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Electromagnetism

Introduction

Seems like an old topic, huh? And it really is! That's why I was especially confused when found ridiculous omissions there. We use electromagnetic devices widely, I think it's inevitable that researchers would return to that subject again and again to add something important, new instruments to improve unfairly low perfomance. Here is my attempt :)

First of all, where is a problem? I presume, we have no intention to fight windmills! Let's conduct a thought experiment: we have a coil in vacuum, at some point there is a current flowing through it and magnetic field around. Let's say, there is no work being performed by this field - it has nothing to attract around e.t.c. - energy remains constant? Obviously it does. However, if you have experience with electromagnets, you can notice some inconsistency, coil does nothing, but on practice it eats power. And heats. Pretty much! Urgh, ridiculous!

My assumption was that these loses are just side effect of wrong control methods. And that there should be a way to do it better by deliberate retention of energy, if only more theoretical info were available... I started a research: after a few wrong guesses, various experiments and metric tons of confusion, I finally did it! And willing to share what I figured out, as it is pretty interesting.

That page would be divided in blocks, like this one, I would assign some sort of an indicator on how hypotetical info in that block is from my perspective, dividing them into two categories: believable ones or questionable ones. I plan to update that page, and it would be pretty handy, as there are a lot of uncerntainty present and I don't believe it's possible to get rid of that even in long term.

Updates

I update this page sometime when I find better explanations or conflicting hypotesis, older versions are still accessible via that button:

Where current comes from? Believable

Ohm's law binds current, resistance and voltage together. Simple formula, real-life process isn't as straight-forward. Ohm's law is more about statics, about final result, being simple, it omits a lot: for example, relationship between inductance and resistance becomes uncertain, as if they are separated from each other, while it's highly possible that they are not.

Let's say what we have an object with a mass, and you want to relocate it. Force is applied, then object starts to move in desired direction. There is a specific order, movement is a product of applied force. Same for current, which is in essense a directional relocation of charged particles. No way they would flow through tangled wire by themselves! It starts with a transient process during which current rises. And it's a funny one, as it gives an answer on a question "why current is usually the same through the whole lenght of a conductor". Let's look at the picture below:

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Then you connect source of a potential difference (battery, e.t.c.) you force electrons to relocate: there is a different density of them and they would always "flow" from areas with a greater density to less dense locations, while statistical nature of electron's jumps between orbits preserves constant speed. It's not like electrons are free to move as fast as they want and at the same time it's not like a friction either.

You can imagine it as a train accelerating slowly: as far as first carriage begins it's fluent montion, it propagates through train. By removing electrons from one end of a conductor, you expose next "layer" to a potential difference (metals have crystalline structure), electrons start to vanish from that "layer", so on, so on - and it influences other end shortly, raising potential differences (dU) and current in that regard. Higher energetical levels - more frequent transitions you see. Now, let's imagine that you have uneven current. Then one "layer" would lose electrons faster than other, by that providing additional potential difference from the one side and reducing potential difference from another, increasing amount of elecrons "layer" gets and decreasing amount it can give away, system would self-regulate! Queer and interesting, equal current is a stable state.

Now let's talk about resistance.

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It's pretty straightforward - with bigger cross-section you can insert more electrons. Therefore providing way to more transitions per second. Crystalline structure of material also matters, as it defines how orbits intersect, how many electrons you can store in given volume, e.t.c., that's why resistance of a different metals... differs wastly. As an exercise - try to imagine how voltage divider works :)

That transient process usually assigned to an inductance, but it's hard not to mark connection with resistance. It conveys the suggestion that electromagnetic field is tied with a potential difference in some mysterious way and it might be an important clue in case of missing efficiency.

Relationship between current and magnetic fieldNot solved yet...

It's a great mystery, still!

Why wire heats up?Believable

That one can lead to a major confusion, especially when you try to find similarities between heating in electricity and heating caused by friction or "bumping". I say that because I was confused too! Then I found out that it doesn't works like friction in some cases. Alternative approach is so intuitive and simple, that it sounds almost like a joke: you have one electrical potential on one end of a wire and another electrical potential on the other end, right? Electron loses part of potential energy on the way through wire! Similar to transition between orbits with different energetical levels, it irradiates energetical difference.

Formula U × I means, what each second we change potential energy of I coulombs of electrically charged particles by amount defined by U which is "occasionally" - potential difference.

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It means, what theoretically you can achieve current through resistance without heat! Or, significantly reduce heat dissipation on practice. It seemed impossible with a friction-based approach. Now we are close to that "deliberate retention of energy" on a coil mentioned in introduction. After next block!

EfficiencyQuestionable

Field-charging process has an end. That means that power pumped into magnetic field alters through time. If we sum up surface charge distribution, relation between current, magnetic intensity and how current builds up, it's logical to conclude: more "distributed" surface charges are - less to do. Therefore, if initial charging power is P, we take 1/2 of that power if current is a half of it's maximum for given voltage and resistance, as surface is half-charged/discharged at this point.

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Click to enlarge

It's not only simple to use, but also gives an accurate results. On the picture above you can see comparison between mathematical model based on this assumption and experimental data. Diagram on the right shows what to expect in terms of overall efficiency: that's why mains supply transformers have ridiculously low resistance, it makes sense to work on leading edge of that graph.

But one question remains - how to calculate that "initial charging power", P? Originally I thought that it's a U² ÷ R, but experiments shown that it's not! Even more, I think that L × I² ÷ 2 formula, designated for calculation of magnetic field energy should look like L × I ÷ (?) instead and there is a good reason for that. First of all, function describing P should have degree similar to magnetic field energy formula, if not - time constant would vary for different voltages, increase of power would exceed increase of required energy or vice versa. On practice time constant is invariable:

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Magnetic intensity and current are linearly dependant - that raises concern about presence of a second degree. Additionaly, with a second degree charging curve would be steep at the begining and it's really complicated to get a curve of a shape which corresponds to reality this way. My bet is that charging power can be calculated this way: $$P = {k_{sc} * U \over R}*{I_{max} - i \over I_{max}}$$ Where \(k_{sc}\) is a koefficient specific (or not) for a conductive material which defines how much power it would drain for given resistance relative to applied voltage. Precise measurement of this one is a subject for future investigation, but first rough approximation is something around 4 for copper.

How to preserve electromagnetic energyBelievable

Except of effective charging process (that can be achieved with low resistance coil) it's important not to waste electromagnetic field thoughtlessly. And there is a trick: coil generates current with help of surface charges, if it's easy to push electrons through, coil wastes a small amount of energy per second. If you detach coil from circuit, you do completely opposite thing by providing hardest possible path for current to flow. It might be a little counter-intuitive, but low resistance attached to a coil preserves energy much more efficiently, as for the same current it's a low voltage drop path.

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On picture above you can see visualisation of this process. Let's say that you have a circular river (how queer!) where water flows with a constant speed all way around. Strangely enough, one part of a river goes upwards with help of your machines, wasting precious electricity. After some thinking you decide to shorten that vertical part, keeping same circular river with same flow, but less energetically demanding, as now you don't have to move water as high. That's a perfect anology - you can't avoid current, however, you can shorten potential difference which electrons should overcome to circulate.

Conclusion

Combining efficient charging and retention of a magnetic field, we can develop great electromagnetic systems without heavy requirements for heat dissipation and even utilise operating modes which were not sustainable before. It gives a room to play: powerful BLDC engines without water-cooling, with improved mass-to-power ratio, awkward actuators of any kind.