the door, since it is a poor conductor.
2.Touching the door actually provides a higher resistive path that touching the door knob.
That might seem strange since charge will have to flow through the door sooner or later,
but the door knob essentially has no resistance (compared to the door) and it touches a lot of the "door area".
You could imagine this like a lot of parallel circuits. So the resistance of the "door knob path" will be lower.

PS: This is sort of getting out of hand.The paper that was posted earlier gave pretty good explanations and I thought the question had been resolved.

 

[davenn]

Moreover, potential is directly related to charge amount, nothing else

That is simply incorrect! The potential IS determined by the distribution.

you didn't define that well EB
Tazerfish is correct

 

[Edison Bias]

We obviously have an misunderstanding here:

That is simply incorrect! The potential IS determined by the distribution.
In your formula, you calculate the energy necessary to bring two charges together from infinity to a distance r.
So if you just take ## U=\frac{W}{Q} ## where U is the potential of your upper formula you get something like this:
## U= \frac{-Q}{4 \pi \epsilon r} ##
So the potential of at the distance r away from a charged point is U.
So assume we have a conductive sphere with some charge on it. Because of Gauss' law we can treat the charged sphere as a point charge at the center of the sphere as long as we are outside it.So you realize the potential of the sphere is exactly what we have worked out for U above.
Here r is the radius of the sphere and not the separation of two charges.
As you can clearly see the potential is NOT independant of the radius.
The distribution does matter.
PS: r is not height.
It makes intuitive sense:
If you put the charges closer together you have to do more work.And since Potential is Work per charge the potential must be higher just like the work.

I will begin with answering this nice reply. First, let's redefine potential (which also makes it positive for positively charged particles) ;)

[tex]Work=qU=\int_{-\infty}^{-r}\frac{qQ}{4\pi \epsilon r^2}dr=[-\frac{qQ}{4\pi \epsilon r}]_{-\infty}^{-r}=\frac{qQ}{4\pi \epsilon r}[/tex]

Which is work done by moving a charge from minus infinity to -r, i.e against the electromagnetic force as well as common direction definition for r. If the upper limit was to be (which is common) r, then I think you will have to move the charge through r=0 and that can't be right, can it?

I am very pleased to finally learn what potential really is (being a Electrical Engineer as I am :D ), that is that the charge itself really does not have a potential by themselves (well they seem to do but let's forget about that for a while), potential is somewhere "in the air" at a distance from the charge. In other words, you may take a DVM (inside a Faraday Cage) and put one probe on the charge and the other in the air and you will read a voltage that is increasing as you move towards the charge and decreasing as you move away, right?

Now, let's consider two spheres (S1 & S2) and begin with equal size, if the amont of charge on each sphere is equal, they will induce a voltage inside each other (S1 induces in S2 over the distance r, and vice versa) which is the same, thus potential difference is zero. If the amount of charge at S2 is lager, there will be a larger potential inside S1, right? If the amount of charge is the same and the size of S2 is smaller then, in compliance with what you have said, something peculiar happens. We need to consider size. Just looking at the formula you may think that if Q1/r=Q2/r the potential is the same, but now we need to consider internal radius (R). Without knowing I would say that we may use the formula for potential inside the sphere too and this would mean that the larger the sphere, the smaller (for same amount of surface charge) the internal potential is at the centre. So a large sphere with the same amount of surface charge as a small sphere, has a lower "internal" potential than a small sphere. Which may pe interpreted as potential not only being depended on amount of charge but also on charge distribution, right Tazerfish?

Edison