What makes the charge gradients within a cloud?

[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) ;)

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}

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

 

[Edison Bias]

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.

I like this explanation, a wooden door is like a capacitor with a dielectrica (high resistance, some permitivity) and the doorknob is one of it's plates.

The door area the doorknob touches is not much but it's a good conductor and the dielectrica/door is in parallell which makes up for some capacitance to ground.

So you are standing there with some strangely accumulated amount of charge and therefore potential due to walk on a carpet and you touch the doorknob with a total different potential (remember, it is clear now that the pure amount of charge does not tell the potential).

If

i=C\frac{du}{dt}

Then discharge current is only limited by rate of voltage change which in this case should mean rate of "potential difference change" which is only limited by the total resistive path of Kirschoff Voltage law. If door-knob plus wooden door is the capacitance to ground, the carpet you are standing on, your shues and your body is the resistive path. So the resistive path limits the current but it does not limit when a discharge should strike because that is purely determined by potential difference and dielectric strength (of air).

Now, can we use this within a cloud? The dielectrica may be moistured air. Clusters of charges of different sign have somehow been built up on both sides of this moistured air. At a certain point in time, these clusters (or plates, actually because they are highly conductive) of charge comes so close together that the E-field exceeds the dielectric strength (V/m) of the moistured air and a discharge/lightning happens.

Okey, this is "my" rough theory but what about the details? I.e how does these charge gradients emerge in the first place and why and how do they accumulate?

One theory has been that friction is important (from davenn), friction between droplets and ice chrystals, this may explain charge separation but why accumulate?

Another interesting theory has been (from Tazerfish):

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.

So we have some explanations for charge separation but they are still very vague, and no good explanation for charge accumulation (not even generally).

I do however promise to read some more of your nicely provided links before I utter a single more ignorant word :)

Edison

 

[Tazerfish]

IPlease don't assume my answer to be true.
I've clarified that it was highly speculative and probably not important.
Maybe it doesn't even separate charges at all.Or possibly the other way around, opposing the main charging.(charging ice negative and droplets positive)
EDIT:Holy moly it was a real effect. (Read interface charging in the paper)

I feel like I didn't understand most of the section of the paper that has been posted earlier, but I will nonetheless try to summarize it because I don't think anyone else will do it.
In the beginning, there are already E- Fields and some ion concentrations.
The air isn't perfectly neutral and the droplets just "absorb" some of the free ions.
There also are drift currents, with which the cloud interferes since it absorbs ions.
Then there are some "positive feedback loops" in the cloud.
A polarized droplet moving through the air in or against the direction of the electric field will accumulate charge in something called the Wilson effect(I didn't find that name anywhere aside from the paper).
So a droplet moving down in a field downwards will accumulate primarily negative charge. (see the diagram in the paper)
A droplet moving upward in a downward field will accumulate positive charge.
Another field enhancing effect is about the interaction of multiple polarized droplets.
The smaller upwards moving droplets end up more positive and the downward moving droplets more negative.
Also, interactions between droplets of different temperature and interactions between ice and water (i think that one is particularly important) also move charge from one droplet to another.

So to sum up EXTREMELY CRUDELY
There already is a field at the beginning and some charges.
The drift currents due to this field enhance the field

The real fun begins when various sizes of droplets appear and start to fall
The droplets acquire a charge dependant on their direction of motion because of selective ion capture
Then because of a lot of phenomena do the smaller more upwards moving droplets become more positive and the bigger more downwards moving droplets become more negative

And then the interactions between ice and water droplets become important.This again results in the more upward moving snow or graupel to be more positively charged, than the more downwards moving more negative water droplets.

It all comes down to some processes transferring charges from one thing to another.
And then the positive things go up and the negative things go down.

If someone finds mistakes feel free to correct them, as I mentioned I didn't really understand the paper.
And I would REALLY appreciate it if someone(who actually understood it and possibly felt offended by the stupidity of comment) tried to summarize it in a more correct way.
PS: There actually is a thunderstorm taking place while I write this sooooo cool :D

 

[Dotini]

@Edison Bias

Two theories exist to explain generation of the main cumulonimbus cloud charge dipole: (1) precipitation, (2) convection, viewed as less significant.

In precipitation theory, heavy falling precipitation particles interact with lighter particles carried in updrafts. The interaction process serves to charge the heavy particles negatively and the lighter particles positively., after which updrafts and gravity separate the opposite charges to form a positive cloud dipole. Charge transfer can be by collision in which two initially uncharged precipitation particles become, after collision, oppositely charged, for example in collision between hail and ice crystals. Or charge transfer can be by induction in which two uncharged but electrically polarized precipitation particles collide in such a way that the small, light hydrometeor absorbs charge from the bottom of the larger heavy precipitation particle, as the light particle moves upward. The induction process serves to enhance the initial field in which it operates.

In convective electrification theory, charge accumulated near the Earth's surface or across region of varying air and cloud conductivity is moved in bulk to the observed locations by the air flow associated with the thunderstorm.

The small positive charge region at the base of the cloud may not be present on all thunderstorms, or may simply be well localized and difficult to detect.

A fundamental problem in developing an essentially static cloud charge model is that neither the fields nor the charges that produce them are really steady in time.

The above is after Uman, 1987

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http://onlinelibrary.wiley.com/doi/10.1029/2006JD007820/full
Abstract
[1] Evolution of lightning activity in a tropical hailstorm of moderate size that developed in the premonsoon season at Pune (18°32′N, 73°51′E, 559 m above sea level) is studied from the measurements of surface electric field, the Maxwell current and thunder. Total flash rate is counted from the electric field record, and the cloud-to-ground (CG) flash rate is estimated from the visual observations. Precise timings of their occurrence were confirmed from the observations of overshoot in the Maxwell current records. The storm exhibited an almost constant rate of one CG flash every 1 to 2 min over the whole life time of the storm. The ratio of intracloud (IC) to CG flashes (IC/CG) increased with the increase in total flash rate. In the convective stage of the storm, field changes from consecutive flashes were generally found to alternate in polarity. Moreover, in this stage, field changes occur in pairs, the first field change of each pair being of negative polarity and the second one of positive polarity. The two field changes in a pair occur with an average time difference of 14.3 ± 8.4 s while two consecutive pairs appear after 29.3 ± 9.1 s. In between the convective and mature stages, our observations suggest the occurrence of the phenomenon of rain gush and the field excursion associated with falling precipitation. Development of the mature stage was marked with rapid transitions in the surface electric field and the Maxwell current polarities from negative to positive. Further, total flash rate and IC/CG ratio sharply increase, and the lightning-induced electric field changes become almost exclusively of negative polarity. Observations suggest possibly a lifting up of the charging region in mature stage of the storm. The dissipating stage of the storm witnessed hail and rain showers, sharp transition of electric field and the Maxwell current from positive to negative polarity and occurrence of a few positive CG discharges. Our observations are consistent with the general belief that that some lightning flashes, by neutralizing and depositing charge in the region of opposite polarity, change the charge distribution so as to trigger another discharge in the storm.

[3]. ...in the most widely accepted of the thunderstorm charging mechanisms, interactions between graupel and ice crystals in presence of supercooled water result into charging of graupels with negative charge and ice crystals with positive charge when the graupels are growing by sublimation. The subsequent differential separation of particles under gravity is then assumed to cause creation of positive dipole.Results of the laboratory experiments of Reynolds et al. [1957], Takahashi [1978], and Saunders et al. [1991]suggest that the same charge separation mechanism can charge the graupel positively and create LPCC in tripole electrical structure when the graupel is undergoing deposition [Williams, 1989; Williams et al., 1991; Murphy et al., 1996]. Mansell et al. [2005] propose that inductive charging of particles in the lower part of cloud under the influence of overhead charge may be responsible for the LPCC. Observations of Holden et al. [1983], Marshall and Winn [1982], Mo et al. [2002], Coleman et al. [2003], Warner et al. [2003], and Rust et al. [2005] suggest that some flashes may deposit positive charge in the base of a thundercloud and thus act to generate the Lower Positive Charge Center (LPCC)...

[4] The presence of ice crystals and graupel is considered as fundamental for strong electrification and lightning

[5] Electrical processes operating inside thunderstorms generate large currents and the charges deposited by them considerably influence the Maxwell currents flowing outside the cloud. Therefore the Maxwell current flowing beneath a thunderstorm has often been interpreted to reflect the electrical processes occurring inside thunderstorms [Krider and Musser, 1982; Krider and Blakeslee, 1985]. For example, Krider and Musser [1982] equate the Maxwell currents to the charging currents in thunderstorms under conditions of low electric field, no precipitation and no lightning currents.

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Figure 9
A schematic diagram to explain the frequent occurrence of pairs of the lightning-induced field changes in stage A as compared to other stages of the thundercloud.