Not really sure I like that link. He seems to suggest that capacitors store "energy" instead of charge, which is just as ambiguous really. It's not like there is some sort of energy particle either. Of course what's really happening is that you are creating an electric potential between two plates. It's true that the net charge is the same, but you are moving electrons from one plate and forcing them (doing work) into the other. Then when you remove the battery and have an open circuit, the potential remains because they have no way to move back to the other plate until you close the circuit again. Also, I don't think the water analogies work very well because water does not attract other water in any way, whereas in a capacitor, the electrons attraction to the electron holes in the opposing plate is an essential part of how a capacitor works and explains why the distance between the plates and the surface area are important.
I think you are missing the point of the water analogies. It is what made electricity make sense to me as well. But don't take it too literally, it's an analogy, not an identity.
If you start with things like "a motor is like a turbine, a generator is like a pump, a battery is like an elevated tank", a lot of things can fall into place. The point is you can visualize it.
There's nothing weak about saying capacitors store charge. That's exactly what they do. You measure charge in coulombs, which is how you count electrons. Capacitance is just the value that relates stored coulombs of charge to available voltage.
I didn't agree with what you wrote and maybe I can explain why. Springs store inches. You measure displacement in inches. Spring constant is just the value that relates stored inches to available force.
(You can swap roles of force and displacement if you wish, the point is the same. It sounds bad to say springs store force or displacement, to me.)
But inches are an abstract measurement of distance. Electrons are a thing.
(Well, depending on who you ask... no one has ever seen one, and some people have claimed half-jokingly there's only one electron in the entire universe: https://en.wikipedia.org/wiki/One-electron_universe .)
Capacitors "store" electrons, like springs "store" steel, or rubber bands "store" rubber. A charged capacitor has exactly the same number of electrons as an "uncharged" capacitor.
When "charging" a capacitor, charge is forced into one terminal, and exactly equal charge comes out of the other terminal. No electrons build up inside, nor are placed into it. They've just been moved around inside, same as the steel spring, or the spherical tank in the water analogy.
What then do capacitors store? EXACTLY! That's the questions that students should be asking. They won't think to ask it, if they've been taught that capacitors are like buckets full of electrons. Well, what does a steel spring store? Or a stretched rubber band? KG of steel or rubber? Nope. Capacitors store joules, not coulombs.
The above concepts open the way to unifying several ideas: capacitors store charge in the same way that inductors store charge! In both components, energy is stored, as e-fields in the case of capacitors, b-fields in the case of conductors.
Fair enough -- a two-terminal capacitor that stored electrons supplied via one terminal could be charged without drawing any corresponding current at the other, violating Kirchoff. I do like your water-filled sphere analogy, and I agree that the word "charge" is an overloaded term.
But what would you say is happening at the top electrode of a Van de Graaff generator? It represents a reservoir of stored (positive) charge. Electrons have been physically moved outside the device, and we use the same language to describe this process -- that of capacitance.
I guess the argument would be that the objects in the room constitute the other terminal of the capacitor, with the intervening empty space forming the "dielectric," and that the electrons removed from the sphere aren't associated with the sphere at all, but have just been moved from one region of the dielectric to another?
Yep, a VDG machine is not a single-ended device. I tell people that there are always two spheres involved, although usually the second sphere is below our feet: planet Earth. Charge conservation says that, with a VDG, the e-field flux extends between the upper metal sphere and the ground below it. So, to concentrate attention on just the charged sphere, while ignoring the oppositely-charged ground surface, is much like concentrating on just one plate of any capacitor.
Better: hang many different metal spheres from insulating threads, then use a HV supply to deposit various charges upon them. "Capacitor" is always taken to mean a pair of opposite-charged objects. But miscellaneous "charged objects" aren't necessarily capacitors.
While employed at MOS in Boston I temporarily threw together a floating, double-ended VDG with a battery/motor inside one sphere. Like this:
http://amasci.com/emotor/vdgdesc.html#diff
I thought it would much better communicate the true nature of electrostatic generators, but it never ended up in our exhibit. VDGs are just constant-current high-voltage power supplies. A long enough chain of 9V batteries would produce all the same phenomena ...aside from the 10amp short circuit current, and the megawatt arcing!
PS, weirdness
With VDGs I was triggering three separate kinds of spark. I've not seen this discussed anywhere. We have the usual kind, the thin straight "needle" that jumps between smooth spheres. Then we have the violet fractal tree. Attach a 1cm ball to a VDG sphere and watch in a darkened room. It periodically spits foot-wide lightning networks, just like the miles-wide kind. And third: occasionally I was getting "silent purple sausage" discharge about an inch thick and a couple feet long. In a lighted room they make a slight "thump" sound, so if you hear that noise from a VDG, try observing in total darkness. Sometimes the "sausage" would even produce branching (possibly nanosecond wave effects,) when it would leap out 1ft, then split into five branches from the tip, then proceed to the adjacent metal wall as five fuzzy pathways. Perhaps the particular "seed" at the micro-scale will determine the type of spark which propagates? Or maybe the "sausage" discharge was actually a relativistic effect seeded by MeV cosmic rays.
Wheeler didn't really claim that the one-electron universe was literally true or even a useful model, but the observation that one cannot draw a clear difference between a particle in a (classical) field in flat spacetime with an enormously complicated worldline and many indistinguishible particles in the same field with straightforward timelike worldlines is a fairly deep insight into the symmetries of flat spacetime, particularly the translation symmetries. They were also on the cusp of spontaneous symmetry breaking while wondering about the missing positrons.
Given that this was decades before the Standard Model was formalized (one-electron, ca. 1940; Glashow electroweak spontaneously broken symmetry, 1967), I think that the one-electron thinking was incredibly productive (especially since Feynman credits it with some insights into what became his path integral formalism).
It's not that one-electron was (or even could be) fully in line with available evidence that was important, but rather that it connected the full symmetries of the Poincaré group (the isometry group of Minkowski spacetime, which is the spacetime of Special Relativity, particle indistinguishability, and representation theory.
The results of the this excited and informal conversation are still found in particle paradigms of quantum field theories (e.g. the Standard Model).
"Electrons are a thing" gets much trickier outside of Minkowski spacetime, however. In non-flat spacetime, the Unruh effect "is a thing", and one consequence is that different observers will disagree on particle count, and even on the interpretation of quantized excitations in the fields as (asymptotic) particles. Unless general covariance is abolished, which seems really hard to do, none of these observers is any more right than any of the others; the number of particles is simply not well-defined locally. Worse, a generally covariant formalism exposes that this is the case in flat spacetime too (e.g. Rindler observers of a patch of a quantum field are not "less right" than another observer at a constant interval from that patch, even if one sees a huge lake of energetic particles and the other sees no particles there at all).
An everywhere-in-spacetime electron field thing is probably a thing in our universe, though. But there are several different descriptions of it... :)
Can you clarify what your point is? I don't know how to answer the question, because springs don't store inches. If you are making a point about why the spring/inches analogy was bad, I'd like to hear it.
Um ... once we've cleared up all the misconceptions about electricity, we might want to move on to this other thing called gravity :-)
The usual reason that people are mislead by "water" analogies—more precisely, the analogy between height and electric potential—is because they misunderstood gravity to start with. If you start by writing Newton's law and Coulomb's law side by side, and develop the analogy in a precise way, smart students will be able to debug their own fallacies.
For example, a capacitor does have a precise gravitational analog, where you have two tanks floating in outer space, and water gets sucked into them by gravitational attraction. Once you understand that, you can think about the effect of removing the minus sign from the gravitational energy law, and about the things you can do with two types of charge, but can't do with only one type of mass.
where you have two tanks floating in outer space, and water gets sucked into them by gravitational attraction
As a person who has always struggled to understand electricity (but understand Newtonian gravity well enough), please tell me more! Water is going from where to where?
Picture a pair of tanks shaped like a parallel plate capacitor, a circuit shaped pipe connecting them, and a mixture of water and air filling the pipe. (The air lets the water move around without creating a vacuum.) All other things being equal, the water gets sucked into the plate shaped tanks to minimise the gravitational energy; the resulting gravitational field is identical to the electric field you would get if you forced positive charge onto both plates of a capacitor.
Some of the differences with electricity are:
Like charges repel, so you have to force the positive charge to go where the water would pull itself.
Mass is always positive (dark energy aside), but charge can be negative, so you can have "negative mass pipes" that cancel out the mass of the water.
You can squash positive charge into one tank, and negative into the other. Unlike the parallel water tanks, this takes work, because the charge on each plate repels itself-mass can't do that. But less work than when there is positive charge on both plates. The resulting dipole field is something that you can't get with gravity. This is how real capacitors work.
My water analogy for a capacitor is a piston with pipes attached to both ends, with a spring system that pushes the piston towards the center position. Is that not a mathematically correct equivalent? (in an idealized system with no water resistance/inertia and disregarding that the piston is of fixed length - not that real capacitors have zero resistence, inductance or can store infinite charge)
That's what I started out with! Fill the entire universe with solid rock (since air and vacuum are insulating.) Bore out a cylinder, fill it with water (electricity), and add a piston and spring. Wires are water-channels added to either end.
But note that, if we use a constant-force spring, then the voltage remains the same until just before the "capacitor" is totally discharged. So, it acts like a battery! To get a "capacitor," the spring must have an unchanging spring-constant, so that the potential-difference rises in proportion to how much water has been pumped from one terminal to the other.
Its risky to speculate on fuzzy analogies stacked on fuzzy analogies but another one I've seen is the water balloon, or balloon over an open piece of pipe. So some voltage pressure pushes the current into the balloon and the balloon kinda sorta works to keep a constant-ish pressure/voltage on the pipes.
Now if that was too easy try an inductor analogy. Something like a waterwheel hooked up to a very big flywheel so it works hard to keep the watercurrent flow constant.
The best thing about learning by analogies is eventually they get so hairy and crazy that reality is simpler in comparison...
From an energetic standpoint, a capacitor is something that takes a trickle over a long time, and releases a flood over a short time. So it would be a water tower with a small input and a large gated output.
But a water tower only has one terminal. A better "capacitor" would be a pair of water towers side by side.
To "charge" this double-water-tower capacitor, pump some water from one to the other. And, when the water-tower capacitor is entirely "discharged," the towers both have the same water level inside. (As with a real capacitor, the total amount of water never changes.)
Capacitors do store energy, in their electric field. Potential energy in general, as far as I'm aware, is stored in fields of some sort -- water turning a wheel (gravitational), tension in a spring (electromagnetic), capacitors (electromagnetic), chemical energy in gasoline (electromagnetic), nuclear energy (weak/strong fields I believe, not as well versed here) and so forth.
Interestingly, cohesion itself is caused by electric fields between water molecules due to their polarity (uneven distribution of charge, oxygen is electron-greedy). Much like a capacitor, separating the molecules (plates of the capacitor in the analogy) requires work which gets stored in the electric field between them.
the op author likens voltage to pressure(o)(i) within the water analogy and your osmotic membrane(ii) functions as a sort of pressure responsive valve
i'm sure there are some mental acrobatics to describe a capacitor's relationships: Q=CV; between charge(Q), capacitance(C), and pressure..er, voltage(V) using osmotic principles in place of the capacitance variable addressing the permittivity of the dialectric(iii)
but you'd have to describe osmotic pressure while waving away incongruencies between the two concepts and i think you'd end up so deep into enervated analogies it would just be better to explain in direct language ;P
gp> because water does not attract other water in any way
though i was merely addressing this quote your comment confuses me both in fillip and content
from cohesion wiki(o):
Water, for example, is strongly cohesive as each molecule may make four hydrogen bonds to other water molecules in a tetrahedral configuration. This results in a relatively strong Coulomb force between molecules.
from coulomb force wiki(i):
Coulomb's law or Coulomb's inverse-square law, is a law of physics that describes force interacting between static electrically charged particles.
Yes I knew water attracts water, but it is not relevant to the capacitor analogy. You might as well have said water attracts water via gravity, it's just not relevant in this situation.
