This experience also taught me to actively mistrust "intuition" and "common sense". Not that there isn't value in intuition (quite the contrary, it's priceless, from design to maintenance), but it's only useful when it rests on a solid theoretical foundation. Prior to earning that foundation, it's nothing but a (very bad) shortcut that people take because they want to feel knowledgeable, but don't want to invest the effort of going through all that math mumbo jumbo.
I never really understood capacitors until I started trying to construct proper water-analogies for them. Then I discovered that my electronics and physics classes had sent me down a dead-end path with their garbage about "capacitors store electric charge." Since my discovery, I've gained significantly more expertise in circuit design, which leads me to a sad thought. Maybe the more skilled of electrical engineers and scientists gain their extreme expertise not through classroom learning. Instead they gain expertise in spite of our K-12 classroom learning. Maybe the experts are experts only because they have fought free of the wrong parts of grade school science, while the rest of us are still living under the yoke of the many physics misconceptions we were carefully taught in early grades.
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.
(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.)
(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 .)
Debunking this particular conception was the whole point of my capacitor article http://amasci.com/emotor/cap1.html
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?
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.
ENGINEER'S CAPACITOR, not physicists'
While employed at MOS in Boston I temporarily threw together a floating, double-ended VDG with a battery/motor inside one sphere. Like this:
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!
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.
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... :)
I don't see why your objection is on inches or otherwise any unit I chose for dimension of length.
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.
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?
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.
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.
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...
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.)
I prefer your clarifications when considering the function of capacitors
That said, water does attract water.. the term used to describe the phenomena is cohesion
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
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.
I think it's because all my teachers operated off the assumption that kids can't possibly understand abstract definitions, so everything must be explained via analogies. So nobody could tell me that fractions are equivalence classes. Everything was instead explained in terms of pies, which certainly seems like it would be intuitive, and there's really nothing technically wrong with it, but it encouraged me to think of, say, 1/2 and 2/4 as different entities instead of two representations for the same entity (since, after all, cutting a pizza into two slices instead of four is just not the same thing). I didn't "get" fractions until on my own I came to the conception that these are actually kind of abstract concepts that go by many different names.
For me, I was taught too much to identify numbers with concrete objects in the real world. This sort of works for integers (as long as you ignore negative integers and even zero to some extent), but it basically breaks down for all other types of numbers, including rational numbers. So it's a really bad expectation to set in my opinion. But you can hardly find an elementary school teacher who will dare approach this topic.
I honestly think that if someone had just explained that "1/2" is a symbol we've devised to represent the solution to the equation 2x = 1 -- an equation which otherwise has no solutions at all in the integers -- I would've grokked it a lot faster. It would've been clear to me that we're introducing an entire new set of numbers distinct from the integers. These new numbers do not have a direct correspondence with physical objects in reality. And it would've been easier to see that the same solution must go by many other names as well. For instance, multiplying that equation by 2 on both sides gives us a new equation which must have the same solution: 4x = 2. So "2/4" must represent the same entity as "1/2". And so on.
But because US educational culture has decreed that basic algebra is more advanced than fractions, the very idea of discussing solutions to an equation will never be allowed in an elementary school classroom. It is assumed as a basic fact of human life that kids cannot understand the concept of solving an equation before learning about fractions. We'll teach kids to perform mechanical manipulations of decimal expansions before we ever begin explaining what any of those digits actually mean.
I remember a bit later in school I discovered algebra on my own and became really interested in it. I asked if I could take a class on algebra ahead of schedule and was virulently refused by the school counselor, who scoffed at the very notion and declared it to be impossible. Her response was so indignant that it offended me very deeply and caused me more or less to rebel against school in general. I ended up turning away from math completely for many years and didn't come back to it with any real interest or passion until I was about to graduate high school.
> If I explain 1/2 and 2/4 using pie or pizza slices and ask you how "much" pizza did you get, I think the equivalence idea clears up quite nicely.
Sort of. But childhood me would have just told you that, no, in one case I got one big piece and in the other case I got two smaller pieces. Combined they might have the same mass or the same number of calories or the same area, but the numbers you just gave me don't have units and can't be measures of area since they're independent of the radius of the pizza.
> Sort of. But childhood me would have just told you that, no, in one case I got one big piece and in the other case I got two smaller pieces.
Why are we using pizza pies in the first place? I vaguely remember being taught something about pie as well. Instead how about this:
You have a piece of string 1 m in length. You cut it into 2 equal pieces. We can denote the length of one piece as 1/2 m.
You have a piece of string 2 m in length. You cut it into 4 equal pieces. We can denote the length of one of these pieces as 2/4 m.
These pieces of string are the same length, therefore 1/2 m is the same as 2/4 m.
Although in my head this feels more like a nice way of demonstrating they are the same, I'm not so sure if it helps a lot with reasoning about fractions. But that's fine, like the article said it's good to be able to explain something in multiple ways.
Personally that's one of the things that absolutely fascinated me about arithmetic when I was young; That you can play around and have multiple ways of arriving at the same answer, and that if you follow the rules of math right, they always end up as the same answer, sometimes even unexpectedly so (for young me).
I realize this is going to go far beyond the thoughts of a toddler learning about fractions for the first time via the pizza analogy, but I think it demonstrates that even the seemingly obvious pizza analogy is more nuanced than it seems.
I've never bothered thinking about this before, but it seems obvious to me now. Using just a straight-edge and compass, it is not always possible to cut a pizza into N standard-shaped slices for all positive integers N. Doing so is equivalent to constructing a regular N-gon, and this is only possible when N takes on the special form
N = 2^k * p_1 * ... * p_M
for some nonnegative integer k and some sequence of distinct Fermat primes (that is, primes of the form 2^(2^j) + 1).
Thus, you cannot slice a pizza into 7 slices using a straight-edge and compass. So in the pizza analogy the number 1/7 corresponds to something that is not physically achievable with standard implements.
I think I've found the Wikipedia article about the effect, and the criticisms section  matches my bias, in that it suggests the children are confused because they are thinking not just about the material presented to them, but also why they're being asked.
I know before a certain developmental state children will say a taller thin glass holds more then a short wide glass even if you pour them back and forth to show they are equivalent. Once they "get" the concept it is for life but before that it is impossible, logic be dammed.
4/32, 5/32, 6/32, 8/32 ... etc
I honestly believe that lots of kids detect these issues on some level, but their curiosity and confusion remain unresolved, possibly for life.
My experience, in contrast to yours, was well-meaning teachers drilling the algorithms while hinting at some underlying structure. I suppose it was enough inspiration to figure out what math was about, and I eventually found myself in a math PhD program. (Despite the fact I had a hard time remembering the so-called "math facts." During competitions, I would try to calculate, slowly, something like 7 x 9 using something like (8 - 1) x (8 + 1) = 8 x 8 + 8 - 8 - 1, since the only "facts" I ever remembered were multiples of five, 6 x 8 and 8 x 8. Those competitions did make me think I was a bit bad at math!)
Though, let me share my story about fractions. In fifth grade, I got a day planner because the school pushed for everyone to get one, and in the front leaves there were various references, like a periodic table, lists of equations, etc., and one which caught my eye was "a/b + c/d = (ad+bc)/bd". For some reason I thought "oh, that is what fractions are" and I tried to explain to a teacher how this defines fraction addition, how finding a common denominator is just a way to calculate this, but instead I was told I was incorrect, and you just find common denominators. I can't say I didn't feel somewhat vindicated when I learned, much later, about the Grothendieck construction.
I also remember trying to find a formula for triangular numbers in sixth grade, and I will never forget the look of horror on my "home-room" teacher's face as she backed away while I explained what I was trying to do.
I believe it. I've known a lot of adults who don't quite get fractions. They generally also have no trouble working with money and giving change, but no ability to understand interest, especially compound interest. Somehow, the educational system is failing here, not the kid.
1/2 of a pie is 2/4 of a pie, 2 slices of four is the same fraction as 1 slice of 2. It's exactly the same idea as the equivalence classes, where the ratio matters but the description does not. You just didn't understand that at the time.
> the very idea of discussing solutions to an equation will never be allowed in an elementary school classroom.
My kid is in first grade and his homework is to solve equations of the form "7+2=__" and "9-__=7"
Another way of putting it:
> 2 slices of four is the same fraction as 1 slice of 2.
The phrase "is the same fraction as" is obviously inappropriate and explicitly circular and self-referential in any definition of "fraction". I don't think you've thought about this as deeply as you think you have.
The teacher would accept 9 or 0 as an answer, not 18. A parent (with math degree even) who was volunteering pointed out that 18 is correct. The teacher ruled against this, arguing that 18 was unacceptable because math with 2-digit numbers hadn't been covered yet.
This was at a "good" school, in a county full of nerds.
Such logic. Poor kids... and people wonder why kids hate math and give up on it.
I suppose the "logic" is that stuff involving 9 could connect up with stuff involving 0 or 9. Since all other 1-digit answers seem more distantly related, and the answer has to be 1-digit because 2-digit hasn't been covered, 0 and 9 are the most attractive answers and therefore correct. ???
Remember, that was a class with smart kids in a school in a good area. Imagine what it might be like in not-so-good areas or in the classes that aren't for smart kids.
People who truly hate math are teaching. My sister-in-law is an example. She got a "degree" in "early childhood education". It's a joke. The hardest math she had to pass was algebra, as is taught in 7th grade. Boy did she complain about that class. She thought it was really hard to pass algebra. I'm horrified she got more than halfway through high school without it, yet there she was, taking it in college.
Teachers have serious credential inflation. Many have Master's degrees... but are those degrees worth anything?
(By the way if anybody out there does have children that age, I recommend the game Fraction Formula which has tubes in which you put cylinders in to representing different fractions).
In middle school they told me, it's electrons moving at the speed of light through a conductor.
In high school they told me, no no, they don't move at the speed of light, just when one electron enters the conductor, another one on the other side will leave the conductor, like with peas in a straw. And this enter/leaf is at the speed of light.
At university they told me, no no, you got it all wrong, it's about the electro static and electro dynamic fields which stand orthogonal on each other and produce electro magnetic waves... what?!
I seriously have no idea anymore.
> In high school they told me, no no, they don't move at the speed of light, just when one electron enters the conductor, another one on the other side will leave the conductor, like with peas in a straw. And this enter/leaf is at the speed of light.
although "entering" and "exiting" the conductor isn't really a good description.
A better way to think about it is that "conductor" is really just slang for "material that has a bunch of free electrons and very little room for more". This is the "sea of electrons" that Beaty talks about. It makes sense that, if all this sea flows steadily (i.e. at the same rate throughout the conductor), forcing a change in the rate of flow in one part of the conductor will be felt almost immediately in another part of the conductor, no matter how distant, even if the flow itself is extremely slow.
(If you're thinking that this is only true if the "pipe" through which the "sea" flows is full, you're right, this is how free electrons behave in conductors; that's why Beaty insists that a good analogy for a conductor is "like a pipe which is already full of water".
> At university they told me, no no, you got it all wrong, it's about the electro static and electro dynamic fields which stand orthogonal on each other and produce electro magnetic waves... what?!
If they taught you that, they are most definitely wrong, it sounds loosely like induction, but with two strange names instead of "electric" and "magnetic" :-).
This is a better description of the physical reality, and it does help you understand circuits better if you think about it, but not in a very practical manner.
I don't think "definitely wrong" is a good description. electrostatic and electrodynamic are perfectly good, if somewhat archaic, terms for the electric and magnetic fields. (E and H fields)
But as I said, since I didn't understand it, I probably don't recall correctly what they told me.
I just remember that the "particles" I had in mind somehow stopped being "the thing" and now it was all abount strange fields that worked without a physical medium and formed waves by being aligned in a specific way.
For what it's worth, though, these are terrible names, archaic or not :-D. If they ever were in use, I'm glad we moved on.
* It doesn't match the way we define electrostatics, magnetostatics and electrodynamics. What defines electrodynamics isn't the fact that charges are moving (they're moving if the currents are constant, too, but the magnetic fields produced by steady currents are in magnetostatics' yard) but the interaction of charges and currents (in more formulaic terms, when both charge densities and current densities are present, not only do you get both electric and magnetic fields, as in magnetostatics, but they also vary in time).
* Charges in motion still produce a voltage across a dielectric. Calling the electric field they produce "electrostatic" when the charges are moving and the field is certainly not static.
I guess it all comes down to the fact that a magnetic field does not exist without an electric current. One way of thinking about it sees it as charges moving, and the other way of thinking about it sees it as a static magnetic field.
I guess that's why the terms are archaic!
E.g., when a mass above Earth is in free fall, it still obeys Newtonian Statics: the weight/attraction force, easily analyzed from moment to moment. The resulting acceleration and trajectory then falls under "Dynamics."
In other words, electrostatics applies to capacitors and to the mechanical forces produced by electric fields. Even if currents are also present, and even if the e-fields are changing with time, electroSTATICS still applies. (A high voltage, high-amperes power line is very "electrostatic," because of the significant e-fields and resulting phenomena.)
Static Electricity then is a chapter title, with no existence in the real world. Neither can we fill a box with Newtonian Statics. To be consistent, we wouldn't say "electrostatic motor," instead call it a capacitor-motor, or an e-field motor. (Heh, a stretched spring is statically charged! Full of Newtonian-static energy!)
ps: this comes from years of self learning music, every now and then my incomplete abilities go through a complete crash, only to reveal a critical misunderstanding, lack of sensitivity in my perception or action, that leads to a sudden and very blissful resolution (your own private eureka moment)
I read a few articles on that page and it's like magic, it makes not much sens to me after all I learned at school.
There are three different concepts that were all thrown under the umbrella term "electricity".
>..little use by educators of the wind/sound electrical analogy:
>AIR is a physical substance.
>SOUND is a wave that propagates rapidly through a volume of air.
>WIND is a flowing motion of air already present.
>ELECTRIC CHARGES are a physical substance.
>ELECTRIC ENERGY is a wave that travels via a column of charge.
>ELECTRIC CURRENT is a flowing motion of the charge already present.
I'm not an expert when it comes to electricity, so someone correct me if I'm wrong, but one thing that has made sense to me when it comes to trying to understand electricity is that not all electrons have equal potential for work.
When studying electricity, you're often told the charge of an electron as a fixed quantity. However, if I've understood correctly, the work that an electron can do in conducting electric energy is not wholly described by the charge of the electron, it's also important to know the relationship that the electron has with the nucleus of the atom it orbits (i.e. the 'shelf' it's on).
To explain in another way, this analogy may be 'wrong' but I think it helps to think of electrons as capable of more work when they are less tightly coupled from the nucleus of an atom. The electrons that can do the most work are those in the outermost orbit of an atom. Whilst it may be wrong to say outer electrons are more charged than inner electrons, I think it might help in terms of visualisation. Again, correct me if I'm wrong.
I think another useful mechanism to consider is that atoms want to return to an electrically neutral state. If they have energy that differs from this neutral state, they will either give out energy or take in energy to reach the neutral state. The movement involved in rebalancing the atoms can be thought of as electric current. Again, happy to be corrected if I'm wrong.
Similarly the speed of light is fixed, and is really the speed of propagation of electomagnetic waves. When you perturb electrons, other electrons will react to that change in the fields as it arrives at them with the speed of light. So even though the flow of electrons down the wire is very slow, the flow of energy or information may be very fast. In fact, you don't need electrons in between to move at all -- you can simply have empty space in between your antenna and the electrons you are moving around ;).
As it happens, these electromagnetic waves have components that stand orthogonal to eachother. If you take relativity into account, you can find a frame of reference where the magnetic field disappears -- really the magnetic field is just a relativistic correction of the electric field and explains why charged particles attract eachother differently when moving versus at rest. In any case, it is really just one field that is called electromagnetic because we used to think it was two completely separate fields!
If there wasn't any chain of electrons inside the conductor, then the EM fields would just fly off into space, like with a transmitting antenna.
Wires can guide the EM energy because each electron can push the next one in sequence. But also, one electron doesn't just push on the next one. Instead, it pushes on a huge number of electrons far upstream and down the long chain of mobile charges going off into the distance. That's why the EM energy can "leapfrog" across the movable charges, at the speed of light. If each electron could only push upon its nearest neighbor, then electrical energy would travel at about the speed of sound.
So, the electric companies are selling us 60Hz photons.
But at the same time, the AC electricity just vibrates back and forth inside the wires, without any net forward motion.
About the only accurate diagram of EM spectrum I've ever encountered was the one made by R. Oppenheimer and sold as a classroom poster by The Exploratorium in SF. At the bottom, below VLF radio, we find audio-freq phone lines, and below that, 60Hz power lines. "Electric power" is on the EM spectrum, down below radio waves.
And yes, if we have a big enough antenna tower, then we can hook it up to a 60Hz dynamo, and spew 60Hz EM radiation out into space. Actually that concept was one of N. Tesla's great breakthroughs: hooking a steam-powered 50KHz alternator directly to an antenna, and broadcasting a silent carrier: CW. A couple years after his patents on this ran out, GE suddenly announced the "Alexanderson Alternator!" Finally making music/voice broadcasting possible! The public wondered how Alexanderson managed to come up with such an amazing idea. (If investors had bought Tesla stock, we'd have had AM radio ~20 years earlier. Tesla clearly grasped the concept that "radio" was the same thing as "electric power," just higher in frequency.)
The EM energy is in the form of propagating waves, while electric charge provides the medium: the waveguide.
It seems like you have a fundamental misunderstanding of how photons are produced, or what they do. At least in DC conditions, no photons are produced at all (since there is no changing magnetic or electric field), yet there is still current.
Current is the movement of charge. Photons are irrelevant, besides being the messengers for the electric and magnetic fields, which still only applies if those fields are changing, as no information is changed otherwise, so no bozon is necessary.
What you may be thinking of is in an AC case, where current is constantly changing as the electric field wave propagates down the transmission line. This does necessitate photons. But even then, the current is still the flow of charge, and oscillates between negative and positive.
The electrical charges in the classic theory of electromagnetism are not electrons, nor ions, nor any other particles that we know of. They're ideal models of "something" that carries charge, but they do not model all the inherent behaviour of electrons (e.g. the electrical charges of classical electromagnetism do not have any magnetic moments, unlike real-life electrons). They are somewhat like the point particles in kinematics, in that they capture an essential feature (electrical charge) of an object while dispensing with other features that are not essential for the study of some (but not all!) phenomenons.
It's ok to model electric current as "the flow of charge", as long as you don't give this model more physical meaning than it's due and attempt to equate the charges of classical electromagnetism with electrons.
Certain phenomenons can be studied within this frame: for instance, the motion of an electron's motion through static electrical and magnetic fields is generally (low enough frequencies, strong enough magnetic fields etc.) OK to do while equating the electron with the charge carrier of classical electromagnetism.
But back when the concept of electrical charge was elaborated, we knew nothing of electrons. The phenomenons gave enough clues for us to hypothesize that whatever "supports" electricity has some of the properties that "real" charge carriers have, but that's all there is to it.
This sounded like he went mad to me...
So obviously a piece of pipe is a circular waveguide and it works more or less like optical fiber.
It helps if you know how optical fiber works, across a boundary with a big enough difference in speed of light in the material, you get total internal reflection and it bounces back in.
Now people are pretty chill with circular waveguide as a transmission line, but there are numerous other schemes and eventually you end up with microstripline or twin-lead that TVs used to use or eventually one wire Goubau line.
Once you're chill with a zillion small steps from circular waveguide to G-line, wait, G-line is what your prof said that initially sounded ridiculous, but its not so ridiculous after all, with some new perspective.
For example, finding answers to questions like "Why does absorption of EM waves in matter rise with lower wavelengths, but at the wavelengths of light matter starts to become more and more transparent again" isn't easy. But so are the involved phenomenons, after all.
One of the devilish things about science is that the mental abstraction model that works for a layperson doesn't really scratch the surface.
It took me a huge amount of time to get rid of all the BS learned in school. In some area I'm even still working on it (eg. analysis).
A more succinct, clearly defined structure would help me a lot. Each topic could be clearer on what is wrong and how is the right way.
It would help a lot just to start with a clear: "What is the right definition of the word electricity?".
Then, maybe a "What is "electrical phenomena" and some examples". "Correct definition and differences of electric charge, energy and current".
For me personally, a structure that explains what is the right thing first, then goes on about misconceptions and consequence of misconceptions is much better.
I became lost while reading this and finished with basically the same confused and mistaken understanding of what is electricity as I began.
1. Memorize this: Assets + Expenses = Liabilities + Capital + Income
2. Everything is positive, no negative numbers!
3. For every transaction, Total Debits = Total Credits
4. "Credit" is source of money, "debit" is destination of money
5. Assets and expenses increase with debits
6. Liabilities, capital, and income increase with credits
7. Expenses and income may only be increased (debited & credited respectively)
8. At the end of the accounting period, distribute income less expenses to capital accounts
Your business buys a property for 90k with 50k cash down and 10k closing costs.
Assets: 90k house (debit), 50k cash (credit)
Expenses: 10k closing cost (debit)
Liabilities: 50k mortgage (credit)
Total Credits: 100k
Total Debits: 100k
But it gets even more confusing when they say "we credited your account" or "your account was debited".
From the perspective of the bank, your account is a liability, so when they deposit into it, then its value increases, hence "credit".
When they say "your account" they actually mean "the account where we track how much money we owe you".
From your business's perspective, your bank account is an asset, so when they deposit into it, then its value increases, hence "debit".
> From your business's perspective, your bank account is an asset, so when they deposit into it, then its value increases, hence "debit".
But what you're describing (a business depositing money into your account) is not what I, as a non-business owner, understand by "your account was debited". Businesses with whom I do (well) business use this terminology to mean that they have removed money from my account. (I'm not arguing with you—I've probably just misunderstood your terminology, and am seeking clarification.)
For example, suppose you go into the bank and withdraw $10 and they charge a $1 fee. The transaction looks like this:
* Credits: $1 (bank income), $10 (bank assets)
* Debit: $11 (customer liability)
So when you get your account statement, it will say "$11 debit", because from their perspective, it was a debit, i.e., their liability went down. If that doesn't make sense, think about how you pay your own credit card bill (a liability): you take money from (credit) your checking account and send it (debit) to your creditor.
Despite your very clear explanation, I'm still confused by:
> > But it gets even more confusing when they say "we credited your account" or "your account was debited".
Is it correct that the 'you' of the first post, in "your account was debited" (me the non-business owner), is the 'they' in the second post, of "when they deposit into it" (written from the perspective of the business owner, so that 'you' is no longer me)?
1) On your books, it is an asset account.
2) On the bank's books, it is a liability account.
When a bank says "your account was debited", they are talking about entity #2. That is, "the account on our books associated with 'you'".
But when you yourself think of the account, you think of thing #1.
Let's say you deposit some cash into your account at the bank. That means you are lending the bank the money (extending it credit). The bank records this as two transaction entries:
* A debit (receiving money) transaction which places more money into their general "money we have" pool: you gave them money.
* A credit (owing more money) transaction: they now owe you more money. This increases the amount of what the bank thinks of as "your account".
The statement they send you at the end of the month only shows the second transaction, because that's the one relevant to "your account" in the sense of #2 above.
If you were keeping books on your side, you would likewise record this as two transaction entries:
* A debit (receiving money) transaction for your bank account (now in the sense of #1 above).
* A credit (having less money in an asset account) transaction for your wallet.
So the upshot is that in the two entities that "your bank account" corresponds to, a debit for #1 is a credit for #2 and vice versa. And when the bank sends you a statement, it describes #2, not #1. Since most people don't interact with the terms "debit" and "credit" normally, this is the only exposure they have to those terms, so they learn them backward....
It doesn't matter whether you are a business owner; your bank account is still an asset to you and a liability to the bank.
Personal & business accounting are the same, except your only investor is yourself, so you don't have to manage capital accounts.
Capital+liabilities explain how your assets are "covered". Either you owe someone for the assets (liabilities), or you own the assets yourself (capital).
Sometimes it's easier to think of this as
"assets - liabilities = capital".
I.e. whatever is left after considering what you owe, you own.
If you have some cash (an asset), then you need to also list it either as a liability or capital, simply because you must always be able to answer "where did this cash from? did we borrow it (liability), or do we own it (capital)?"
When you receive capital in the form of cash, you debit your assets (cash) and credit your liabilities for the same amount (capital). It's "double-entry" accounting, total debits should equal total credits for every entry so that it balances out.
A balance sheet doesn't really speak to who might have claims to ownership of the company under what terms and the dollar amount of equity on the balance sheet doesn't imply that investors are owed that specific dollar amount.
A balance sheet is like charge on an array of loosely connected capacitors (or batteries). I know I got a pile of electrons (and holes) stacked up somewheres, and the balance sheet shows where. All "accounting circuits" are electrically neutral and the number of electrons and holes on your balance sheet MUST match.
A income sheet is like looking at the individual cell results from a solar array in parallel. So you got 10 aH out of that entire array, now which cells contributed more or less of their share, and which battery cells soaked up more or less than their share of charge?
The cash flow sheet tells you how fast electricity energy moved, essentially a power. So your 99 watt-hour laptop battery holds 99 watt-hours, but how many times did you fill and empty it in a year, how many times did you turn over the energy in the battery?
Once you learn op-amps you can do some hideous analog computing analogies, but don't call up what ye can't put down, so I'm not even trying that. So a financial derivative is like a sample and hold ckt connected to a four quadrant analog multiplier and a log/antilog ckt, or maybe this is just too far of an analogy not to be nonsense.
The purpose of accounting (aside from mere control fraud prevention, at least optimistically) is to squirt out some ratios to help make management decisions. Much like the transistor collector current is not terribly interesting nor is the emitter current at a large enough scale, but the ratio is exciting because back in the old days people made management decisions to select one transistor over the other based on the ratio of those currents, which is essentially how good of an amplifier it is. Much as income statment vs cash flow ratio tells you a lot about a retail establishment compared to its peers, how long "stuff" is sitting on shelves before getting sold. That current ratio is a bipolar transistor alpha ratio which no one uses anymore. Kind of like how people used to make investment decisions based on the ratios in the famous Graham and Dodd book, but no one has invested on fundamental ratios in, gosh I donno, 30 years? Its been a long credit bubble and fundamentals don't matter in a credit bubble.
I have no idea what a credit bubble is in EE terms. Some twisted analogy of trapped charge on a Teflon dielectric resulting in an integrator getting saturated eventually, but until it does the ride is pretty exciting.
I would extend this post with my traditional HN automobile analogy but I'm not sure there's enough liquor in the world to achieve that level of debauchery. So ... Keynesian economics policy sees the role of the government as like an electronic speed control on the automobile, uh, kinda.
I don't, I think it stays too much on the surface, in order to make the belabored analogy work.
This may also be interesting to you: http://www.dwmbeancounter.com/tutorial/Tutorial.html
I feel better :-)
You would have to go back to James Clerk Maxwell's original 20 equations to see what it's all about. Okey, quaternions are kind of hard, I'll admit to that, but all in all it makes much more sense.
It's useful to be able to explain things to laypeople and the not mathematically inclined, which means tightening up the metaphors.
So you can't just do the math because we don't have all the math.
You won't really run into the atom stuff until you try to do something like calculate dielectric constants analytically, though self-energy is definitely a pretty easy trap to fall in even for macroscopic stuff.
I teach my children that we live in a sea of energy and that you can feel it when you move. It makes much more sense to them than trying explain inertia.
I tell them that of you rotate something, it will make an energy vortex making stuff seem heavier - and I show them with a gyroscope.
Then I explain that electrons are just like little gyroscopes, but of only energy. And it all makes sense to them. They don't think it's hard at all.
Not ... really. The problem is that we teach electromagnetics using a 19th century pedagogy that assumes the existence of the Ether.
This works well for some things and makes them nicely closed form and simple. Of course, it breaks down for other things (motors are one of the big ones) where you really want a field description.
Of course, a field description makes nothing simple and closed form. So, it isn't good for making exams out of.
If you can deal with 4-vectors, "Collective Electrodynamics" is a really good book.
Am I just a pedantic nitpicker?
To deeply grasp physics, often one must UN-learn the common misconceptions which were acquired in our early school careers. The misconceptions in this list are the ones believed by educators, and taught to students.
The index to the large collection is here: http://amasci.com/ele-edu.html
The entire system must be solved simultaneously, and there is not a well defined "input" or "output". This can be seen from the fact that when we analyze a circuit we also include the model the power source and the load.
The combination of non-locality and complex boundary conditions makes it hard to apply ordinary intuition. We would like to say that the power source "does something" to the circuit but causality actually runs both ways. E.g. if we have a constant voltage source, then the circuit will determine how much current flows through the source. If we have a constant resistance load, then the load will determine how much power the circuit applies to it.
So: does electricity have 'mass'? What I mean is, when current flows, is there a transfer of electrons (or something else) from the power source to whatever it is send to? And is there a difference between AC and DC?
The context of this question is that the core argument of a legal paper (of all things) I was reading at the time (on property rights of virtual goods) hinged on there being a transfer of mass, however small. I wasn't so sure.
(my SE question devolved into a semi-legal argument - I have a law degree, the context of the question is a lot more nuanced still than the above description, and is very much tied to some specific 80 year old Dutch case law - just saying that to point out that a legal argument on whether or not the question matters won't add much to the discussion.)
An excellent example of electron movement is a DC current in a metal plating tank or refining tank. Every atom of aluminum or copper or plated anything took the movement of precisely one electron (simplification because there are some non-electroplating methods for some base/plate combos, but yeah pretty much aluminium is a block of solidified electricity)
With a battery (DC/direct current), there's a surplus of electrons available at the negative end, a deficit at the positive end. The electrons flow through a circuit (from - to +) to perform work.
With AC/alternating current, the electrons flow in one direction, then the reverse direction several times per second. The purpose of this is to push energy further down transmission lines with less loss. Pushing DC from a plant to everyone's houses is very lossy.
Do electrons have mass? Yes. Does the circuit or device increase in mass when current is involved? No. You're actually not introducing additional electrons into the circuitry. The conductors and semiconductors already have electrons on the outsides of their atoms. We introduced an electron at one end, it hops onto an atom, pushing an existing electron over to the next atom and so on. It's the movement that produces "energy" and allows work to be performed.
Strictly speaking, you can hold extra electrons for short periods of time in capacitors, but the mass is so small as to be negligible.
Electric circuits are much like drive-belts, but using charged particles rather than rubber or leather. If a drive-belt extends across the border between two countries, what is being transported? It's not mass, since for every KG of rubber belt going out, an exactly equal amount is coming back. (Go further and use rotating shafts. Then the mass just spins in place, and doesn't actually cross the border at all.)
With circuits, with AC, the charges are just wiggling back and forth, and not proceeding forward. But with DC the charges are taking a closed circular path, so still are not proceeding forward. The thing which proceeds forward is radio waves. Sixty-cycle radio waves, forced to follow a waveguide composed of two or three conductors. EM waves are being sold to us by the utility companies. We live in a "radio-powered" civilization, but where the 60Hz EM waves are forced to follow waveguides, rather than leaping across empty gaps.
Humorous "legal" chapter in Feynman: IS ELECTRICITY FIRE?
Electrons do have mass, but a device powered by an electric current will generally have the electrons flowing out at the same rate that they flow in.
I've occasionally tried to clear up misunderstandings of this kind on https://electronics.stackexchange.com/ , they're a common stumbling point for beginners. Especially speed of electrons vs. speed of signals.
V = IR
I = V/R
R = V/I
Navier-Stokes equations are not easy to understand.
It breaks down as an analogy as soon as magnetic fields come in to play, which is pretty much any AC circuit.
Similarly H+ ions in aqueous solution can carry a current, as in electrolysis.
Too bad we don't have metallic hydrogen. It would be a solid conductor, just like any other metal.
"Conductor" actually means "contains mobile charges." Conductor doesn't mean "a hollow pipe which electricity flows through." Conductors are more like long, narrow ponds. They're made of 'electric fluid,' so if we have a ring-shaped pond, we can push the water along so it starts moving in a complete circuit, like a drive-belt.
It took 495 GPa pressure to create. The sample is being held in the cryostat in liquid nitrogen.
They can then check the possibility that, once formed, it remains stable at low pressure.
BEN FRANKLIN SHOULD HAVE SAID ELECTRONS ARE POSITIVE? Wrong.
EE would be much HARDER if Franklin had swapped positive and negative, since then our confusion wouldn't lead us to shatteing our own misconceptions. We'd never sit down and figure out what "conventional current" actually is. No, it's not backwards. And no, electricity is not made of electrons. In acids, the electric current is entirely a flow of protons. In dirt, oceans, and human bodies the current is at least two separate flows: clouds of positive ions passing forwards through clouds of negative ions travelling backwards. With two opposite charge carriers, what then is the "true" direction of electric current? What if there are five: +Na, +K, +H, -OH, -CL ?
Cute notion: Ben Franklin's kite string was an acidic conductor, a piece of twine which becomes insulating in dry conditions, so it's an electrolyte. And acid conductors have mobile +H ions to carry the current. (What's a hydrogen atom, with one missing electron?)
In other words, Ben Franklin's kite string is a Proton Conductor.
SO HE GOT THE DIRECTION RIGHT!!!!
He only was wrong in the case of metal wires. In his day, a typical "conductor" was a small boy hired to hang from silk ropes, to connect the Leyden Jar to the "Electrical Machine." Or rather than commoners, sometimes they used chains of Elizabethan royalty, all standing upon insulating stools.
OH THE HUMANITY!!!!
So, a hydro dam is actually a method for sucking the energy out of the entire surface of a lake, all at the same time! (Actually the pressure-waves travel at the speed of sound in water, a few thousand MPH.) It doesn't happen instantly, but damn close.
I messed it up last time I was getting slashdotted by reddit and ycombinator, and everyone was complaining that the raw unedited notes were just a bunch of raw unedited notes.
Heh, it's still a 1995 gopher-era design, back when we put all our chapters on a single long page, to compensate for 300/2400b modem speeds. If it was broken up into many separate pages, you'd be waaaaaaiting for the text to finally appear.
E: Yes, I was thinking standard AC for household appliances, my bad
For DC, no it does not.