Grover Inductance Calculations Pdf To Word

• Grover Inductance Calculations Pdf To Word Converter
• Coil Inductance Calculation Formulas
• Cable Inductance Calculation
• Inductance Calculation Formula

419 Figure 2. Calculated resistance depending on the frequency for different values of K parameter. Self-inductance calculations Self-inductance for a straight conductor according to Grover’s equations extracted from (5), is. Get Free Read Online Ebook PDF F W Grover Inductance Calculations Dover Publications at our Ebook Library. Get F W Grover Inductance Calculations Dover Publications PDF file for free from our online library PDF File: F W Grover Inductance Calculations Dover Publications. Grover Inductance Calculations Pdf. 1/1/2018 0 Comments. Grover, Inductance Calculations: Working Formulas and Tables, Dover Publications, Inc., New York, 1946. Hindawi is one of the world’s largest publishers of peer-reviewed, fully Open Access journals. Built on an ethos of openness, we are passionate about working with.

• 8Article lead

Loop of wire

I have reverted this edit which has the edit summary changed 'wire loop' to coil of wire. The quoted formula contains N respresenting a number of turns of wire. For a wire loop N is 1 and would not be included in the formula. I agree that the use of loop here is problematic and could , perhaps, be improved, but coil of wire is even more so. I think the definition only works if all the turns are essentially co-incident - that is, lying on the same loop. Furthermore, the change was not done consistently, the section continues to talk about wire loop further down. SpinningSpark 16:29, 9 August 2010 (UTC)

The equation for the inductance of a thin solenoid is not correct; one should use Babic and Akyel, Improvement in calculation of the self- and mutual inductance of thin-wall solenoids, eq. (8), IEEE Trans on Magnetics, Vol. 36, No. 4. July 2000Prof. J.C. Compter —Preceding unsigned comment added by 194.25.102.189 (talk) 10:04, 2 September 2010 (UTC)

The Lorenz expression for the inductance of a coil is the inductance of a cylinder with a current around its surface (might be indicated in a footnote), and as such is as exact as Maxwell's equations. Improvements (wire or coil thickness, wire spacing) are more complicated and less instructive. B&A use numerical methods. Appears that FEM and numerical methods should be mentioned (with references) under calculation techniques. —Preceding unsigned comment added by Rdengler (talk • contribs) 08:21, 4 September 2010 (UTC)

Original research or lack of references

The section on 'coupled inductors' has a paragraph at the bottom about tuned circuits, starting 'When either side of the transformer is a tuned circuit, the amount..'. This paragraph is not referenced and may be original research. Does anyone know where this material comes from? —Preceding unsigned comment added by 121.98.140.35 (talk) 00:01, 20 May 2011 (UTC)

I don't know where the material comes from but this is a well-known effect much used in the design of RF amplifiers and covered in numerous textbooks (eg [1][2][3]). Whether it beklongs in an article on inductance is another question. 09:29, 24 June 2011 (UTC)

Nomenclature

In the section on non-linear inductance the Greek symbols are not defined. Even i and t are not obvious to all readers (instantaneous current and time) but Φm is not, and doesn't seem to be defined explicitly anywhere in the article. Please remember that people often read these articles because they want things EXPLAINED, they do not want to be frustrated by unexplained symbols. — Preceding unsigned comment added by 210.48.109.11 (talk) 06:44, 9 August 2011 (UTC)

Self-induction

The entire section on calculating self-induction needs to be re-written. It is neglecting explainations of internal and external inductances, and not properly explaining the Neumann formula. Also it doesn't mention the method of partial inductances (Rose, Grover, Ruehli). — Preceding unsigned comment added by 129.139.1.68 (talk) 14:37, 21 June 2011 (UTC)

The changes done under 'self inductance' are misleading in several ways, I undid these changes. 1) The text now repeatedly mentions filaments, while self inductions isn't defined for filaments. 2) To say R >= a/2 is outside the filament makes no sense. 3) The distinction between external and internal inductance makes no sense. The total inductance simply is the sum of the product of current elements i(x)i(x')d³xd³x' divided by distance R(x, x') (see Self inductance. It really is as simple.) The expression for M_i,i consists of two contributions only for technical reasons, and the choice R >= a/2 is a matter of convenience. Partial inductancies are a different thing. Hic est Rhodos. radical_in_all_things (talk) 07:38, 24 June 2011 (UTC)

The formula for inductance in coaxial cables is only missing the constant mu-nought = 4*pi*10^-7 (as a coefficient at the beginning) (cite: Giancoli Physics for scientists and Engineers vol.2, 4th edition) — Preceding unsigned comment added by 152.7.59.119 (talk) 01:54, 18 October 2011 (UTC)

No, the constant mu-nought isn't missing, it is in the column caption describing the columns content.radical_in_all_things (talk) 14:56, 19 October 2011 (UTC)

A reference for the self-inductance curve integral is [4]. It will be added to the article when on arXiv.org.radical_in_all_things (talk) 13:18, 3 December 2011 (UTC)

Consistency

Someone should fix Inductor so it matches the consensus Wikiphysics here. --Wtshymanski (talk) 01:08, 5 August 2012 (UTC)

Inductance with physical symmetry merged here

Immediately after Inductance with physical symmetry was created as a spinout of this article in November 2009, a user proposed merging it back in. Based on the sizes of the articles, I found this to be reasonable and performed the merge. Notably, that article offered no context and had no lede. Without that context, though, I'm not sure exactly where the content best fits. I've added it as its own section, but more knowledgeable editors should feel free to pick it apart and scatter it wherever. If you do so, please edit Inductance with physical symmetry, which now redirects to its section, to Inductance generally. Thanks, BDD (talk) 03:30, 16 August 2012 (UTC)

Actually, I think I did pretty well. Immediately preceding the new section was 'Details for some circuit types are available on another page.' That wikilink went to the page that has now been redirected right below. I've removed it now. --BDD (talk) 03:34, 16 August 2012 (UTC)

confusing wording

In the opening paragraph, I find the following sentence to be confusing: 'This is a linear relation between voltage and current akin to Ohm's law, but with an extra time derivate.' In fact, the voltage across an inductor is not proportional to the current -- it is 90º out of phase with it if the reactance is perfectly inductive.Jdlawlis (talk) 01:43, 18 December 2010 (UTC)

I agree. The statement is technically correct and mentions an important point, but should not be in the introduction. --Chetvorno^TALK 04:27, 18 December 2010 (UTC)

-Shouldn't be confusing, taking the time derivative is a linear operation, the statement is mathematically correct.radical_in_all_things (talk) 08:30, 19 December 2010 (UTC)

Most people reading the introduction will be nontechnical people looking for the simplest possible explanation. The defining equation belongs there, but discussion of its linearity does not. The connection of inductance with magnetism isn't even mentioned until the 4th para. This is why people complain wikipedia articles are too technical. --Chetvorno^TALK 20:16, 19 December 2010 (UTC)

The statement is not mathematically correct. It would be correct if it were written: 'This is a linear relationship between voltage and the rate of change of current akin to Ohm's law, except that current is replaced by its derivative.' The fact that the derivative is a linear operation does not relate to this particular issue. As an example, take an ideal RL circuit with an AC generator. Let ${\displaystyle V(t)=V_{0}cos(\omega t)}$ be the voltage generated by the AC generator. It follows that the current ${\displaystyle I(t)=\frac{V_0}{Z}cos(\omega t-\delta )}$, where the impedance ${\displaystyle Z=\sqrt{R^2+(\omega L{)}^2}}$ and the phase constant ${\displaystyle \delta =ta{n}^{-1}(\frac{\omega L}{R})}$. The voltage drop across the inductor, ${\displaystyle V_L=\frac{\omega L{V}_0}{Z}sin(\omega t-\delta )}$. If the voltage across the inductor were indeed proportional to the current, you would be able to multiply the current times a constant to achieve the voltage. Multiplying a cosine function times a constant will only change its amplitude -- it cannot transform it into a sine function. Hence the voltage across the inductor is not proportional to the current through the circuit. These equations can be found in any introductory E&M textbook such as Tipler or Purcell. Jdlawlis (talk) 23:36, 20 April 2011 (UTC)

It is mathematically correct to state that inductors are governed by a linear equation. It is not correct to state that there is a linear relation between voltage and current, and it is even more incorrect to state that the governing equation is analogous to Ohm's law. The Ohm's law analogy only applies to the r.m.s. values of sinusoidal voltages and currents and requires the introduction of the concept of reactance to replace resistance in Ohm's law. SpinningSpark 06:13, 21 April 2011 (UTC)

I agree with everything you say, SpinningSpark. I think it would be clearer if the Ohm's law reference were removed. Jdlawlis (talk) 14:11, 21 April 2011 (UTC)

What really gets mixed up here is proportionality (linear equation) and linear relation. The statement is correct in that the voltage generated by the sum of two (time dependent) currents is the sum of the voltages generated by the individual currents (as it is in Ohm's law). This would be a practically useful information, but if it is confusing, it need not be in the introduction. radical_in_all_things (talk) 06:49, 22 April 2011 (UTC)

I would suggest a compromise solution here. You can begin with a simple explanation stating, 'We can view this in similar terms to Ohms Law, except that unlike Ohm's law..'

Well you can see what I am saying. Mostly, this article should be written so that any layman, or high school student can understand.

Your thoughts?Sunshine Warrior04 (talk) 07:44, 26 October 2011 (UTC)

Seems to me that the confusion of the meaning of 'linear' comes up just about everywhere the word is used. Even in the case of Ohm's law, which still applies even if there is a voltage offset. That is, a resistor in series with a battery still follows Ohm's law, not V=RI but dV=RdI. Derivative is a linear operator in math, and in EE. And that is without getting into complex impedance, where the linearity is more obvious, and where you can get from sin(x) to cos(x) multiplying by a constant. Gah4 (talk) 19:43, 11 March 2014 (UTC)

Article lead

The one thing the article lead does not do is tell me what inductance is. Inductance is a very specific property of an electric circuit (just like capacitance is very specific property). I would change the lead to describe this, but with the established disruptive editor, Wtshymanski putting his oar in, it would be a waste of time, because he obviously doesn't know either, and he reverts anything that does not fall within his limited sphere of knowledge. 109.145.22.224 (talk) 15:05, 3 May 2012 (UTC)

In thinking on how to make inductance understandable to someone with no EE background, it occurred to me that a favorite analogy is with mass. (Inductance as mass and capacitance as spring, and you get a mechanical oscillator. Add friction (R) for an RLC circuit.) So, looking at inertia it starts: 'Inertia is the resistance of any physical object to any change in its state of motion (including a change in direction).' (With a possible complication using the word resistance.) Or maybe the analogy is to mass, and inertia to induction? Anyway, seems to me that it should be as understandable as mass and inertia. Gah4 (talk) 21:24, 11 March 2014 (UTC)

But otherwise, I often refer to articles for details that I forget. It doesn't have to be only for beginners, though the first line shouldn't be too discouraging. Gah4 (talk) 21:24, 11 March 2014 (UTC)

Let me say, that I myself nearly am giving up. The lead may be improved, yes. But it should contain the definition, and a definition should be exact, generic, simple and immediately applicable. This only is true for the definition in terms of current and voltage (no magnetic flux). This relation follows from maxwell's equations for arbitrary current loops (Jackson, or see online C.B. Thorn, EDynLectures1.pdf). A definition in terms of flux is a poor man's derivation from an integral form of maxwell's equations, worthless except for thin wires. Think about headaches*(number of peopes) that causes this in the case of loops consisting of extended conductors, for instance flat strips on printed boards. What about Wikipedia's quality?radical_in_all_things (talk) 16:03, 3 May 2012 (UTC)

I agree with most of the above criticism, but I think the rest of the introduction has the basics of inductance. The current lead shows a problem common in technical WP articles; the editor tries to make the lead sentence or paragraph a rigorous or all-inclusive definition of the subject. This ends up making it so general or esoteric that it's incomprehensible to nontechnical readers. I feel that the lead should back off and come in slow with an elementary description of what inductance typically is, in electrical circuits. As long as there's a good technical definition somewhere in the introduction (which there already is), the lead paragraph doesn't have to be comprehensive. --Chetvorno^TALK 17:31, 3 May 2012 (UTC)

What inductance is can be stated in one sentence. That sentence is applicable to any sitiuation where inductance is present. That's what a definition should be. I see that our resident non genius has now replaced the original with this nugget, 'inductance is an effect caused by the magnetic field generated by electric currents flowing in a circuit.' Great definition - NOT! It's a pity that it fails to enlighten us as to what the actual 'effect' is. Also, it tells us that there has to be more than one current in the circuit, something that every other physicist, scientist and engineer was previously unfamiliar. 109.152.145.86 (talk) 11:55, 4 May 2012 (UTC)

Please, what is that sentence? After all the bulletins on the love-lives of Singaporean schoolchildren, someone did this [5] which inadvertanly pluralized current. One might argue that even a steady current creates a magnetic field and links flux and so has inductance, but that's a bit philosophical. --Wtshymanski (talk) 13:26, 4 May 2012 (UTC)

And demonstrates your total lack of understanding of the subject perfectly. A DC circuit with a steady state current exhibits no inductance at all. If you ever find the right definition of 'inductance' (because you obviously don't know it) you will realise this. And the definition in the lead, inspite of your recent edit still leaves the reader non the wiser as to what the 'effect' is. Let's be honest now; you haven't got a clue, have you? And the other point that you have completely missed is that the 'electric current' has to have a specific characteristic which the definition failed to mention. 109.152.145.86 (talk) 15:02, 4 May 2012 (UTC)

A DC circuit still has inductance, and you can still calculate it. From E=LI²/2 and integrating the magnetic energy you can find the inductance, without changing the current. Even so, DC circuits aren't created with current already flowing, it has to get there somehow. Gah4 (talk) 21:24, 11 March 2014 (UTC)

Here's your chance to fufill the educational mandate of the Wikipedia. What is the property that we're missing in the lead? --Wtshymanski (talk) 15:28, 4 May 2012 (UTC)

A definition needs to be vague enough to catch all examples where the phenomenon of inductance exists. Searching on line for a citation to back up the definition (which I'll come to in a moment) turns up some interesting contributions. There is much that attempts to define it in terms of energy storage. Well, inductors do store energy in their magnetic field, but that is not the primary property of inductance. Another source tries to define it in terms of an e.m.f. being induced in an adjacent circuit. That might be mutual inductance (a side effect of inductance), but not inductance itself.

Storing energy is the primary property of inductance. It is the stored energy that has to go somewhere when you try to decrease the current, or has to be created when you increase the current, that is the direct cause for inductance. Also, in many cases it is easier to calculate the inductance by computing the stored energy and equating to LI²/2. Gah4 (talk) 21:24, 11 March 2014 (UTC)

The best one that I can find is here. It gives us 'that property of a circuit by which a change in current induces, by electromagnetic induction, an electromotive force.' Good, but no cigar. It still misses a very important property. Completing the definition to include the missing property would be something like, 'that property of a circuit by which a change in current induces, by electromagnetic induction, an electromotive force, which opposes the change in current'. That last bit is important. It tells us why the current in a inductor cannot change instantly. Everything else flows from that definition. Unfortunately, I can't find an online citation that gives the complete definition so I won't put it in the article (for now). If I can find one online, or even in a book, then I'll probably go for it. The trouble is, electrical engineering text books rarely go back to first principles and dive straight into telling the reader what inductors are and what effect they have in A.C. circuits. Perhaps I need a physics book .. DieSwartzPunkt (talk) 15:42, 4 May 2012 (UTC)

This gets a little abstract..where does the inductance go when the current stops? A coil with DC flowing has no inductance? Unfortunately the definition that talks about 'flux linkages' is not much less abstract. I like a definition I saw that says this is fundamentally a geometric property. In the pathological case, we can devise circuits that produce a voltage proportional to a rate of change of current that have no significant magnetic field at all. --Wtshymanski (talk) 16:33, 4 May 2012 (UTC)

┌─────────────────────────┘Any definition would require a reference. That's why I haven't changed the article. The current definition is equally unsupported, but it is too narrow in its scope.

To answer your question, a DC circuit carrying a steady current does not display the phenomenon of inductance. That is not to say that the circuit has no inductance as most poeple understand it (you can measure it on an suitable LCR meter - although, of course, the meter uses an AC current, thus inductance shows up). The circuit does display the phenomenon of inductance as soon as you try to vary the current. The value that you have measured in the last step allows you to calculate what effects that change of current will have. The effect that you get is that the inductance attempts to oppose the change, thus the current will change over a finite interval.

In circuits using OP amps (or any active devices come to that) to emulate inductance, you are right in your assertion that have no magnetic field (at least responsible for the phenomenon of inductance). What they, in fact, do is to include capacitance. Then exploit a phase invertion of either the voltage or current element (but not both). This turns a current lead of ninety degrees into a current lag (or the characteristics of capacitance into those of inductance). The circuit isn't really an inductor and it doesn't display the phenomenon of inductance by definition. What the circuit does do is behave as though it were an inductance, even though it isn't really. The active devices monitor the current, differentiate it and then produce the necessary e.m.f. to oppose the current change. The e.m.f in this case is not directly induced by the current change.

To extent this line of thinking: you can even make active circuits behave as if they were a negative resistance, of which there is no such component in reality. As a final feat, you can connect a negative resistance circuit in parallel with a simulated inductance (which has shunt resistance). The resistances cancel and you have a (simulated) perfect inductor (and there isn't one of those either). Put a capacitor in parallel with that, adjust the negative resistance to cancel the capacitor's leakage and you have a lossless tuned circuit that will oscilate forever. Voila! An electronic version of perpetual motion? Not really: the energy is, of course, coming from the active elements. DieSwartzPunkt (talk) 17:00, 4 May 2012 (UTC)

A difficult definition. Where does the inductance go in a DC circuit? Surely whatever property that is responsible for inductance doesn't just appear the moment we decide to pull the wire off the terminal to see the fat spark? See, at least with the definitions that talk about flux linkages, the reader can say 'Oh, I can understand 'inductance' if I can just figure out what a 'flux linkage' is', which might be necessary. Maybe we should just redirect this article to 'Maxwell's Equations', where the truly superior will grok the phenomenon by inspection, and we lesser lights will just have to remain mystified. Or, we could just talk about the coils and effects in a circuit, and leave the question of what happens to the inductance when you don't have any wires to the electromagnetism articles. --Wtshymanski (talk) 18:10, 4 May 2012 (UTC)

Firstly, this is an encyclopedia. It cannot run with a definition plucked out of the air that you happen to like. The definition above is the one that is taught in colleges and universities all over the world. It is the one that I had to teach in the days when I taught electrical engineering principles.

The phenomenon of inductance as defined is not present in a steady state DC circuit. As you correctly surmised above, the phenomenon appears the moment you '.. pull the wire off the terminal ..' because you are now changing the current. You have to remember that 'inductance' is a phenomenon - nothing more. You are thinking in terms of the man made component which we have called an 'inductor' that happens to exploit the phenomenon and exhibits inductance under the right conditions. The inductor may always be there, but the phenomenom not necessarily so.

To illustrate further: consider that I have 3 identical lengths of wire. All 3 have a resitance of 5 ohms. One I leave as a long length (its actual inductance is negligible); one I wind around an iron core such that it has an inductance of 1 henry and the remaining one I wind around another iron core such that it has an inductance of 2 henries. I pass a steady state current of 2 amps through each of the 3 pieces of wire. The voltage appearing at the ends of all 3 wires will be 10 volts (by ohms law). The inductance of each wire makes not one jot of difference to the current because the phenomenon of inductance (from the definition) is not present in the circuit. Further, from the 3 (DC) parameters that we can measure, resistance, current and voltage, we cannot even speculate on the magnitude of the inductance if we didn't already know.

BUT: if we now vary the current from 2 amps to 3 amps over a period of one second, our phenomenon of inductance rears its head and the 3 circuits behave differently. Our purely resistive circuit shows a voltage that changes from 10 volts to 15 volts during the change in current. The 1 henry inductor has a voltage that varies from 9 volts to 14 volts (because it is generating an e.m.f. of 1 volt opposing the change - 1 henry is one volt for 1 amp/second change). The 2 henry inductor has a voltage varying between 8 volts to 13 volts (because it is generating an e.m.f. of 2 volts opposing the change). At the start of the change the voltage undergoes a step change from 10 volts to whatever the voltage at the start of the change is. At the end there is a similar step change to 15 volts as soon as the current stops varying. Knowing the rate of change of the current, and the magnitude of the reverse e.m.f. generated, we can figure out the magnitude of the inductance (if we didn't already know).

Once the current stops varying, the phenomenon of inductance disappears, and once again the steady state parameters tell us nothing about the magnitude of the inductance that we both know is really still there.

This might all sound a bit philosophical, but the fundamental principles often are. Inductance, like many phenomena, is a fundamental principle. I would often start a year of second or third year students in my principles classes with a question (under the guise of seeing what they have forgotten over the summer break). My question would be, 'What is capacitance?' (No peeking at the article!). I could reckon it would take between 20 and 40 minutes before the students nailed what capacitance is. They would invariably start by telling me what a capacitor is. The problem for them was that were drawing on their current knowledge and were initially unable to work it back to first principles and come up with a simple catch all definition.

The article must start with the established definition (with a suitable reference of course. [1]). It can then develop the phenomenon into all the characteristics and uses of inductance that we are all familiar with.

[1] Still haven't found one. I think I may have to make the spiders homeless in all my old text books up in the attic. I know I will find several in that lot. DieSwartzPunkt (talk) 08:42, 5 May 2012 (UTC)

Wtshymanski's point was that the inductance is a function of the circuit itself, and not of the state of current in the circuit. That's important; if it isn't clear, maybe we can put a sentence in explaining that. DieSwartzPunkt, there is no requirement in the MoS that the article start with a formal definition, or even contain one: WP:EXPLAINLEAD, WP:MOSINTRO. The first paragraph could be an informal explanation, leaving the definition to later. However, your capsule definition, 'inductance is that property of a circuit by which a change in current through the circuit induces a proportional electromotive force across it' (improved it a little), although stuffy and opaque, is actually not too bad. I could probably support some variant of that as the lead sentence, as long as it is followed by a more elementary explanation (along the lines of the present lead) for general readers. It's important to remember that the largest group of visitors to this page will be nontechnical readers who want the simplest possible explanation. Hopefully, not too many will be scared off by the first sentence. --Chetvorno^TALK 11:28, 5 May 2012 (UTC)

I'm not so sure. I think that article needs to start with something that tells us what inductance is. It is important to remember that the article is about 'inductance' and not inductors. I know many people erroneously call an inductor, an inductance. My problem with your improved definition is that it fails to state that the e.m.f. opposes the current change (an important point, without which, the whole subject collapses). The definition is what God gave man. Everything else that follows is what man did with it. DieSwartzPunkt's definition (he admits most of it was lifted), could be shortened a bit to 'that property of a circuit by which a change in current induces an electromotive force which opposes the change in current'. The word 'induces' implies electromagnetic induction rendering those words redundant. An any case, I do not believe the e.m.f. would be induced any other way. That definition is concise and covers the point without being obscure. A mention of Lenz's law would not be out of place (somewhere). I know Lenz is mentioned but not his law which is where inductance actually comes from. 109.152.145.86 (talk) 14:36, 6 May 2012 (UTC)

EMF only opposes the current change when inductance is positive. Yes it is always positive for passive circuits, and is nice to remember when answering physics problems. If I and V are defined in advance, then one might find that the appropriate L has the wrong sign. In the case of active circuits, it is possible to build negative inductance. Gah4 (talk) 21:24, 11 March 2014 (UTC)

I have no problem with that shortened version. DieSwartzPunkt (talk) 16:09, 6 May 2012 (UTC)

A splendid illustration of how the phenomenon of inductance is not present in a steady state circuit, but '.. rears its head ..' as soon as you change the current flowing.

My problem: I think you might have the effect the wrong way around <racks brain trying desparately to remember the basics from so long ago>. If the e.m.f. induced is opposing the current change, then the total volts dropped across the inductor must increase to oppose the change. If they decreased as you claim, then that would assist the current flow. Or put another way, the delta V = L * (dI/dt). For 1 henry and +1 A/sec, delta V = +1 volt. Thus the voltage would be 11 to 16 volts while the current change is occuring (for 1 H) and 12 to 17 volts for the 2 H inductor. I'm fairly sure, I have got it right. Anyone else agree or disagree? 109.152.145.86 (talk) 14:36, 6 May 2012 (UTC)

You spotted it! I couldn't resist. It was a technique I often adopted with my students. I would introduce a basic error into my lecture, and await someone to point it out. Sometimes it happened quickly (if not too many people had dozed off). Otherwise, I was left trying to develop an incorrect point. It usually got spotted when the developed point descended into absurdity. The objective was that the students would always remember the point that 'sir' had go so obviously wrong. An unintended effect of my deliberate mistake is that Chetvono's précised definition (unintended because he posted after my mini monograph above), is that what I wrote could fit with his definition, precisely because he omitted the important part of the opposition to the current change. DieSwartzPunkt (talk) 16:09, 6 May 2012 (UTC)

The flux through a circuit can be related to the current in that circuit and the currents in other nearby circuits. (We shall assume that there are no permanent magnets around.) Consider the two circuits in <the adjacent figure>. The magnetic field at some point P consists of a part due to I₁ and I₂. These fields are proportional to the currents producing them and could, in principle, be calculated from the Biot-Savart law. We can therefore write the flux through circuit 2 as the sum of two parts; one is proportional to the current I₁ and the other to I₂: Phi_m2 =L ₂ I ₂ + M₁₂ I₁ where L₂ and M₁₂ are constants. The constant L₂, called the self-inductance of circuit 2, depends on the geometrical arrangement of that circuit. The constant M₁₂, called the mutual inductance of the two circuits, depends on the geometrical arrangement of both circuits.

Although a good definition, my concern is for the general nonscientific reader, and I feel that this definition is just too complicated. As you say, it brings in another abstract quantity, magnetic flux, and it also brings in mutual inductance, and two separate circuits and currents. In most usage 'inductance' means self-inductance. I would rather see the first sentence just cover self-inductance, and introduce mutual inductance a few sentences down. Secondly (a minor point), if the goal is to start the article off with a technically correct definition of inductance, this sentence fails, because it doesn't take into account DieSwartzPunkt's point above, that inductance can be synthesized in a circuit without magnetic flux, using feedback. From an electrical engineering (not physics) perspective, inductance is a property defined by how a circuit responds to changes in current. --Chetvorno^TALK 19:18, 6 May 2012 (UTC)

The point is that it is 'synthesised'. The inductance does not come from any electromagnetic effect so it isn't real inductance. It's just a circuit constructed to behave as though inductance were present. If you pass an A.C. current through the synthesised inductor and place another coil of wire near the circuit, it will not pick up any coupled magnetic energy because there isn't any to pick up (neglecting the normal fields around any conductor). Thus the definition does not need to cover gyrator circuits because there is no real inductance present. 109.152.145.86 (talk) 08:15, 7 May 2012 (UTC)

Your claim that this 'definition' doesn't mention varying currents, is because it is not a definition. It is an explanation which is indeed out of context. The reason varying currents is not mentioned is because they will be mentioned in the context that is omitted. If a voltage is being induced in a second circuit, then the fields and current must be alternating (i.e. varying). Steady DC fields induce no voltage. This renders both the explanation and the reference unuseable in the context of this article. 212.183.128.78 (talk) 13:43, 8 May 2012 (UTC)

No, the thing with the op-amp isn't synthesizing inductance - inductance, by definition, requires magnetic fields. I'd take the physics text over Wikipedia. --Wtshymanski (talk) 03:29, 7 May 2012 (UTC)

Inductance is the proportionality between voltage and changing currents. Now, currents, changing or not, generate magnetic fields, and you can't get away from that, but the definition should be based on the result, not how it is created. Note that the subject is inductance, not inductors. For the inductors section one should describe the physical device. Gah4 (talk) 21:24, 11 March 2014 (UTC)

They're called active inductors. They are used to synthesize inductance on a chip, where there isn't room for a spiral inductor. Usually they are built with a capacitor in a gyrator circuit. The gyrator can invert reactance, so the capacitive reactance is converted to inductive. 1, 2, 3, 4, 5, 6, 7 --Chetvorno^TALK 06:42, 7 May 2012 (UTC)

Spot on. It's using one phenomenon (capacitance) and making it behave as though it were another (inductance). But the inductance isn't really there. Further, the circuit only behaves this way as long as there is a power supply powering the active parts of the circuit. Remove the power supply and the behaviour is gone. 109.152.145.86 (talk) 08:15, 7 May 2012 (UTC)

The definition does not (or should not) say that where there is inductance there is magnetic fields generating e.m.f.s. It's the other way around, it says that where there is a changing current, which induces an e.m.f., then there is inductance. Man by is ingenuity has managed to create circuits which behave as though they contain inductance even though they don't. As has been said, man has also created circuits which behave as though they are negative resistors even though there is no such thing - ergo there can be no real negative resitance in such a circuit, but it behaves as though there were. Have a look at this. It clearly shown no coil of wire to produce any magnetic field even though the equivalent circuit obviously does, so where could such a field possibly come from?

Forget this whole gyrator business because it is just a distraction. Gyrator has its own article. None of it belongs here. Wtshymanski as ever is resorting to techno-babble that he doesn't understand just to enforce his view in Wikipedia to the exclusion of all others. 109.152.145.86 (talk) 08:15, 7 May 2012 (UTC)

Agreed. Gyrator circuits do not contain real inductance and should not be discussed further. They do not belong in either the article or the discussion. Any simulated inductance that they demonstrate is not caused by magnetic induction because, as has been said, there is no magnetic induction. At least nowhere near enough to explain the behaviour. 212.183.140.12 (talk) 09:09, 7 May 2012 (UTC)

You've absolutely nailed it. It's not relevant because it isn't inductance. It's a circuit that just happens to behave in a similar way to an inductor. DieSwartzPunkt (talk) 15:27, 7 May 2012 (UTC)

WP:MoS says that WP should follow the usage in the literature of the field. The 7 citations I gave above, all from professional electrical engineering sources, describe active inductor devices as having inductance. In electrical engineering, a circuit has inductance if it acts like an inductor: if it responds to changes in current with a back-EMF. ('If it quacks like a duck . . .') Similarly a synchronous condenser doesn't have capacitor plates, and only functions when its shaft is turning, but still has capacitance. --Chetvorno^TALK 10:48, 7 May 2012 (UTC)

┌─────────────────────────┘ But if there's no magnetic field, it's not inductance. The current lead as it stands this morning doesn't mention magnetic fields at all! Inductance is a physical geometric property, not the emulation by an op-amp. And if we're going to drag in mysterious notions like 'electromotive force' anyway, why not drag in the correct notion (magnetic flux) rather than spend the reader's time on a generalization which doesn't apply to the underlying physics? --Wtshymanski (talk) 13:30, 7 May 2012 (UTC)

You are getting the general idea. If there is no magnetic field, it cannot induce anything. The word 'inductance' comes from the phenomenon that something (changing magnetic field) is inducing something else (e.m.f.). The e.m.f. is not a mysterious notion. It is what the changing magnetic field induces and it is what opposes the change. It's fundamental to the concept. Just call the e.m.f. voltage if you feel it is easiler to visualise. The gyrator simulates the property of inductance, and some may call it an inductor only because they have made a concious decision to do so. But like it or not, it does not display the property of inuctance precisely because there is no magnetic field to induce anything. It's existence is irrelevant to any discussion of the phenomenon of inductance. DieSwartzPunkt (talk) 15:27, 7 May 2012 (UTC)

Now I've found a good definition in a rather unlikely source. From a Collins 'Gem' pocket encyclopedia. I reproduce verbatim (OCR errors excepted). It's a bit wordy and could easily be trimmed, but here it is.

Inductance, electrical, property of an electric circuit by which a changing electric current in it produces a varying magnetic field. This magnetic field may induce a voltage in the same circuit opposing the change in current (self induction) or in neighbouring circuits (mutual induction).

The wordiness probably comes from the fact that this is the entire entry in an encyclopedia that is general in nature. I have no problem with the inclusion of the concept of mutual inductance as it is introduced in the main body of the article anyway. I don't like the 'may' because if it doesn't there is no inductance, but that may just be semantics. The current definition in the article is unacceptable because it omits to mention the e.m.f. generated (or voltage if you prefer - same thing) by the changing current and the important point that it opposes that change in current. In fact it is what inductance most definitely is not. It could just as easily be describing an electromagnet, which operates from DC as well as AC. But in steady state DC, there is no phenomenon of inductance for reasons previously discussed. DieSwartzPunkt (talk) 15:27, 7 May 2012 (UTC)

Electromagnets don't have inductance? They have currents and make magnetic fields..that sounds like its good enough for Tipler's definition (which doesn't mention time at all). Making a magnetic field from a current is sure-enough a phenomenon of inductance, and the opposing-voltage time-varying stuff is just more consequences of inductance. --Wtshymanski (talk) 16:26, 7 May 2012 (UTC)

You are getting a bit confused again. You need to separate the phenomenon of inductance from what man has called an inductance (really an inductor). An electromagnet (I wish I hadn't mentioned it now) supplied with a steady state DC current does not exhibit the phenomenon of inductance. There is no current change and hence no e.m.f. generated to oppose this non existent current change. There is a steady state magnetic field, but that is not inductance. I know you can connect it to an LCR meter and measure it's inductance, but the LCR meter supplies it with a varying voltage (and hence gives rise to a varying current) and thus it now exhibits the phenomenon of inductance. But in the steady state DC circuit, non of the circuit parameters (voltage, current or resistance) provide any clue as to the magnitude of the inductance of the electromagnet because the phenomenon is not present. You can paste a label with the measured inductance to the side of the electromagnet if you wish, but the numerical magnitude of the measured inductance is entirely a man made concept (and indeed it was man who decided, not entirely arbitrarily, how big a henry is). But however you dress it up, the magnitude of the inductor (that we both know is there) has no effect whatsoever on a DC steady state circuit because the phenomenon of inductance is not present. At present, I'm counting at least 3 people who are trying to tell you this.DieSwartzPunkt (talk) 17:02, 7 May 2012 (UTC)

I cannot disagree with anything that DieSwartzPunkt has said in that last post. Your problem is that your 'Tipler's definition' is not all encompasing enough to define inductance. It is a very specific discussion, and I suspect that you are quoting it out of its context. If you cannot grasp the fundamental basic concepts, then you cannot understand anything associated with inductors and inductance. 109.152.145.86 (talk) 17:15, 7 May 2012 (UTC)

You asked in your edit summary, 'Why the hangup on time-varying currents?'. Because it is fundamental to the concept. The voltage (e.m.f.) induced in an inductor courtesy of the phenomenon of inductance is expressed by:

${\displaystyle v=L\frac{di}{dt}}$

That last bit, di/dt is the mathemetician's way of saying, 'the rate of change of the current'. If the current does not change, the induced voltage is zero and thus the phenomenon of inductance is not present, because the inductance of the inductor has no effect on a non changing current. Yes, the inductor carrying a steady state current will create a magnetic field, but that unvarying field will have no effect on the circuit. 109.152.145.86 (talk) 17:53, 7 May 2012 (UTC)

So, then, what is the name for that property of a DC coil that relates the intensity of the magnetic field produced to the current circulating in that coil? It's also measured in webers/ampere. --Wtshymanski (talk) 18:12, 7 May 2012 (UTC)

Professor Grover spends a couple of hundred pages explaining how to calculate inductance of various geometriesFrederick Warren Grover Inductance Calculations, Working Formulas and Tables (Dover Publications, 1946) ISBN 0486495779, and doesn't seem to say ever that the inductnace of a coil (or other configuration) with DC is zero. Any of his formulas that I can read on the Google preview only talk about lengths, never about times. --Wtshymanski (talk) 18:27, 7 May 2012 (UTC)

I agree. Inductance is defined by a circuit's response to changing current, so that should be part of the definition, but is a property inherent in the circuit itself. The definitions being considered even SAY that: 'Inductance, electrical, is a property of an electric circuit by which a changing electric current in it produces a varying magnetic field.' A banana is yellow whether the light in the room is on or off. DieSwartzPunkt, I think your definition is easier on nontechnical readers than the Tipler definition, but the second sentence is badly phrased: 'This magnetic field may induce a voltage in the same circuit opposing the change in current..'. May? The induced voltage is the effect we're talking about. --Chetvorno^TALK 22:23, 7 May 2012 (UTC)

You might have missed the bit where I did say that I had a problem with the word 'may'. If there is a neighbouring circuit, and the varying field from the first intersects the second, then an e.m.f. will be induced. DieSwartzPunkt (talk) 08:25, 8 May 2012 (UTC)

Wtshymanski, I see what you are trying to do with the lead sentence in the article, and you're right, but I feel for elementary readers the intro should refer to changing currents and magnetic fields. Don't you think the construct: 'Inductance is a property of a circuit that..' expresses the point sufficiently for the lead? We could add a sentence further down that inductance is a property of the circuit itself and not the state of current in it. --Chetvorno^TALK 22:20, 7 May 2012 (UTC)

Your are right - and wrong. Yes, from various formulae that you can find in appropriate books, you can calculate the inductance of a coil of wire, given various parameters about it, such as number of turns, the geometry, the characteristics of any core material etc. etc. But regardless of the answer that you come up with, the magnitude of that number has no bearing whatsoever on the behaviour of that coil in a steady state DC circuit. That behaviour is determined entirely by the resistance of the wire and nothing else (See my comprehensive example above - with the correction noted). All the magnitude does is tell you how the coil will behave when you try to vary the current. DieSwartzPunkt (talk) 07:51, 8 May 2012 (UTC)

It isn't. It's magnetising force and it's measured in Ampere Turns. And it isn't called inductance. It's just fundamental electromagnetism. If you want to take the inductance concept back one step, you get to 'induction'. From the electromagnetic viewpoint, this is the induction of an e.m.f. from a varying magnetic field (from anywhere - but there is that pesky 'varying' again). DieSwartzPunkt (talk) 07:51, 8 May 2012 (UTC)

Now that is another good example of how the 'inductance' has no effect on a DC circuit. The magnetising force is proportional to the number of turns of wire multiplied by the current. The inductance has no bearing on that magnetising force whatsoever. If you have an inductor with 1000 turns of wire and you pass 10 milliamps through it, the magnetising force is 10 Ampere turns. This remains true regardless of whether the inductor is 1 millihenry, 1 henry or 1000 henries.

It is measured in Ampere Turns, but Wtshymanski correctly noted that it could be expressed in Webers per Ampere for a particular inductor. This is not a convenient way of doing it, precisely because the actual value of Wb/A varies from inductor to inductor as it is dependent on the number of turns of wire. Thus they are not equiavalent. Interestingly, Wtshymanski has unwittingly introduced his time varying concept again, because the dimensions of the Weber include time squared. Indeed the definition of the Weber is based on a change of 1 Weber/second. 109.152.145.86 (talk) 08:51, 8 May 2012 (UTC)

There's an unfortunate typo in 'the definition of the Weber is based on a change of 1 Weber/second.' The number of webers you get per amp varies in different coils and components because they have..some different property..could it be..inductance? The formulas given for inductance never talk about the number of amperes or AC or DC, only about the geometry and linear dimensions (Professor Grover's book does acknowledge that the distribution of current in a wire may be non-uniform due to frequency but the snippets seem to indicate this is more of a problem for a standards lab than for buying chokes at Radio Shack.)

Of course there's a DC effect of inductance..the magnetic field stores energy that would not be stored in the case of a non-inductive circuit. Take a length of wire with a current flowing in it,ascertain (by some physics lecture theoretic method) how much energy the system contains with the wire a) in as big a loop as you can manage or b)made up into a hairpin turn that encloses as little area as possible or c)in multiple turns. Which system has the most stored energy? (This is probably a good physics tutorial problem..given a length of wire, what geometry maximizes its inductance..big loop, long skinny solenoid , etc.? )Just because the units have 'seconds' somewhere in their dimensions doesn't mean the situation is time-varying; the unit of force of my butt against my chair has the dimensions of mass*length/time squared, but the situation is sadly not varying. --Wtshymanski (talk) 13:45, 8 May 2012 (UTC)

Where is the unfortunate typo? Weber: The weber is the magnetic flux which, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second. One weber, reduced to zero in one second. That's a change of 1 weber/second. The different property that gives varying Wb/A? No, it's not inductance. It's the number of turns of wire (from the definition above) but can also be affected by anything that concentrates the field in any way (like a lump of iron). I acknowledge your points about skin effect etc. That is a whole more complicated issue best left undisturbed.

You are also correct when you state that an inductor stores energy in the DC circuit. But you miss the point yet again: that that stored energy has no effect on the DC current that flows through the inductor or on the volt drop across it under steady state conditions. You keep trying to claim that the inductance affects the DC conditions - and keep failing. The issue of energy storage is, in any case, adequately covered in the inductor article. And force does imply a time varying quantity, because force=mass*acceleration. Are you suggesting that acceleration is not time dependant? Your problem here is that since you are not moving, acceleration is zero and therefore force (in this case) would appear to be zero (from the formula). The reality is that the force is real and present, but is the force that would result in an acceleration (of 1g) if the chair were to suddenly not be there (a time dependant quantity). 86.167.20.121 (talk) 16:36, 8 May 2012 (UTC)

What is the property of a DC coil that is increased by adding turns and wrapping it around a ferromagnetic core, that *also* increase the inductance only observed with changing currents? I'd like to know. And why confuse MMF with flux? That's like confusing amps with volts. Surely a DC circuit produces a magnetic field. Barring non-linear effects in saturating ferromagnetic substances, that magnetic field is proportional to the curernt. If you try to change the current, you also get the field to change, adn all kinds of consequences result. There's a force between my butt and my chair, but no acceleration. --Wtshymanski (talk) 19:25, 8 May 2012 (UTC)

You have clearly understood nothing - as usual. If you don't understand what you are trying to discuss, then don't try to hide your ignorance by introducing one red herring after another. And I count 5 red herrings so far. 86.167.20.121 (talk) 12:08, 9 May 2012 (UTC)

I had a discussion with a colleague when I got back to work this morning. He is a better theoretitian than I am and he made a very good point. He observed that the definition from dictionary.com is a perfectly acceptable one. As it was a long time ago, here it is again, 'that property of a circuit by which a change in current induces, by electromagnetic induction, an electromotive force.'. He points out, that though important, there is no need to define the point about opposing the change in current because the induced e.m.f. will not do anything else. It can then be added as a following sentence. So our lead could now start.

In electromagnetism, inductance is that property of a circuit by which a change in current induces an electromotive force (e.m.f.).<ref>http://dictionary.reference.com/browse/Inductance?s=t</ref> From Lenz's law that e.m.f. will oppose the change in current that induces it. The varying field in this circuit may also induce an e.m.f. in a neighbouring circuit (mutual inductance).).<ref>Collins Gem Encyclopedia</ref> ..

There we go. A definition with a reference, and a couple of short sentences just to fill in the blanks for the less technical reader with another reference. DieSwartzPunkt (talk) 07:51, 8 May 2012 (UTC)

Hmm. Thinking about, your colleague is probably right. There is no need to define that which is immutable (because that is a law - and in this case Lenz's law).

I like your current lead, I might have phrased it slightly differently, but what the hell. It covers the points that need to be made. 109.152.145.86 (talk) 08:51, 8 May 2012 (UTC)

You might as well say 'that property of a circuit.. that induces, by God's will, an electromotive force' - hanging a label on the phenomenon doesn't explain it. We should just describe what inductance is observed to do, and leave the labels till later on. Energy gets stored, magnetic fields appear, changing current causes changing voltages in this circuit and the one on the next lab bench, etc. It might be helpful to mention practical consequences of inductance in telegraphy, radio, and power transmission, for that matter. It's not just a topological property like genus, it bites you every time you open a light switch. --Wtshymanski (talk) 13:45, 8 May 2012 (UTC)

'Lenz's law' is a description of an observation, not an explanation. --Wtshymanski (talk) 13:45, 8 May 2012 (UTC)

If you believe in that sort of thing, it is God's will. Why don't you just accept that at least 4 people are in some sort of agreement. Lenz's law is an unchangeable statement as to an effect that occurs. It is not a description of an observation - that would be a hypothesis. A law is more than that, it has been proven to be true and without exception.

You must also have strange light bulbs where you are if you can observe inductance every time you turn one off. DieSwartzPunkt (talk) 13:55, 8 May 2012 (UTC)

That looks perfectly OK to me. And the reworded and expanded version this is now in the lead is even better. 212.183.128.78 (talk) 13:45, 8 May 2012 (UTC)

wvbailey edit of first para of lead

I expected the revert, no problem. Here's the wiki policy: 'The BOLD, revert, discuss cycle (BRD) is a proactive method for reaching consensus on any wiki with revision control. It can be useful for identifying objections to edits, breaking deadlocks, keeping discussion moving forward. Note that this process must be used with care and diplomacy; some editors will see it as a challenge, so be considerate and patient. This method can be particularly useful when other dispute resolution for a particular wiki is not present, or has currently failed.'

Here's the edit:

In electromagnetism and electronics, inductance is that property of a circuit by which a change in current in the circuit 'induces' (creates) a voltage (electromotive force) in both the circuit itself (self-inductance)^[1][2][3] and any nearby circuits (mutual inductance)^[4][5]. This effect derives from two fundamental observations of physics: First, that a steady current creates a steady magnetic field (Oersted's Law)^[6] ; second, that a time-varying magnetic field induces voltage in a nearby conductor (Faraday's law of induction)^[7]. From Lenz's law^[8], in an electric circuit, a changing electric current through a circuit that has inductance induces a proportional voltage which opposes the change in current (self inductance).

1. ^Sears and Zemansky 1964:743
2. ^http://dictionary.reference.com/browse/Inductance?s=t
3. ^Collins Gem Encyclopedia
4. ^Sears and Zemansky 1964:743
5. ^Collins Gem Encyclopedia
6. ^Sears and Zemansksy 1964:671
7. ^ Sears and Zemansky 1964:671 -- 'The work of Oersted thus demonstrated that magnetic effects could be produced by moving electric charges, and that of Faraday and Henry that currents could be produced by moving magnets.'
8. ^Sears and Zemansky 1964:731 -- 'The direction of an induced current is such as to oppose the cause producing it'.

I've been watching this page, mulling over what you're trying to do. My sympathies. What I offered in the edit was good sourcing with decent quotes (your sources in the lead so far are lousy) and a perspective derived from Sears and Zemansky. I created a new page re Oersted's Law as a consequence, plus I added the Sears and Zemansky source. Really, the whole business is straightforward, and based on two observations of magnets, compass needles and electricity in wires that occurred back in the early-mid 1800's:

Observation #1 [Oersted]: Electric currents (symbolized by i) in a wire effect magnetized needles (e.g. a compass). This “force”, call it B, that is created by the electric current is indistinguishable from that of a bar-magnet. Experiments demonstrate that in tightly-controlled [time-invariant] geometries:

Steady magnetic [force]-field B ∝ i, the force (field) B is proportional to the current i.

Observation #2[Faraday]: Changing magnetic fields with respect to time (ΔB/Δt) 'induce' electrons to move as if they are driven by a voltage.

V ∝ ΔB/Δt

Plug the first formula for the (steady) field B into the first formula for 'induction' we obtain:

V ∝ Δi/Δt.

In words: if a loop of wire has a changing electric current (Δi/Δt) in it a voltage V is 'induced' in the loop wire. To change the proportionality to an equation we introduce the constant L, called 'inductance':

V = L*di/dt

In the simplest geometry of a current-carrying coil of wire that's all there is to. But when mutual inductance of nearby coils of wire, and time-varying geometries (motors) are included the formulas become complicated. I agree that Lenz's law should be included in the lead.

The above was my best shot after a week's mulling, so I don't have anything more to add to the discussion. I'm just going to leave my opinion here like this, and let you folks soldier on. Bill Wvbailey (talk) 16:27, 8 May 2012 (UTC)

OK, my observations are with your Observation 1. While it is accurate in what it says. It is not really a property of the phenomenom of inductance. I grant that a wire or coil of wire will deflect a compass needle due to magnetism. But this effect has no infuence or outcome on a DC circuit (which the steady state current implies). The phenomenon of inductance is limited to what happens when you try to change the current flowing through it. Your observation 2 covers that correctly. The two observations together are fine for the derivation of the formula to establish V given L and di/dt. Great in the main part of the article, but I do not believe that it belongs in the introduction. 86.167.20.121 (talk) 16:49, 8 May 2012 (UTC)

Just as I thought we got it nailed! I'm not so sure about what you said. Faraday's law of induction followed on from Oesterd's law, so there is an argument for a logical progression of ideas. I'll ponder this over night. DieSwartzPunkt (talk) 16:57, 8 May 2012 (UTC)

That is what Wtshymanski was trying to get across to you. Inductance can be defined as the ratio of the magnetic flux through a circuit to the current

${\displaystyle L=\frac{\varphi }{I}}$

This is true for steady as well as time varying currents. Faraday's law says the induced voltage (EMF) is the time derivative of the flux

${\displaystyle \mathcal{E}=\frac{d\varphi }{dt}}$

So the relation between current change and induced EMF can be derived

${\displaystyle \mathcal{E}=\frac{d(LI)}{dt}=L\frac{dI}{dt}}$

A number of texts define it that way Pelcovits p.646, Wadhwa p.18, Serway p.898, Singh p.65, Glisson p.302 --Chetvorno^TALK 20:37, 8 May 2012 (UTC)

Be careful here. It isn't ${\displaystyle \mathcal{E}=\frac{d(LI)}{dt}=L\frac{dI}{dt}}$, but ${\displaystyle \mathcal{E}=\frac{d(LI)}{dt}=L\frac{dI}{dt}+I\frac{dL}{dt}}$. There are solenoid problems where the latter term is significant. Also, consider a DC circuit if you change the geometry after building the circuit. Does E or I change? Only if you can be sure that L doesn't change can you ignore that term. Gah4 (talk) 21:24, 11 March 2014 (UTC)

Well, I'm not going to argue over one sentence. I shall therefore restore Mr Bailey's contribution. as there seems to be some concensus toward it (Ignoring Wtshymanski's restoration of hi nonsensical out of context contribution, that says what he wants it to say and not what anyone else wants. 86.167.20.121 (talk) 11:48, 9 May 2012 (UTC)

Chetvorno is correct. I have another source to add to his list as well as the Sears and Zemansky references above (e.g. Sears and Zemanski p. 741 for mutual inductance M₂₁ =def N₂Φ₂₁/i₁ ) and page 743 for self-inductance L =def NΦ/i). Both sources derive Ldi/dt using the two equations.

The discussion, definition and derivation appears on pages 8-9 of:

Fitzgerald, Kingsly Jr, Kusko 1971 Electric Machinery: The Processes, Devices, and Systems of Electromechanical Energy Conversion', Mc-Graw Hill Book Company NY, LCCCN 70-137126.

In all cases, the books define the notion of 'inductance' in terms of flux or 'flux linkages'. The problem is: what is 'flux' and/or a 'flux linkage'? These notions are not trivial, and they introduce more questions than can be answered easily in a sentence or two. What can be derived from these 'treatments' is that the formulas for inductance, in particular aircore transformers, is purely 'geometrical' (cf usage in F-K-K p.9) and requires only an added proportionality constant (permeability of free space for air core transformers and a 'core constant' for ferromagnetic materials if present: cf discussion in Sears and Zemanski p. 743: 'The self-inductance of a circuit depends on its size, shape, number of turns, etc.'). BillWvbailey (talk) 22:27, 8 May 2012 (UTC)

I was hoping a vague reference to a 'magnetic field' would suffice in the lead, where this notion could be nailed down later on - 'sometimes a little imprecision saves a ton of explanation'. --Wtshymanski (talk) 01:32, 9 May 2012 (UTC)

I still think the definition in terms of rate of change of current would be easier on newbies, but this definition does bring in magnetism, and gives a more inclusive view of inductance, showing it is important in DC circuits as well. Guess it grew on me. Maybe if this is to be the definition, we should use the correct term magnetic flux as you suggested, and the defining equation ${\displaystyle L=\varphi /I}$ up front? What do you think? --Chetvorno^TALK 02:35, 9 May 2012 (UTC)

I still don't see where this effect of inductance in a DC circuit comes from. As has been discussed exhaustively above, the magnitude of the inductance has no effect at all on a steady state DC circuit. You can have 0.1 Henry; 1 Henry or 10 Henries, the current in the circuit is determined solely by the resistance in the circuit. I grant that the inductance will produce a steady state magnetic flux, but unless you really are trying to shift some scrap iron, so what? 86.167.20.121 (talk) 11:57, 9 May 2012 (UTC)

Stored energy is one effect - a steady current of I amperes thorugh an inductance of L henries will store 1/2 I^2 *L joules in the magnetic field. And, a steady current of I amperes in an inductance of L henries will link I*L webers of flux (but that's really the same effect). And if you try to *change* the current..but I don't have to sell you on that one. Ever watched a contactor open on a scrap handling magnet? It makes a big fat arc if the snubber network has failed due to the stored energy in the magnetic field of the (DC) coil. Consider the issues with DC on capacitors. After all, they won't pass any DC current so there's no such thing as DC capacitance, if you define capacitance solely as the proportionality constant between a changing voltage and a changing current. --Wtshymanski (talk) 13:19, 9 May 2012 (UTC)

Which part of 'steady state'are you too stupid to do you not understand? 86.167.20.121 (talk) 13:49, 9 May 2012 (UTC)

┌─────────────────────────┘ The part I don't understand and that none of my esteemed, respected, and evidently knowledgable co-editors have seen fit to impart to me is 'What is the property that describes the proportionality between the magnitude of the magnetic flux produced by a current and the magnitude of that current, in the case of a steady current, which in the AC case we call 'inductance'?' We're all agreed that putting AC on a loop of wire induces a changing magnetic field, produces a counter-EMF, etc.; What I have been saying, with at least one citation, is that this property is also still there even if the current isn't changing. Even with direct current, inductance stores energy and creates fields - rather like putting DC on a capacitor. --Wtshymanski (talk) 14:44, 9 May 2012 (UTC)

How many more times? The man defined inductor is there - it just doesn't do anything apart from create a mostly useless steady magnetic field. The God given phenomenon of induced e.m.f. due to changing current is not present. And, several of your co-editors have been pointing this out you for over a week. As usual, you are just trying to complicate the issue to disguise your lack of understanding or to leverage your unwanted point. 86.167.20.121 (talk) 14:54, 9 May 2012 (UTC)

86.167.20.121, take a look at the references I gave above. It's an alternative way of defining inductance. And let's try to discuss this without ad hominem attacks. --Chetvorno^TALK 16:19, 9 May 2012 (UTC)

Let me see if I can express how I understand it in words: All the same properties of a circuit which increase the magnetic field through it when a steady state current is applied (winding the wire into a coil, adding an iron core) also increase the back-EMF when a changing current is applied. They really refer to the same quality in the circuit and should be called by the same name. Any strong electromagnet is also a good inductor (although inductors and electromagnets are constructed differently) Why is that? It is because Faraday's law is linear. Therefore the same proportionality constant that relates the magnetic flux to the current, also relates the induced EMF to the change of current. It is called inductance. --Chetvorno^TALK 17:01, 9 May 2012 (UTC)

It is not the definition found in most mainstream references which is what we should stick with. The phonomemon of inductance (which is what the article lead should be nailing) at its most fundamental is based on the effect of a changing current. This is what it currently states, backed up by no less than three references. This side discussion is really nothing more than yet another distraction. Mr Bailey contributed the current lead. I am in full agreement with it. 86.167.20.121 likes it (bar one point - which he has accepted). There, I think it should remain.

Of, course, there is no problem with this sort of information being included elsewhere in the article (backed by references). Could it be more appropriate in Inductor though? DieSwartzPunkt (talk) 07:07, 10 May 2012 (UTC)

I gave 5 references that use it above. Here's some more: Sagar p.124, Ida p.558, Misra p.357. It is obviously a mainstream definition. Whether it's the best one to use in this article, I'm undecided. I think these texts introduce inductance with the flux equation rather than the EMF equation to emphasize the same point which has been so difficult to get across here: that inductance is a geometric property of the circuit which has applications beyond AC circuits. --Chetvorno^TALK 10:23, 10 May 2012 (UTC)

It's also worth bearing in mind that the S.I. definition of the Henry as a unit of inductance is solely the one where one volt is induced with a current change of 1 Amp/second (i.e. describes a specific effect of current change). But, as I say, there is no reason at all why this information shouldn't be in this article or the Inductor article somewhere. I don't believe that it belongs in the lead, because the 'definition' does not refer to any effect when the current changes, and it is not the one used by the S.I. definition of Henry. DieSwartzPunkt (talk) 15:11, 10 May 2012 (UTC)

Magnetic field B is called magnetic induction B

I've experienced a 'sea change' with respect to the proposed wording. Chetvorno's suggestion that we use the flux definition is the correct way of doing this. Here's where I think the confusion has come from (including mine):

I happened to glance at a drawing in Sears and Zemansky, and I noticed the words “line of induction' applied to the 'B-field' around a wire. Now B in this drawing derives from utterly steady-state (DC) current (it's the relativistic derivation from moving charges). I explored backward into the book and discovered that the word 'induction' occurs in three different ways even though the index lists only #1 and #2 below. The confusion arises because 'magnetic inductance' L also appears in the formula #3

1. Electrostatic induction: put two neutral metal spheres together so they touch. Bring a [electrostatically] charged rod up to one of them, and at the same time separate the two spheres. Each is now charged, one “plus” and one “minus” (p. 533-535).
2. Magnetic induction: B-field is the “magnetic induction”, B = Φ/A (see quotes below)
3. EMF induction: V = -N*dΦ/dt; L =_DEF NΦ/i so NΦ = Li; differentiate both sides: V= -L*di/dt (p. 729)

Sears and Zemansky refers to the “B-field” aka “flux density” as: the “magnetic induction B ”, measning that a DC current in a wire induces a DC magnetic field B. This usage appears very early in the discussion of static magnetic fields (p. 674)

'It follows . . . that the magnetic induction B set up by a long straight wire, at a distance r from the wire, is

B = 2*(k/c^2)*I/r [I is current, r is radius from the wire, k is a constant from electrostatics, c is the speed of light].

In an adjacent drawing they show: “The force on a charge q moving with velocity v in a magnetic field of induction B is F’’’ = q(v x B). (p. 675)

On page 678 is the sub-chapter 30-4 Lines of induction. Magnetic flux. Here they state:

“A magnetic field can be represented by lines called lines of induction, whose direction at every point is that of the magnetic induction vector.

They go on to state and prove:

'The mksc unit of magnetic induction B is 1 n/amp-m, and hence the unit of magnetic flux in this sytem is 1 n-m/amp [Φ = BA]

“ . . . the magnetic induction equals the flux per unit area, across an area at right angles to the magnetic field . . . The magnetic induction B is often referred to as the flux density. . . . The total flux across a surface can then be pictured as the number of lines of induction crossing the surface, and the induction (the flux density) as the number of lines per unit area.” (p. 678)

So yes, the definition is L =_DEF NΦ/i. This plus the fact that “the magnetic induction' [B] equals the flux per unit area [Φ/A]” or Φ = B*A we have (l is the magnetic path length):

L = N*(B*A)/i

For a coil, for instance, is B = u₀*N*i/l

L = N²*(u₀*A/l)

And this agrees with the 'geometrical form' of inductance (formula 1-15) in Fitzgeral-Kingsly-Kusko:9.

Notice that there is no mention or use whatever of AC or varying fields in this derivation for L. the reason is, is because L is defined around the notion of 'induction of a magnetic field B by a [any sort of] current i', not the notion of 'induction of a voltage (EMF) by a changing current i'.

RE Chetvorno's proposal to use the flux-linkage definition for inductance: the notions of 'flux linkage' and 'flux leakage' and 'lines of induction' really do simplify the notion of mutual inductance in magnetically-coupled devices. “Lines of induction” is “visual”, it can be illustrated for an air-core coil of N turns and current i that some of the flux generated by turns in the middle do not link with turns at the ends. So if you increase the linkage of the flux with the turns that created them, you get more magnetic induction (aka greater inductance L i.e. stronger B-field), and you do this with a shorter coil wound in layers (same N, same i, stronger B, greater inductance L).

As for #3 above, 'electrical induction', it just turns out that V_induced = L*di/dt. Historically I wonder, though, how this definition of L came about: was it from DC considerations alone, or working backwards from electrical induction?

Maybe someone else has a take on this? Bill Wvbailey (talk) 22:15, 10 May 2012 (UTC)

Good points. Yeah, I like that it emphasizes that inductance doesn't just 'appear' in a circuit when time-varying currents are applied. I didn't actually propose using the flux definition, that was Wtshymanski. Another point in its favor is that it is a dual of the definition of capacitance, C = q/V which also doesn't use time-varying quantities. On the other hand, DieSwartzPunkt raised an important objection that the unit of inductance, the henry is defined using the EMF definition. --Chetvorno^TALK 01:19, 11 May 2012 (UTC)

Well, one volt per amp per second is one volt-second per amp, and a volt-second is a weber, and a weber per amp is a henry, so it all works out. It's easier to measure volts and amps and seconds than to directly measure webers, so the definition works with what's realizable. --Wtshymanski (talk) 01:29, 11 May 2012 (UTC)

I thought you all may be interested that I managed to stumble across, the text book that I used to use for first year electrical engineering students.

Chapter 1, covers magnets and magnetism (no surprise there). By chapter 3 we are onto electromagnetism. It discusses Oersted's law (which now belatedly has its own article). It discusses electromagnets. Among many other things, it discusses how to calculate the magnetic properties knowing various parameters. It even talks about the B/H curve of various core materials. The essential point is that it doesn't once mention inductance or inductor.

Chapter 4 moves onto magnetic induction. It introduces Faraday's Law of Induction. (Incidentally, a very good friend of mine is Michael Faraday's great great great great great great grandson, give or take a great.) It discusses the effect a moving permanent magnet has on a coil of wire (with some calculation thrown in). Once again, the words inductance or inductor do not appear anywhere.

Chapters 5, 6 & 7 moves onto DC circuits. Ohm's law naturally. Kirchoff's laws etc. But no reference to inductance or inductor.

Chapter 8 and we are onto AC circuits. Inductance is introduced for the very first time. And I rather like the explanation given.

'Inductance, or the self induction of a coil, can best be understood by considering Faraday's experiments on induced electromotive force (page <in chapter 4>), but instead of using a permanent magnet, a coil is supplied with a varying current. This has the effect of producing within itself a magnetic field which not only cuts across the turns of the coil, but rises and falls with the current, and consequently generates an E.M.F. in the coil.

'the generated E.M.F., according to Lenz's law, is opposed to the E.M.F. which causes the current to flow through the coil.'

Mutual inductance is discussed in a later chapter. My point here is that although it is possible to discuss inductance in terms of the magnetic properties produced in response to a steady (D.C.) current, few people in fact do so, and it certainly isn't taught that way. What's good for first year students is good for this article. DieSwartzPunkt (talk) 15:00, 11 May 2012 (UTC)

All unit systems have four fundamental units. In the SI system of units, these are, length, mass, time and electric current. The magnitude of each unit is defined around (ideally) invariable physical constants.

All other units are derived units, that is that they are defined in terms of the fundamental units where possible, or failing that, in terms of fundamental and derived units (with as few derived as possible). In the case of the unit of inductance (Henry), it is defined as that inductance that produces an e.m.f. of exactly one volt when the current flowing through it changes at exactly one ampere per second. There is only ever one definition in the S.I. system (or indeed any unit system). DieSwartzPunkt (talk) 15:39, 11 May 2012 (UTC)

I should have pointed out that any definition of Henry based on magnetic fields produced would be unacceptable. This is because the unit of magnetic flux, the Weber, is not defined solely in terms of fundamental and units derived from those fundamental units, but also in terms of the first temporal derivative of itself (a recursive definition). DieSwartzPunkt (talk) 16:58, 11 May 2012 (UTC)

---

But we want the lead to be accurate and true and not pander to bad teaching. We have to continue to dig deep until we get to the nut of it: Here's the nut from the quote below, elegant in its simplicity: 'Any inductor has a characteristic known as inductance whereby it sets up an electro-magnetic field when a current is passed through it.' The fact is this: inductance has to do with Oersted's Law first and foremost, but it comes to the fore when the current is varying.

My oldest reference is the Radiotron Designers Handbook (4th edition 1952, 1st edition 1934). One of their references goes back to 1912 (Bureau of Standards Scientific paper No. 169 (1912)). Here's how Radiotron defines 'inductance' and 'inductor':

'An inductor, in its simplest form, consists of a coil of wire with an air core as commonly used in r-f tuning circuits. Any inductor has a characteristic known as inductance whereby it sets up an electro-magnetic field when a current is passed through it. When the current is varied, the strength of the field varies; as a result, an electromotive force is induced in the coil. This may be expressed by the equation [e = -Ndφ/dt] . . . the direction of the induced e.m.f. is always such as to oppose the change of current which is producing the induced voltage. In other words, the effect of the induced e.m.f. is to assist in maintaining constant both current and field [interesting!]. We may also express the relationship in the form: e = -Ldi/dt.' (p. 140-141).

'When two coils are placed near to one another, there tends to be coupling between them, which reaches a maximum when they are placed co-axially and with their centers as close together as possible.

'If one such coil is supplied with varying current, it will set up a varying magnetic field, which in turn will induce an e.m.f. in the second coil. This induced e.m.f. is proportional to the rate of current change in the first coil (primary) and to the mutual inductance of the two coils: [e₂ = -Mdi₁/dt, etc].' (p. 145)

So there we go, the beginnings of a succinct lead-paragraph. With some word-smithing we could have something like this:

Inductance is a characteristic of any inductor, in its simplest form a coil of wire with an air core, whereby it sets up a magnetic field¹ when a current is passed through it (Oersted's law). When the current is varied, the strength of the field varies; as a result, an electromotive force is induced in the coil Faraday's law of induction. The direction of the induced e.m.f. is always such as to oppose the change of current which is producing the induced voltage Lenz's law; the effect of the induced e.m.f. being to assist in maintaining constant both current and field.

¹ More accurately a 'magnetic induction field' more commonly called the 'B'-field or magnetic-flux field, cf usage in Sears and Zemanski 1964:675.

Then we'd have to introduce mutual inductance as flux linkages perhaps, or maybe the 'coupling of magnetic fields between them'.

Actually, 'flux coupling' or 'field coupling' is the way I've always thought of 'inductance', especially after I had to design a 20KV air core transformer with a specified amount of primary leakage inductance to create a primary resonant circuit at about 3 Mhz, but at the same time maintain a coupling coefficient of about 0.6 etc etc (used for igniting plasma torches). Mutual induction is really hard. BillWvbailey (talk) 16:04, 11 May 2012 (UTC)

<Reaches into toolbox; grabs spanner and casually tosses it into the works> The problem with that definition is that it is too specific. It says, An inductor, in its simplest form, consists of a coil of wire ..'. Sorry to be picky, but that is not correct. In its simplest form, it is a perfectly straight conductor. Even this exhibits inductance (maybe not much, but enough to have an effect as the frequency rises). Open up a UHF TV tuner. It's full of inductors, but not a 'coil of wire' will be found anywhere. A definition has to vague enough to catch all instances where inductance exists. So how about (substituting 'circuit' for 'coil'):

Inductance is a characteristic of any circuit, whereby it sets up a magnetic field¹ when a current is passed through it (Oersted's law). When the current is varied, the strength of the field varies; as a result, an electromotive force is induced in the circuit (Faraday's law of induction). The direction of the induced e.m.f. is always such as to oppose the change of current which is producing the induced voltage Lenz's law; the effect of the induced e.m.f. being to assist in maintaining constant both current and field.

But this is pretty much what the intro says already. DieSwartzPunkt (talk) 16:58, 11 May 2012 (UTC)

And we end up with the point I've been making all along. 86.169.33.6 (talk) 17:07, 11 May 2012 (UTC)

---

[Kind of funny, but I was unaware that my reverted lead was reinserted when I proposed the above paraagraph]. I agree that the new paragraph seems like the existing version, but the first and last sentences are significantly different and it's more succinct. Anyway, I like your first sentence, it's fine, it is more general and still correct (methinks). Here's another crack at it to insert the ideas of self-inductance and mutual inductance:

In electromagnetism and electronics, Inductance is a characteristic of any circuit, whereby it sets up a magnetic field¹ when a current is passed through it (Oersted's law). When the current is varied, the strength of the field varies; as a result, an electromotive force (e.m.f.) is induced (per Faraday's law of induction) in the circuit itself (self-inductance) and any nearby circuits (mutual inductance). The direction of the induced e.m.f. is always such as to oppose the change of current which is producing the induced voltage Lenz's law, the effect of the induced e.m.f. being to assist in maintaining constant both current and field.

With respect self- and mutual inductance and the henry, Sears and Zemansky explain (sort of) why both self- and mutual inductance seem to have two definitions:

'An emf is induced in a stationary circuit whenever the magnetic flux through the circuit varies with time. If the variation in flux is brought about by a varying current in a second circuit, it is convenient to express the induced emf in terms of the varying current, rather than in terms of the varying flux.

They define the flux-linkage version of mutual inductance as M₂₁ = N²Φ₂₁/i₁ (formula 33-14 p. 741) and the flux-linkage version of self-inductance as L = NΦ/i (formula 33-16 p. 743).

But . . .

'If the current i₁ varies with time . . . the mutual inductance can be considered as the induced emf in coil 2, per unit rate of change of current in coil 1 . . . The mksc unit of mutual inductance is 1 volt/(amp/sec). This is called 1 henry, in honor of Joseph Henry.' (p. 742)

And . . .

'Hence any circuit in which there is a varying current has induced in it an emf, because of the variation in its own magnetic field. Such an emf is called a self-induced electromotive force. . . The self-inducatance of a circuit is therefore the self-induced emf per unity rate of change of current. The mksc unit of self-inductance is 1 henry.' (p. 743).

And . . .

In the 'Problem' section they ask for the student to show that the expressions for self-indutance NΦ/i and V/(di/dt) have the same units, and 'show tht 1 weber per second equals 1 volt'.

So I think the lead paragraph as written above is correct, but there's still the subtle issues of mutual and self-inductance having the unit of the henry. Again I wish I knew more about the history (and word usage) of these notions and formulas. Bill Wvbailey (talk) 14:44, 12 May 2012 (UTC)

Grover Inductance Calculations Pdf To Word Converter

Good, we are getting somewhere. I agree that the pesky but important concept of mutual inductance gets the briefest of mentions at present. The version that current one replaced had this sentence after the point about self inductance, 'The varying field in this circuit may also induce an e.m.f. in a neighbouring circuit (mutual inductance).[ref]'. There is a section on mutual inductance in the main body of the article (called 'Coupled inductors') which seems fairly comprehensive, but can always be improved. DieSwartzPunkt (talk) 16:25, 12 May 2012 (UTC)

Also keep in mind addressing that it sort of has two meanings..the phenomena, and the measure of that phenomena. North8000 (talk) 22:00, 25 May 2012 (UTC)

Capitalization of variables

I'm wondering why in the math electric current is symbolized by a lowercase i, while voltage is an uppercase V? The equations apply to time-varying currents and voltages, which are usually designated by lowercase variables. Shouldn't V be lower case? --Chetvorno^TALK 22:08, 30 January 2014 (UTC)

Changed it. To be totally consistent the time-varying flux Φ(t) should also be changed to lower case φ, but I don't see that as a biggie. --Chetvorno^TALK 23:24, 11 March 2014 (UTC)

Mutual inductance redirect

Previously it directed to the #Mutual inductance heading under “Calculation techniques”. In the current article, mutual inductance actually seems to be better introduced and covered in more breadth beforehand, under #Coupled inductors, so I am targetting the relevant redirects there. Vadmium (talk, contribs) 00:51, 4 February 2012 (UTC).

Can we maybe get a link to Big_O_notation too. It took me a while to figure out what that was. I'm not sure where the best place for it is though. The first time it appears is in the 'Self-inductance of a wire loop' section. — Preceding unsigned comment added by 130.183.100.96 (talk) 15:19, 23 May 2014 (UTC)

• 2Definition

Unitism[edit]

The first section mentions SI units, and that H is the SI unit of inductance. Much of the rest of the article assumes SI units, unnecessarily. While SI units are popular, should the article assume that the reader uses SI units? Specifically, the SI value of μ₀ is often mentioned. Gah4 (talk) 16:54, 12 March 2016 (UTC)

What about the units in the formulae? The equation for the inductance of a loop of wire contains a radius term but no units are specified. Am I to assume SI? Wouldn't it be helpful to remove all doubt and state clearly what units apply?RDXelectric (talk) 03:16, 4 November 2016 (UTC)

In CGS units, μ₀ is 4π/c² and inductance is in s²/cm. Gah4 (talk) 06:40, 4 November 2016 (UTC)

The formula given for the inductance of a single-layer solenoid is not correct. It also contains infinite series formulae, which do not show how many terms are needed to achieve a given accuracy.

Shown below is a formula that has a closed mathematical form, and has been proved to be accurate.

The correct formula for a single layer solenoid is given in Grover (Inductance Calculations Frederick W. Grover 1946). Grover collected the formula, and proved its accuracy by careful and accurate measurements.The formula given by Grover is L(μH)=0.002 * π^2 * N^2 * (a/Ratio)* K + G + HIn this formula N is the number of full turns, a is the mean winding radius (centre of coil to half wire diameter) in cm.Ratio is the ratio b/2a, where b is coil length in cm.K is the Nagaoka constant (which is a function of b/2a)G is the Rosa correction for self-inductance.H is the Rosa correction for mutual inductance.K and H are defined by infinite series. K is very difficult to calculate because it has alternating positive and negative terms that are only slightly different each time. Grover solved these problems for the reader by giving tabulated values for K and H, which need then to be interpolated.David W. Knight (G3 YNH) has produced closed formulae that match K, as a function b/2a, and H, as a function of N, accurate to around 1 ppm.The formulae have been shown to give the same values as the tabulations in Grover.The David W Knight formula for K is given here:For b>2a, K = (1+0.383901/ratio^2+0.017108/ratio^4)/(1+0.258952/ratio^2)-(4/(3*PI()*ratio))For b≥2a, K = (2/PI())*ratio*(((LN(4/ratio)-0.5)*(1+0.383901*ratio^2+0.017108*ratio^4))/(1+0.258952*ratio^2)+0.093842*ratio^2+0.002029*ratio^4-0.000801*ratio^6)G = 1.25-LN(2/Ratio2) where Ratio2 = wire diameter/pitch, and pitch = b/N (turns per unit distance)The David W. Knight formula for H is given here:H = LN(2*PI())-1.5-LN(N)/(6*N)-0.33084236/N-1/(120*N^2)+1/(504*N^5)-0.0011923/N^7+0.0005068/N^9 — Preceding unsigned comment added by BrianAnalogue (talk • contribs) 19:29, 3 December 2017 (UTC)

The formula given for the inductance of a single-layer solenoid is not correct. It also contains infinite series formulae, which do not show how many terms are needed to achieve a given accuracy.

Shown below is a formula that has a closed mathematical form, and has been proved to be accurate.

The correct formula for a single layer solenoid is given in Grover (Inductance Calculations Frederick W. Grover 1946). Grover collected the formula, and proved its accuracy by careful and accurate measurements.The formula given by Grover is L(μH)=0.002 * π^2 * N^2 * (a/Ratio)* K + G + HIn this formula N is the number of full turns, a is the mean winding radius (centre of coil to half wire diameter) in cm.Ratio is the ratio b/2a, where b is coil length in cm.K is the Nagaoka constant (which is a function of b/2a)G is the Rosa correction for self-inductance.H is the Rosa correction for mutual inductance.K and H are defined by infinite series. K is very difficult to calculate because it has alternating positive and negative terms that are only slightly different each time. Grover solved these problems for the reader by giving tabulated values for K and H, which need then to be interpolated.David W. Knight (G3 YNH) has produced closed formulae that match K, as a function b/2a, and H, as a function of N, accurate to around 1 ppm.The formulae have been shown to give the same values as the tabulations in Grover.The David W Knight formula for K is given here:For b>2a, K = (1+0.383901/ratio^2+0.017108/ratio^4)/(1+0.258952/ratio^2)-(4/(3*PI()*ratio))For b≥2a, K = (2/PI())*ratio*(((LN(4/ratio)-0.5)*(1+0.383901*ratio^2+0.017108*ratio^4))/(1+0.258952*ratio^2)+0.093842*ratio^2+0.002029*ratio^4-0.000801*ratio^6)G = 1.25-LN(2/Ratio2) where Ratio2 = wire diameter/pitch, and pitch = b/N (turns per unit distance)The David W. Knight formula for H is given here:H = LN(2*PI())-1.5-LN(N)/(6*N)-0.33084236/N-1/(120*N^2)+1/(504*N^5)-0.0011923/N^7+0.0005068/N^9 — Preceding unsigned comment added by BrianAnalogue (talk • contribs) 19:32, 3 December 2017 (UTC)

About approximations. The expression in terms of elliptic functions is exact, and the first terms of the expansions in two limiting cases are given to show how the induction of a solenoid changes or diverges in the limiting cases. For instance, what is the connection with the inductance of a ring? How large is the error of the standard formula when the solenoid is not long? Numeric approximations are practically useful, but don't explain anything in the first place (some kind of interpolation).They rather belong into computer programs and online calculation tools.--radical_in_all_things (talk) 18:40, 4 December 2017 (UTC)

All these are approximations, as they depend on the distribution of current in the conductors. If you make the conductors infinitely small, the current density and inductance go to infinity. Skin effect puts the current close to the surface, which is usually close enough. Gah4 (talk) 19:09, 8 March 2019 (UTC)

Definition[edit]

Now that the sock puppets have been suppressed, can we fix the definition here? Seems needlessly roundabout. --Wtshymanski (talk) 01:13, 9 December 2017 (UTC)

The opening sentence of the lead, I presume you mean. It's exactly true. electromotive force is rather obscure (though of course I'm pretending) I have to go look it up. I might suppose from that quip, that I needn't be too concerned about that electromotive force: it's a voltage, and of course electricity always has a voltage, yahde, yahde, yahde.. it won't affect my current much, so I can move on. Yeh? Sbalfour (talk) 17:53, 11 December 2017 (UTC)

I'm going to take a crack at it. Only I'm going to bite big, and write my own introduction. Sbalfour (talk) 20:17, 11 December 2017 (UTC)

Inductance [lead][edit]

Inductance is a property of an electrical conductor which opposes a change in current. It does that by storing and releasing energy from a magnetic field surrounding the conductor when current flows, according to Faraday's law of induction. When current rises, energy (as magnetic flux) is stored in the field, reducing the current and causing a drop in potential (i.e, a voltage) across the conductor; when current falls, energy is released from the field supplying current and causing a rise in potential across the conductor.

The inductance of a conductor is a function of its geometry. A straight narrow wire has some inductance; a conductor which is configured such that sections of its magnetic field overlap (for example a coil) may have more or less inductance than a straight wire. The inductance of a conductor may be greatly increased by its adjacency to a magnetic material like iron. In this case, a magnetic field is induced in the iron, and it also stores and releases energy in response to change in current, so that the opposition to change in current from the combined geometry is much greater than that of the conductor alone.

A conductor with a fluctuating current adjacent to another conductor (or another portion of itself) will induce, via its incident magnetic field, a fluctuating current in the other conductor or portion of itself; the effect is reciprocal, and is called mutual inductance. Mutual inductance is the basis of operation of a transformer. To distinguish this from the inciting inductance, the inciting inductance is referred to as self-inductance.

Inductance is one of three fundamental properties (along with resistance and capacitance) of electric conductors and components. The circuit component intended to add inductance to a circuit is called an inductor. It is usually a coil of insulated wire, and may have a core of iron or other magnetic material. Inductors are also called electromagnets when their magnetic properties are of more concern than their electrical ones. Inductance in circuit analysis is usually represented by a related quantity called inductive reactance which is part of the impedance of the circuit. For AC circuits, inductive reactance is a nearly linear function of frequency, though at high frequencies like RF, nonlinear effects dominate.

Inductance has a variety of functions and effects in electric circuits including filtering, energy storage and current regulation. It may be a favorable or unfavorable property: electric generators and motors depend on it for their operation; but in electric transmission lines, it reduces capacity.

Inductance is measured in units of Henrys, named for Joseph Henry who independently with Michael Faraday discovered inductance in the 1830's; its symbol is customarily designated ${\displaystyle L}$ in honor of physicist Heinrich Lenz.

Sbalfour (talk) 03:24, 12 December 2017 (UTC)

Notes[edit]

• In the Circuit analysis section, it says: This design [coil of wire] delivers two desired properties, a concentration of the magnetic field into a small physical space and a linking of the magnetic field into the circuit multiple times. Hmmmmm.. ever taken a look into the power substation down at the corner? It'd take a crane to move the coils in some of those transformers. That's not exactly small. Then there's the inference that if not for this design, then some other viable design - not a coil? - would be bigger still. A magnetic field doesn't concentrate in a small space; any magnetic field is a smooth gradient that extends through all of space-time. grumble, grumble.. now linking the magnetic field into the circuit.. this is just vacuous?! There's a magnetic circuit and an electric circuit in an inductor, and their relationship is quite well defined. I'm just not sure what's being referred to here; is something being said that's not already said? Sbalfour (talk) 21:41, 11 December 2017 (UTC)

I think what this sentence is trying to express (and doing it badly) is why coils of wire are used for inductors. Your utility transformer would be much larger if the wire winding was uncoiled straight, but it would have lower inductance. The reason a coil of wire has a higher inductance than a straight wire is because the magnetic field lines link the circuit multiple times; it has multiple flux linkages. A 5-turn coil of wire has approximately 5 times the inductance, and with the same current produces a 5 times stronger magnetic field, than a single turn, because each magnetic field line passes through the circuit 5 times. --Chetvorno^TALK 22:57, 11 December 2017 (UTC)

Fun with inductors. If you have five separate inductors, with no mutual coupling, in series then the inductance is five times. But for a five turn coil, the inductance is 25 times the single turn coil, as the field from each turn goes through all five of them. Note the N² in the formula. (Assumes 100% coupling.) Gah4 (talk) 19:19, 26 December 2017 (UTC)

Oops. You're right, thanks for catching my screwup! Happy New Year, Gah4 ----Chetvorno^TALK 20:41, 26 December 2017 (UTC)

I know you know your stuff, and I think maybe the previous editor didn't. We talk tech, or we talk to the common folk, and we need to be careful about mixing and matching. Sbalfour (talk) 23:16, 11 December 2017 (UTC)

I'm on board with trying to make tech articles more understandable to general readers. I've spent most of my last few years on Wikipedia rewriting articles to try to do that (don't know how successful I've been). I don't think math should be eliminated, but a lot of WP technical articles get edited by highly educated people to the point where they're incomprehensible, just abstract gibberish. Glad to meet another editor who thinks this is important. --Chetvorno^TALK 00:43, 12 December 2017 (UTC)

• Inductance has some notional aspects that just aren't here. As a child, I made an inductor for a toy motor with a fat steel nail and a vaguely egg-shaped rat's nest of wire wound around it. It wasn't good enough. My father showed me by example and instruction, how to make a good one, because he knew something about how magnetic coupling works. Now I do, too. I could take that rat's nest of wire and read down the article to figure out what needs to be done. No, we aren't a lab manual. But to improve the child's model, one needs to understand first. If all I knew was what I read here, I'd have to figure the child's model is what you get. I wouldn't know whether it should be a different shape, and if so, what. Sbalfour (talk) 22:16, 11 December 2017 (UTC)

• There's a paragraph on applications in the middle of the Circuit analysis section, incongruous, and interrupts the flow. Sbalfour (talk) 22:44, 11 December 2017 (UTC)

• The section uses self-inductance without defining it; the lead sort of describes it- that's supposed to be a summary of the text, so where is the actual definition it summarizes?

• The Circuit analysis section jumps from nothing to the calculus; this is more like the definition of inductance. Circuit analysis is like looking at a schematic, with voltages and currents, and etc. Considering the next related thing is a matrix model of K electrical circuits, what are these? I'm supposing they contain resistors, capacitors, etc. I just a little fizzy about what's in the matrix. It seems a whole lot like someone took college lecture notes, the professor drew something on the board, and that something is not in the notes.

• A whole lot of rather important concepts are concealed behind phrases that aren't defined, and unless you're a graduate in EE, no one knows: Lenz's Law, Faraday's Law, Oersted's Law, Maxwell's equations, Ampere's Law. There are wikilinks in case you want MORE information; we don't get ANY information in the article. It's more important to describe the concept we're relying on than to know its name - it doesn't matter what its name is. Sbalfour (talk) 22:52, 11 December 2017 (UTC)

• Derivation from Faraday's law of induction section - academic blather. We don't need derivation in the article, it is what it is (and we don't yet even know what that is).Sbalfour (talk) 22:56, 11 December 2017 (UTC)

I agree with some of your complaints above; I don't like this whole Circuit analysis section. The article should start with a general discussion of where inductance comes from, before it brings up inductors. I do think we need the 'academic blather' of a mathematical derivation of inductance, and that unavoidably involves calculus. However I absolutely agree that there should be a word description that doesn't include mathematics. The natural place for that is in the introduction. I have done a rewrite, renaming the section 'Source of inductance' which can be seen here: User:Chetvorno/work11#For_Inductance. I'm planning to replace the existing section with this. What do you think? --Chetvorno^TALK 22:57, 11 December 2017 (UTC)

I'm not the judge, jury and executioner (watch out when I swing the axe). I read through your 'Inductance lite' sections. I say bring them on, though we may need to coordinate on concepts and phraseology, because I wrote a new lead (see above). Sbalfour (talk) 23:20, 11 December 2017 (UTC)

Yes, sorry, I didn't see your intro above. Looks better than the current one. I like the first paragraph. One thing I noticed is that it's a little long; the introduction is supposed to be a maximum of 4 paragraphs. Maybe some could be moved into the first section? By the way, I'm not quite done with the 'Source of inductance' section; I want to make it less mathematical and clearer for general readers. --Chetvorno^TALK 00:43, 12 December 2017 (UTC)

Yeh, you're right, a little long and a little too much detail, that's why I figured part of it gets merged with your stuff. Sbalfour (talk) 01:06, 12 December 2017 (UTC)

• The last para of the lead summarizes the history beginning with who named the property? I just think that's a bit of trivia best left for the text, or maybe even just left out. We don't need Heaviside for anything else, unlike Faraday, etc. I think it's more relevant when it was discovered, and how that came about, which are not in the article. This is a pretty fundamental aspect of electronics, and a History section with at least a paragraph or two seems warranted. I'm not going to fix trivia first - we've got a lot bigger issues to address.
• I don't see any mention of the fact that voltage lags current in an inductor/inductive circuit. That's really pretty fundamental. While there is ONE mention of inductive reactance buried in the where clause of an equation, that relationship is also pretty fundamental and ought to be front and center. You can't do any circuit without integrating that.
• I'm beginning to consider, not how the article can be repaved, but whether any of it can be saved. All those formulas belong in a sidebar, or footnote, not in the article. The article looks like a Schaum's Outlines manual for professional engineers. I think this is the first order of business - vacate those formulas; they're hugely distracting. The initial step might be to move them all beyond the textual end of the article. Like some articles have a Gallery section; we have a Reference formulas section just before the References section. They are sort of a reference. Someone who wants one of those, doesn't want to read the article, he digs in a reference manual. He isn't going to rely on WP anyway. So we give him a tidbit, we list the formula and cite it.
• No discussion of serial and parallel inductance?? (goes under Circuit analysis)
• No discussion of inductance cancellation when conductors cross at right angles? As in non-inductive resistor windings, and perpendicular mounting of inductors in circuits.
• Need to summarize somewhere what inductive circuits are actually used for, filtering, energy storage, current regulation, and of course electromagnetic effects (refer to articles on inductors and RLC circuits for more info)
• No mention of inductive resonant coupling (goes in Mutual inductance, I suppose)
• How about negative inductance as an incident circuit component? (= brain damage) if not in this article, then where?
• inductive reactance is usually the other leg of the triangle when we need to distinguish between apparent power, reactive power and real power; as in VA of transformer, power regulation, etc worth a mention
• Now, what's the article structure going to look like? Chetvorno has the two top sections ('overview' and 'Faraday's law'); everything below Mutual Inductance gets shoved down and parallelized (those sections have a catywampus organization); but rescue Phasor circuit analysis and impedance and drop it under Circuit analysis, since that's the beginning of the text for inductive reactance in a circuit. The section Nonlinear inductance - you got to be kidding me - in layman's terms, that a magcore, so the section gets retitled. And the two most prominent nonlinear properties of a magcore are hysteresis and eddy currents, not mentioned at all. We can tread lightly here, there's already an article on magcores as well as real inductors. The Mutual inductance section needs to be kept, but split into two: mutual inductance formulas parallel to the other formula sections below, and mutual inductance as a phenomenon (little or no math here). Add a History section. Inductance and magnetic field energy goes in a sidebar - is an article on inductance really the best place to discuss energy storage in a magnetic field?
• I'm not done yet, but the sheer number of bullet points indicates the paucity of useful and interesting content in the article.

It appears editor Chetvorno and I agree on the definition as in the above talk section Inductance [lead], and editor Wtshymanski also deprecated the existing definition in the lead. So I have plugged in the new one. Now, though, part or most of the second paragraph in the lead is redundant. Sbalfour (talk) 17:33, 12 December 2017 (UTC)

• I disagree with the proposal to move all the mathematical formulas into a separate section or sidebar. Inductance is a technical term in physics and electrical engineering, it's defined by mathematical formulas, it's used in mathematical analysis of circuits, so I don't think the main sections of the article can do without math. And I definitely don't agree that a derivation of inductance is unnecessary; explaining where inductance comes from is the most important part of the article. However I think there could be more text explanation of the equations, and a nonmathematical introductory section describing inductance in simple terms.
• The fact that voltage lags the current in an inductor really only applies to a sinusoidal current. I feel just stating that 'the voltage lags the current' without introducing alternating current will confuse readers, so I think this should be put in the phaser section.
• I agree with adding what inductance is used for in electronics, and serial and parallel inductances (although Inductor and Series and parallel circuits already includes this). A History section would be fine. I feel resonant transformers are a little off topic as there are already the articles Inductive coupling, resonant inductive coupling, Transformer, and Transformer types#Resonant transformer.
• One change that I think would ease the 'too much math' problem is to move all the mutual inductance stuff into a separate 'Mutual inductance' section at the end of the article. Mutual inductance and ordinary inductance ('self-inductance') are really separate topics, applying to separate components (inductors vs transformers), and readers that are interested in one are probably not interested in the other. The mutual inductance stuff has a lot of opaque matrix math that, as you say, is clogging up the Circuit analysis, Derivation from Faraday's law, and Inductance and magnetic field energy sections. Rewriting these sections without it will make them a lot simpler. The reason previous editors have lumped the self- and mutual-inductance derivations together is because physics textbooks often do it that way. But there's no reason we need to. This is a change I've wanted to make to the article for years.

Would you, please, mind to add some connections of your pet-section to the article? As it stands, I perceive them as fully disconnected, apart from using indexed Ls and Ms, almost screaming for re-removal. :) Purgy (talk) 10:49, 12 September 2018 (UTC)

Done! I'm not completely sure this is what you suggested. If not, please clarify. Nijoakim (talk) 10:18, 19 September 2018 (UTC)

sum[edit]

The section on magnetic field energy is written in the form of an integral, but use Sigma for sum. Specifically, it has di for an integral over i. Seems to me it should use integral signs instead of sigmas. Gah4 (talk) 07:57, 13 December 2017 (UTC)

Its a sum of integrals. I believe he didn't show the integration to get the final result. I think the calculation went something like this:

${\displaystyle dW=\sum _m^K{i}_m{v}_{m}dt=\sum _{m=1}^K\sum _{n=1}^K{i}_m{L}_{m,n}d{i}_n}$

${\displaystyle W(i)=\int \frac{1}{2}\sum _{m=1}^K\sum _{n=1}^K{i}_m{L}_{m,n}d{i}_n=\frac{1}{2}\sum _{m=1}^K\sum _{n=1}^K\int i_m{L}_{m,n}d{i}_n=\frac{1}{2}\sum _{m=1}^K\sum _{n=1}^K{i}_m{L}_{m,n}{i}_n}$

I'm not quite sure where the factor of 1/2 comes in but its clearly due to the fact that the double sum counts each induced current twice.

Of course this little mathematical brain fart is way, way too complicated as an introduction to inductive energy. For many editors, when the duty to write an understandable article comes up against the desire to show off, the ego wins out. I moved it into the Mutual inductance section, and wrote a simpler section just covering the energy in a single inductor, Self inductance and magnetic energy to replace it. --Chetvorno^TALK 15:11, 13 December 2017 (UTC)

Oh, OK. I saw the sigma and the di, and missed the dW on the left. I was trying to figure out why it had sums and di. Thanks. It does look nicer in integral form, though. Gah4 (talk) 01:24, 16 December 2017 (UTC)

In the m=n case, the 1/2 comes from ${\displaystyle \int i_m{L}_{m,n}d{i}_n}$. Also, W should be ${\displaystyle \int dW}$ without a 1/2. I am not sure about the m≠n case, though. Gah4 (talk) 01:35, 16 December 2017 (UTC)

Geometry of inductance[edit]

Most people probably don't consider that a straight wire has any inductance, because ordinarily it escapes our notice. It's important to understand fundamentally how that works to use it for anything. From there, we usually jump to a coil's inductance, again because our ordinary experience isthat coils have recognizable and usable inductance. It's not that simple. I can wind a coil that will have negligible inductance; it's called a non-inductive wire-wound power resistor. One might suppose that winding wire perpendicularly in all three directions around a cube would make a rather compact and efficient inductor. Or, that a disk-shaped concentric spiral of wire (seashell-like) might be a good one. Maybe two long thin coils twisted together in a double-helix (an efficient shape for a totally unrelated purpose) might work well. How about a planar layout of long zig-zags accordion-like, rolled up like a carpet? Because a cylindrical open radius coil (solonoid) is also a natural shape, it's likely to be discovered that such a shape is rather good. Some of these shapes were tried in the early days of electromagnetism, before the time of Faraday's law and Maxwell's equations. When the mathematics caught up, we confirmed that coils are good shapes and learned how to make coils with efficient geometries for the inductance desired.

Adding magcores greatly complicates things. Again, the power of such a core (x1000's of times) obscures understanding of the phenomenon. A 'good enough' inductor can be made with rather poor materials and technique as long as one of them is iron or mild steel and the shape is mostly cylindrical. Many circuit component inductors tend to have bobbins that are square cylinders (diameter = length). Many small transformers have coils whose diameter is greater than their height. So in our ordinary experience, short squat ferromagnetic cylinders and their fat coils must be a pretty good shape. We imagine that the magnetic field is quite compact, or 'compressed' in one of these (similar to the 'cube' analogy above). It's counter-intuitive that that is not a very good shape. We can do the mathematics (if we know calculus or can confront those nasty sigma's) and attempt to backtrack the right shape. But that's not what we ordinarily do (except mathematicians and professional engineers). I understand the shape and orientation of the magnetic field around a straight wire, and can visualize what happens when I bend it into some shape so flux flows in some direction to and from the core to all the other coils, and what does that imply? Then I can construct the coil. (I just skipped quite a large chunk of understanding, and where would I get that - that could be the crux of the article). That understanding prohibits shapes like the wound cube - we don't need to go try it, because we know why it won't work.

I should be able to read the article, and construct an efficient inductor with or without a magcore, and justify to another knowledgeable person, why some other shapes probably won't be as good without ever looking at any of those equations (yes, with those, and careful measurement of the magnetic and electrical properties of the materials, I would be enabled to refine my intuitive notions of goodness, and construct a better coil. Now I'm an engineer reading the article.)

Sbalfour (talk) 19:53, 13 December 2017 (UTC)

Yeah. I think a good general principle to get across to readers is that anything that increases the total magnetic field (flux) through the circuit for a given current, increases the inductance. Then we can give examples of what geometries do that. This article could probably use some good diagrams of simple loops and coils. I can probably draw some in Inkscape, if it would be helpful, if my work allows it.--Chetvorno^TALK 23:35, 13 December 2017 (UTC)

One purely mathematical problem always comes up when trying to explain calculating inductance: For the simplest shape you want to start with, a loop of wire, the inductance comes out infinite when the wire is idealized as infinitely thin, as is usual in 'paper' circuits. This is because the magnetic field next to an infinitely thin wire goes to infinity, so the magnetic flux through the loop does too. The calculation of the inductance of individual wire loops has to include the cross sectional area a of the wire; then the current distribution and skin effect have to be considered and everything gets mathematically ugly (check out the formulas in the Inductance of simple electrical circuits section!).

For this reason most books usually start by calculating the inductance of a long solenoid. As long as the wire windings are adjacent they can be modeled as a current sheet, and everything comes out nice and simple. Besides, the formula for a solenoid is really useful in practical electronics. The section Inductance of a solenoid gives the formula. I was thinking of moving this section up under the 'Magnetic energy' section as an example, and adding a simple derivation. What do you think? --Chetvorno^TALK 23:35, 13 December 2017 (UTC)

Yeh, I know the single loop problem, confound it! I haven't encountered an infinite magnetic field around #40 wire yet, so there's obviously some room for interpretation :-? The Solonoid section is 'stringy' or upside-down or something. The bottom part is only for pencil-lead thin cores, and who does that? I'm looking to redraft the section, and probably cut the bottom half because there must be something more useful to say. You wanna take care of this? Sbalfour (talk) 04:38, 14 December 2017 (UTC)

Relation between inductance and capacitance[edit]

For high-frequency transmission lines, where ε and µ denote the dielectric constant and magnetic permeability of air.

This is not what we usually mean when we talk about inductance vs capacitance. It's pithy but hokey; the current follows the surface of the conductor, but the relevant constants are those for the air because the signal propagates through the air, NOT through the conductor. The conductor just provides the electrons, because we can't easily dissociate the air. (I envision trying to transmit 60hz electric power through the air. I think we'd have something like a Romulan disruptor.) Air, like every other physical object, has inductance and capacitance. Without the conductor to supply electrons, they could come from nitrogen and oxygen molecules, and we'd have lightning.

In an article about inductors, we usually don't consider the current conductor as air. The phenomenon isn't inductance in the ordinary sense. I just don't think this quip belongs in the article.

Sbalfour (talk) 21:09, 13 December 2017 (UTC)

I suppose, but if you look at the formula for capacitance and inductance of coaxial cylinders, or parallel wires, you find them similar. You might be able to make a duality argument for it, though I won't do it right now. The result is TEM00 wave propagation, with the appropriate boundary conditions, such that the velocity is the velocity of an EM wave in the appropriate permittivity and permeability, which of course, it has to be. I first learned about this, after measuring the velocity through a coaxial cable with a coiled center conductor, increasing its inductance. Interesting math. Gah4 (talk) 22:00, 13 December 2017 (UTC)

I thought about the duality angle, but there's a whole 'nother dimension to wave propagation that has little to do with inductance, and best fits into another context, like transverse mode or transverse wave. Here it's just a quip. The relationship of capacitance and inductance is a rather vital topic in power regulation at the consumption end. At the generation end, synchronous and asynchronous generators are complementary because one is capacitative and the other inductive. Whether stuff like this belongs in inductance, capacitance, or somewhere else I don't know. Sbalfour (talk) 23:03, 13 December 2017 (UTC)

This section seems to be pretty peripheral and off-topic for this article, considering the amount of other stuff the article is trying to cover. Also the formula is already given in Coaxial cable. Maybe delete it? --Chetvorno^TALK 01:13, 14 December 2017 (UTC)

Done. Sbalfour (talk) 03:53, 14 December 2017 (UTC)

There is a section for the inductance of a coaxial cable. As above, the interesting part is that the capacitance of a coaxial cable follows similar math, and the velocity of propagation down the usual coaxial cable equals the speed of electromagnetic waves through the dielectric. (It sort of has to do that, but is interesting to see in the math.) At low frequencies (wavelength long compared to cable length) the capacitance of a cable is more important (so not for this article). Also, you can build a coaxial cable with a helical (think solenoid) center conductor, which increases its inductance, and so decreases the propagation velocity. Especially useful in delay lines. Gah4 (talk) 19:41, 6 March 2019 (UTC)

Mutual inductance of two wire loops[edit]

That integral pains me to look at besides the fact nothing is defined, so I don't know how to use it. Presuming that I can figure out what the parameters mean, I'm going to go to the lab and check it out. I have several sets of wire loops to verify the formula:

• one set is two loops of identical diameters, mounted one inside the other (squeeze a little) with their axes perpendicular to each other
• one set is two identical loops which pass through each other's centers and whose axes are perpendicular
• one set is two loops mounted side by side but one is twisted, so that the current runs in the opposite direction through it

That doesn't exhaust the possibilities, but it's probably enough. What do you think I'm going to find? I believe the encyclopedia, it says that's the formula. Is there a problem here? Sbalfour (talk) 00:56, 14 December 2017 (UTC)

Oh, I forgot, the final setup is a

• pair of loops side-by-side in a cylindrical coil, and the current is DC

My standard benchtop power supply is a 12/5 VDC 5A unit. Of course, it's a natural choice. Most things I need to test are either 5 or 12V and milliamps. Sbalfour (talk)

Wow, that's cool. I wish I had access to a lab. Do you have instruments to actually measure the inductance of wire shapes? --Chetvorno^TALK 19:13, 14 December 2017 (UTC)

Actually, I do, laboratory quality voltmeter, ammeter, distortion analyzer, signal generator, etc. They're confounding to use, because when measuring things that small, nearly everything has charge, some current flows here, there, and everywhere. Of course, a loop needn't carry a small amount of current, it can be amps, if necessary (as amps mount, losses scale disproportionately). There's measurable mutual inductance between two loops carrying an amp. Don't forget, they can be big loops. Inductance varies with the square of the radius, so there's a favorable ratio there. Sbalfour (talk) 19:40, 14 December 2017 (UTC)

Maxwell's equations[edit]

The first mention of Maxwell is in the section Inductance of elementary and symmetric geometries: 'In the most general case, inductance can be calculated from Maxwell's equations.' This is kind of like 'SPLAT! Was I supposed to know about those?' Actually, I think we was. They need to be described at least topically somewhere early along with Faraday's law as the definition of classical electromagnetism. Sbalfour (talk) 15:57, 14 December 2017 (UTC)

Well, the specific thing that Maxwell added was the displacement term. Well, and then put it all together. Otherwise, it is Poisson, Gauss, Faraday, and Ampere (if I remember), and that should be enough for inductors. But it is usual just to say Maxwell, instead of the four separate laws. But more specifically, you can calculate the inductance from the stored energy in the magnetic field. Gah4 (talk) 17:12, 14 December 2017 (UTC)

Yes, I feel the sentence '..inductance can be calculated from Maxwell's equations.' is way too general and doesn't say anything. Specifically, the inductance is equal to the flux through the circuit (or conductor) per ampere of current ${\displaystyle L=\mathrm{\Phi }(I)/I}$ and to calculate the flux you need the magnetic field. Ampere's law is the Maxwell's equation which gives the magnetic field of a current, and so inductance is ultimately calculated from it. But the form of Ampere's law is too cumbersome to use practically except in a few cases (a long solenoid is one) so more specialized equations derived from Ampere's law are used to calculate the inductance formulas in this section. One is the Biot-Savart law, which gives the magnetic field by adding up the contributions of the current ${\displaystyle Id\mathit{\ell }}$ in each small segment of wire

Neumann's equation in this section is derived from the Biot-Savart law. I think a brief overview of this stuff should replace the Maxwell's equation line. I found a good book Grover (2013) Inductance calculations] with a comprehensive overview of how inductance is calculated in the chapter: 'Methods of calculating'. --Chetvorno^TALK 18:48, 14 December 2017 (UTC)

'azimuthal'? What's that?[edit]

In section Inductance#Inductance of a coaxial line, we say that the magnetic field points in the 'azimuthal direction'. Here's a typical definition of that word:

The direction of a celestial object, measured clockwise around the observer's horizon from north. Azimuth and altitude are used together to give the direction of an object in the topocentric coordinate system.

A magnetic field radiates uniformly in all directions from the current; magnetic flux flows in the field in a direction defined by Lenz's right-hand rule. The current flows in opposing directions in inner and outer conductors, so the incident magnetic fields will also be opposed, but that's rather intuitive (I think). It's a big stretch trying to figure out what the term means, and if that is relevant. Sbalfour (talk) 18:31, 14 December 2017 (UTC)

Yeah that definition's not exactly relevant to electromagnetics. Azimuthal when used for something with cylindrical symmetry means radial, perpendicular to the center line of symmetry. In this case it means outward from the cable's central wire. --Chetvorno^TALK 19:02, 14 December 2017 (UTC)

Crapiola. I just noticed that this whole section is predicated upon 'Assume a DC current flows..'. A DC current contains no signal information. The whole purpose of coaxial or shielded cable is to avert corruption of small (AC) signals. The math is daunting. And at the end, after all that, the section bails and simply says, what we really do is this other thing [..] (which presumably addresses skin effect, but I don't see any term for it). The text is an academic exercise -> because it happens to be a symmetric object? I'm swinging an axe (but I'd like to expand on the last equation) - any objections? Sbalfour (talk) 19:09, 14 December 2017 (UTC)

The section is also completely unsourced. Coaxial cable already has the math. I'd say delete it. --Chetvorno^TALK 19:25, 14 December 2017 (UTC)

Done. Sbalfour (talk) 19:56, 14 December 2017 (UTC)

Inductance of elementary objects[edit]

I don't think given the article as it stands today, that we even know the self-inductance of a straight wire. It matters a whole lot, because that's an electric transmission line. It'd be nice if we could initially assume that it's unidimensional, but it looks like we run into the (${\displaystyle 0\cdot \mathrm{\infty }}$) problem. So it has to have some negligible radius. That's the logical start of the Inductance of elementary and symmetric objects section. Then maybe a high-frequency straight wire. Then maybe a fat straight wire (skin depth matters). Then two parallel wires with parallel currents, then two parallel wires with opposing currents (that's a lamp cord). Then two perpendicular wires (in general, ones that aren't parallel). Then maybe a straight square wire. Then maybe a straight iron wire (now that gets interesting - in it's elaborated form, that's a square steel busbar). All of this before we even get to mutual inductance of loops. Sbalfour (talk) 20:32, 14 December 2017 (UTC)

Yes, but we're not a textbook. Hit the high points, give the 'physics for poets' explanation and point at the copious and boring literature. Once you can solve econd-order Bessel functions, you don't need the Wikipedia any more. --Wtshymanski (talk) 20:41, 14 December 2017 (UTC)

Yeah, we can list the inductance formulas for any additional useful wire shapes in the table. Here's a book with a lot of formulas Grover (2013) Inductance Calculations. Also there are other articles that need improvement. --Chetvorno^TALK 22:55, 14 December 2017 (UTC)

Ok, I got it: KISS. Is two parallel wires fundamental or instructive enough to include as an full section? Sbalfour (talk) 00:45, 15 December 2017 (UTC)

KISS is the cancerous truism that KISSed emergence (=power÷effort) to death. We need BOTH a simple AND complete in-depth explanation in one! Not just simplism for the sake of simplism. Aka the iOS/Notepad of explanations. Aka uselessly simple. Simplicity should never come at the cost of completeness/power.

I often enough use WP as a reference for something I should know, and probably do, but want to look up anyway. Yes WP is not a textbook, but it is a reference book, so things that might be found in reference books should be fine. Showing the inductance per unit length for a coaxial cable, from the radii and dielectric constant seems useful. I remember a physics lab where we measured the impedance and propagation velocity of some coaxial cables, and then compared that to the calculated values. (And I don't believe this was in any textbook that we had.) There was also one cable that has a spiral wound (high inductance) center conductor to use for a delay line. The interesting thing about that is that you can consider the inductance increase, which decreases the velocity, or consider that the signal follows along the spiral, and get about the same answer. As above, these are complicated by knowing the current distribution. At high frequencies, the skin effect is important, and the current stays close to the surface. We should be able to find a real reference book and use the ones that they use. Gah4 (talk) 16:44, 6 May 2019 (UTC)

Mutual inductance: Equivalent circuits: π-circuit[edit]

There are 7 inductors in that figure. That's pretty far out. More matrix math we don't need. It'd be a lot simpler if it were a plain 3-inductor pi section. I don't know that we need T and pi sections at all. Wouldn't a simpler presentation of mutual series/parallel, parallel/series, series/series, and parallel/parallel inductors (I'm not at all sure all those are unique) be more fundamental and understandable? Do I smell a chop/chop? Sbalfour (talk) 00:51, 15 December 2017 (UTC)

I deleted most of π-circuit section, as it's mostly incomprehensible except to professional EE's, and they won't come to wikipedia for their info. I could implement the content of this section with a conventional pi section of mutual inductors (two shunt inductors separated by a series inductor). But there are at least several other configurations both more practical and more theoretically interesting. Like two transformers in series. I often have that situation in the lab: an isolation transformer, followed by a variac, followed by the circuit, possibly a transformer, under test. There's inductive interaction there, and it's noticeable. I'd choose to write about that, instead. Sbalfour (talk)

Self-inductance of thin wire shapes[edit]

Self-inductance of thin wire shapes/Single layer solenoid gives the Lorentz current sheet elliptical formula for solenoids. It won't work at all for short large-radius open spiral RF single layer solenoids. The formula is impeccably sourced (Lorentz himself). It's show-off erudition. Nobody uses that. If you need that formula, you don't need the encyclopedia. If you remember the name Wheeler, it's all you need to know. It's more important to understand the validity of any methodology (the geometries it's applicable to), and the deficiencies of any approximation within the geometry. We should probably cover some of that in the text section. Some other editor, long in the past, complained that there were differing formulas for solenoid in the article, as if one were right and one were wrong. Probably an observant neophyte. Ha! These are not like differing approaches for calculating the volume or surface area of a conical section. The other formulas in the table are simpler, but still not simple, and come from several sources (and some are unsourced). Unless we're going to derive these formulas in the text (theoretical approach), then we should stick to just what's generally useful and used.

The straight wire/conductive wall entries are ambiguous; since I don't know, would the wall be electrically conductive but not magnetically 'conductive'/permeable (aluminum), or permeable but not electrically conductive (ferrite or other ferrimagnetic material), or both (steel); however, high-alloy steels are neither very electrically conductive nor very permeable.

Here's my proposal for the table (even if they're in the text, the table is a nice compendium):

• straight wire
• pair of parallel wires a) current in same direction; b) current in opposite directions (lamp cord)
• wire loop
• rectangular wire loop
• long flat thin strip (PCB trace)
• +flat spiral round-wire coil (i.e. like a disk)
• flat rectangular spiral thin-strip coil (PCB trace inductor)
• +single layer solenoid (Wheeler's)
• +multilayer solenoid and Brooks coil
• coaxial line
• single layer open spiral RF coil
• conical coil

Considering high-frequency signals could double the number of entries; I doubt it's useful enough except for the RF and coaxial geometries. I don't think the round wire/flat wall geometries in the existing table are useful at all. 3 of these (denoted '+') are also in the table in the Inductor article and could be omitted, but someone reading an article on inductance and doesn't find the Wheeler formula might be pretty disappointed. Would he go look in the other article?

Sbalfour (talk) 19:27, 15 December 2017 (UTC)

• Proposal for table: Sounds fine. I agree some of the most important shapes, multilayer solenoid, flat spiral, and PCB trace, are missing and should be in there. One thing I think is important is that each of the formulas be attributed to a source.--Chetvorno^TALK 02:06, 18 December 2017 (UTC)

Yeh, because the possibility of a mistype is acute, and different sources sometimes have different wrinkles on the formulas

• Inductance of a solenoid: I noticed that too; the simple formula that everyone uses

${\displaystyle L=\frac{N^2{r}^2}{9r+10l}}$

(I didn't know it was called the Wheeler equation) is missing. I vaguely remember a few years ago there was a big edit battle over which formulas in the table were most accurate, so I assume the simple, useful, approximate ones were deleted in favor of the huge useless monsters now in there. The Wheeler formula should certainly be added to the table; preferably the one for metric units, not the inch one above.--Chetvorno^TALK 02:06, 18 December 2017 (UTC)

Yeh, cgs units are good, but I added the English version too because that's what we all remember

Just a suggestion - I would leave the complicated ones in there, otherwise some erudite accuracy-obsessed engineer is just going to replace the simple ones with complicated ones again.--Chetvorno^TALK 02:06, 18 December 2017 (UTC)

I just couldn't suffer the Lorentz one; nobody is going to use that - they're going to look at it, stick their thumbs in their ears, wag their tongues, and go 'yahde, yahde, yahde..'.

• On high frequency formulas: Yeah, I doubt separate formulas for high frequency would be worth the space. Maybe it should be mentioned in the section somewhere that the inductance of wire coils declines somewhat with frequency. Some of the formulas have the correction factor Y which already accounts for frequency.--Chetvorno^TALK 02:06, 18 December 2017 (UTC)

At RF and higher (coaxial is often associated with VHF/UHF TV frequencies), the decline is more than somewhat, or maybe I should say losses are more than somewhat. In the early days, I wasn't too careful about inductors on my breadboards, and had a mix of audio and RF inductors. Circuits worked strangely or not at all. I could clearly see the ratings of those inductors, I just didn't understand..

Sbalfour (talk) 23:10, 15 December 2017 (UTC)

As far as I know, for high frequencies the skin effect puts the current (close to) the outside of the wire, and the table should have the formula for all the current on the surface. For low frequencies, uniformly distributed is probably a good approximation, and the table should have that. Of course the actual distribution can be different from either of those. In a solenoid, there will be a force pushing the current to the outside of the solenoid, so the previous approximations aren't so close. Gah4 (talk) 00:04, 7 February 2018 (UTC)

Self-inductance of a wire loop[edit]

We have this section, and an entry in the table below for circular loop (planar in euclidean geometry), with a simpler formula. I idly thought the table entry must be a usable approximation, but now realize that the referred-to loop in the named section needn't be circular! Is it planar? Can it have kinks? If it's a rectangle, is that a special case that reduces to the formula in the table? Does the loop perimeter have to be uniformly convex? Even if it does, it could be stretched until it's basically two parallel wires with opposing currents. Even a planar loop wouldn't necessarily be forbidden to cross over itself, like a figure 8; now we have two loops. Topologically, it's like defining 'what's a knot?'; that's distinctly non-trivial. So what's a loop? Is that non-trivial, too? Or is it just the flip side: if it's not a knot, then it's a loop?? Sbalfour (talk) 06:20, 16 December 2017 (UTC)

Are you talking about the formula in the section Inductance#Self-inductance of a wire loop? (the one in the table just applies to a circular loop, doesn't it?) Those are good questions. I think that formula applies to most shapes, kinked, concave, rectangle, nonplanar. etc. If the loop actually self-intersects, of course, it will short out and then you have two loops. --Chetvorno^TALK 00:47, 17 December 2017 (UTC)

However I think you're right that a 'knotted' loop would be different. The loop formed by a wire running along the single edge of a Mobius strip is knotted, right? That loop will give zero inductance, I think [1], although their seems to be some argument about it [2]. Because if you applied Ampere's law to get the magnetic flux due to a current flowing through that wire, the magnetic flux through the Mobius strip, it only has one surface, so you can't calculate the flux. There's something called a Mobius resistor which consists of a conducting coating on both sides of a Mobius strip, that is supposed to have no inductance. --Chetvorno^TALK 00:47, 17 December 2017 (UTC)

I just saw a source that underlined the double integral, and stated that its dimension was length, and it's magnitude, ${\displaystyle l}$. I had already surmised that the integral must collapse to some function of length or perimeter of the loop if length >> radius of conductor. Magnetic field strength declines as the square of the distance from current source, right? Is that still true for a point-to-point vector? The integral sums point-to-point vectors and treats the decline as linear (x -x'); the resulting integrated quantity is logarithmic. What happens when the loops are 'infinitely close'? The transverse distance between loops is meaningless, constant or not. So the integration is constrained by another condition, s-s' >a/2 which in the original text was erroneously stated as x-x' >a/2. s is an axial separation, not transverse, because the vector can't get too short or we have the infinity problem all over. So 'arcs' of the integrand are missing. Therefore, we need to add back in some function of length to fix it. That's ${\displaystyle \frac{{\mu }_0}{4\pi }lY}$ it seems. Ostensibly, this must represent the flux inside the wire, because when there is no current inside the wire, there is no flux, and the length term disappears. When the current is uniformly distributed over the cross-section of the wire, the term is ${\displaystyle \frac{{\mu }_0}{4\pi }l/2}$. This term isn't ignorable, or we wouldn't need it; the cited source doesn't mention any bounding conditions, so may we assume that in the limit, this length term is the whole integrand? Now, what is that limit?

Sbalfour (talk) 20:04, 18 December 2017 (UTC)

@Sbalfour: Are you talking about the formula in Mutual inductance of two wire loops or the formula in Self-inductance of a wire loop? --Chetvorno^TALK 00:51, 19 December 2017 (UTC)

There is no unambiguous definition of the inductance of a straight wire.[edit]

There is no unambiguous definition of the inductance of a straight wire. I suppose, but there is no unambiguous definition for inductance in other shapes, without consideration of the distribution of current within the conductor. The inductance per unit length of an infinite straight wire is well defined. (Again, with consideration of the current distribution.) Lead inductance of lumped components is significant at higher frequencies, which is mostly the straight wire inductance. If the wire radius of curvature is much larger than the wire diameter, the straight wire approximation should be close. Another important case is PC board vias, which are like very short straight wires. Gah4 (talk) 23:20, 17 December 2017 (UTC)

Yeah, that was an ambiguous point in the traditional theory of inductance; inductance is defined as the magnetic flux through the circuit divided by the current. The flux through the circuit is the B field integrated over a surface spanning the circuit, but how do you calculate the flux through a portion of a circuit? Yet any portion of a circuit clearly has an unambiguous inductance, which can be measured by measuring the back EMF across that part of the circuit when a changing current is applied. The inductance can be calculated by using partial inductance [3], [4], [5]. There should probably be a section on partial inductance in the article. --Chetvorno^TALK 01:54, 18 December 2017 (UTC)

Easiest way is to equate the energy stored in the inductor with the energy stored in the magnetic field. Gah4 (talk) 15:50, 12 September 2018 (UTC)

That's the problem; you can't attribute the magnetic field at any point to the current in one specific part of the circuit, the magnetic field at any point has contributions from the current density throughout the entire circuit. You can easily calculate the flux through the whole circuit and thus the magnetic energy stored by the whole circuit, which will give you the inductance of the whole circuit, but how do you calculate the inductance of a segment of the wire? Calculating the magnetic field and stored energy due to an arbitrarily shaped segment of wire is difficult. There is a mathematical technique for doing this, called partial inductance ([6], [7], [8]). --Chetvorno^TALK 20:29, 19 September 2018 (UTC)

Technically, a short wire, or wire segment, isn't a circuit. It isn't hard to calculate the inductance per unit length of an infinitely long wire, closing the circuit through 'the point at infinity'. Sometimes you can determine that a non-infinite segment is close enough. That is, its field doesn't interact with any other parts of the circuit, or if it does, small enough to ignore. In usual circuit design, inductors (coils) are assumed to keep the field inside enough, not to affect the rest of the circuit. Sometimes that means not placing them too close together. Or, to look at it another way, you can separately calculate the self inductance, and then add in the mutual inductance between parts of the circuit. In many cases, though, the leads of circuit components, such as capacitors, can be considered as short wire segments, and an inductance value given that is close enough. One can also measure, for example, the internal inductance of an electrolytic capacitor possibly at different frequencies. (At some frequency the inductive impedance crosses the capacitive impedance.) Gah4 (talk) 22:38, 19 September 2018 (UTC)

Yes, in PC board and IC design you have long circuits composed of many small straight segments. You have to calculate the inductance of these segments, for example to determine transients on ground and power pins when digital circuits change state, or crosstalk between adjacent PC runs. The technique that has been developed for calculating the inductance of segments when the circuit is made of multiple straight segments is called the 'partial inductance' method. The 'partial self-inductance' of a straight conductor can be easily calculated by integrating the vector potential over a path that follows the conductor segment, then goes to infinity along lines perpendicular to the conductor. The partial mutual inductance can be calculated by a similar integration. To find the actual inductance of the segment, the partial self inductance is corrected by the mutual inductance of each of the other segments in the circuit. This method is used widely in manual digital and RF analog design, as well as in EDA design tools which automatically simulate ground and power bounce and crosstalk. --Chetvorno^TALK 23:29, 19 September 2018 (UTC)

Shielding Back EMF[edit]

I wonder if the section Shielding Back EMF should be here. That is, if it is encyclopedic, and if it is, appropriate here. I understand the usual shielded transformer, which shields out capacitive coupling, which allows some high frequencies that would normally not go through a transformer. I don't completely understand this one, though. Gah4 (talk) 22:45, 25 December 2017 (UTC)

How am I doing regarding my inclusion of a subtopic at Inductance?[edit]

I've removed Shielding Back EMF and have submitted a new article which I hope will be more appropriate in its stand alone location.

Vinyasi (talk) 02:32, 26 December 2017 (UTC)

big or small[edit]

There are recent edits and reverts related to current being ${\displaystyle i}$ or ${\displaystyle I}$. It seems to me that ${\displaystyle i}$ is more often used for time dependent currents, and ${\displaystyle I}$ for DC, or RMS value of AC currents. Also, ${\displaystyle i}$ can be confused with the ${\displaystyle i}$ used in complex math. (The reason why ${\displaystyle j}$ is used, but that would probably confuse readers of this article.) Gah4 (talk) 23:51, 6 February 2018 (UTC)

I have not come across sources who use ${\displaystyle i}$ for time dependent currents, rather I found the notation ${\displaystyle I(t)}$ to be much more prevalent. Searching a few well known undergraduate physics textbooks (their most recent editions: Giancoli 4e, Young and Freedman 14e, and Griffiths 4e) to use the notation for ${\displaystyle I}$ and ${\displaystyle I(t)}$ although the Halliday series seems to use ${\displaystyle i}$ for currents in general. The notation is not very uniform admittedly. Therefore, I think that this article should use ${\displaystyle I}$ as ISO 80000 Part 6 mandates it to be either ${\displaystyle I}$ or ${\displaystyle i}$, yet uses the notation ${\displaystyle I}$ throughout the rest of the document, showing a preference. --- Potchama 23:23, 20 February 2019 (UTC)

I reverted, since I see no consensus on these changes, and I confirm the use mentioned by Gah4. Removing arbitrary mutual induction indices deprives the article of relevant information. Purgy (talk) 07:47, 21 February 2019 (UTC)

One additional thing: It should be V=d(Li)/dt. or d(LI)/dt. Most of the time, this isn't important, but it turns out to be important for solenoids, with a big dL/dt. Gah4 (talk) 09:17, 21 February 2019 (UTC)

Mutual inductance of two parallel straight wires[edit]

For one, this section doesn't actually say anything about the values. I believe that the mutual inductance, with proper signs applied, is the same for the currents in either direction. The total inductance, self+mutual, will be different because of the different signs. Gah4 (talk) 15:53, 12 September 2018 (UTC)

Inductance vs induction[edit]

I tried in the formulation of the first sentences in the lead to precisely mention the relevant characteristics of the topic.

• Inductance is a proportionality factor relating two electric quantities (induced EMF and time-derivative of flowing current).
• Inductance is solely determined by the geometric setting of conductors and material properties, guiding the relevant fields.
• In a discrete setting of several conductors inductance comes as self- and mutual inductance, both as figures (not vectors, e.g.) in henry.

I am sorry for not being qualified to express these facts in a parseable, comprehensible and recognizable form, but I humbly ask to replace

• .., by which [inductance!] a change .. induces an electromotive force ..

which is improperly relating to induction, by a formulation in appropriate English quality that honors the mentioned facts. Purgy (talk) 15:44, 6 March 2019 (UTC)

Could some user who is fluent in pidgin English, kindly translate the above into something vaguely comprehensible. 81.129.194.214 (talk) 17:06, 6 March 2019 (UTC)

I don't think I can translated it, but note that electromagnetic induction is the process by which inductors generate inductance. If this page doesn't link electromagnetic induction and inductors, they should probably be added. Gah4 (talk) 19:10, 6 March 2019 (UTC)

While I fully agree to a certain analogy of inductance and capacitance (both determined by geometry -for coaxial cabels: cylindrical symmetry of a linear and a barrel formed conductor plus dielectric in between- and by material properties), I am reserved to the wording of inductors 'generating' inductance. Inductors are electr(on)ic components, having a specified value of inductance as a property reasoning their application within a circuit. For themselves they do neither generate inductance nor induction. The former is their inherent property, and the latter is their effect according to use (no varying current - no induction; in spite of inductors).

I am rather skeptic regarding insertion of time-varying inductance in this article. I can imagine some parametric effects, but I think it is more distracting than elucidating. Purgy (talk) 11:02, 7 March 2019 (UTC)

This will require translation into comprehensible English as well. It is difficult to discuss the issue with someone who cannot write English to even a basic standard. 86.158.241.195 (talk) 15:19, 8 March 2019 (UTC)

OK, hoping for technical knowledge and sufficient fluency in using the English language, instead of hoping for good will:

${\displaystyle \text{Could someone with pertinent expertise and fluency in English, please,}}$

${\displaystyle \text{−remove the misleading referral to inductance in the first sentence of the lead,}}$

${\displaystyle \text{−and perhaps add facts about inductance (I hinted to a few above)?}}$

Thanks for your attention. Purgy (talk) 11:02, 7 March 2019 (UTC)

I only can assure that this procedure works great. Xen windows 7 template. The server will find the nic again I don’ t know exactly why you need step 6.

Why would anyone want to remove any reference to inductance in the first sentence? It is what the article is about. In any case, the current lede of the article is far too complex and contains too much extraneous clutter. The lede should tell the reader what the property of inductance is. Simply put: Inductance is that property of an electrical circuit where a change in current through it induces an E.M.F. which opposes the change in current. That is it, nothing else is required. Similar wording can be found in any decent work on the subject. Optionally, one could additionally mention that the change in current will induce an E.M.F. in any adjacent conductor that is magnetically coupled. All the extraneous additional facts and material belongs in the main body of the article as long as it is not describing inductors which is a separate article. 86.158.241.195 (talk) 16:52, 7 March 2019 (UTC)

- .. because the reference in the first sentence does it wrongly.

- I agree to there being clutter and complexity, as far as it belongs to the dubious formula. However, I consider mentioning the defining facts of inductance is a proportionality factor of electric quantities, and of inductance is determined by geometry and material only as certainly belonging to the lead. These elementary facts are now missing.

- Certainly, the lead should tell, but the current tale is -at least- misleading.

- The 'simply put' is similarly misleading, as the current lead is. The words about 'changing currents inducing EMF' belong to induction; inductanceis not this effect, but the proportionality factor, governing this effect - see also the hat note.

- I think mutual inductance should be in the lead, it is necessary for explaining even most simple things like transformers.

- Describing an inductor' as a paradigma for applying induction at a gauged inductance might be perfectly reasonable in this article.

Currently, the lead is in no way excessively long. Purgy (talk) 08:31, 8 March 2019 (UTC)

Yes, the first sentence is wrong because it is too specific. The bits about 'proportionality factor' and 'inductance is determined by geometry and material only' are peripheral to what inductance is. Inductance is a phenomenon displayed by electrical circuits to changing levels of current, nothing more. The extra bits that you give are determinants of the magnitude of the inductance, but that is a development of what the phenomenon is. Most of what is in the lede belongs in the main body. It is certainly far too early to introduce a formulae (which is not even right). Nearly all of it belongs in the main body of the article and not the lede.

Try: ${\displaystyle v=L\frac{di}{dt}}$ (induced voltage is inductance times rate of change of current - simples).

Oh, and please learn how to spell 'lede'.

The corresponding article on Capacitance is equally bad, and the first sentence is not even correct. The ratio of change in electric charge to change in potential is a constant and totally independent of the actual capacitance. Double the voltage on any given capacitor and you double the charge - always. Lose the two 'changes in' and it would be right, but not simple enough to describe the actual phenomenon. 'Capacitance is the ability of a body to hold an electrical charge' (just copied it from an electrical text book, but all such books pretty much say the same thing.

If 'Capacitance is the ability of a body to hold an electrical charge' then, from duality, 'Inductance is the ability of a body to hold an electrical current', but I don't think that is what we want here. In circuits, capacitors follow I=C (dV/dt) and inductors V=L dI/dt. (Assuming both L and C are not changing.) Capacitors store energy in an electric field, as $\frac{{\displaystyle C{V}^2}}{2}$ and inductors as $\frac{{\displaystyle L{I}^2}}{2}$. Inductance and capacitance are duals, so the formulae should show this. Gah4 (talk) 19:29, 8 March 2019 (UTC)

dL/dt[edit]

Ah! Just discovered: someone had recently changed the formuala in this article. Unfortunately, the replaced formula cannot be correct because the two sides do not dimensionally balance (The RHS side has gained a surplus T^-1 because of the differentiation of L). 86.158.241.195 (talk) 15:14, 8 March 2019 (UTC)

The equation is correct. That is not a surplus t, but the time dependence of L, as in L(t), not L×t. It seems that many books leave out the dL/dt term. this one mentions that many leave it out. The given formula is only correct if dL/dt=0. Does it state that anywhere? Should it state that anywhere? More specifically, from the chain rule, d(LI)/dt= L di/dt + i dL/dt. Gah4 (talk) 16:46, 8 March 2019 (UTC)

Nope: Equation is dimensionally incorrect. As soon as you differentiate the inductance term, you introduce another T^-1 into the RHS, which unbalances the equation.

${\displaystyle v=L\frac{di(t)}{dt}.}$ gives:

M L² T^-3 I^-1 = M L² T^-2 I^-2 * I T^-1

= M L² T^-3 I^-1 = M L² T^-3 I^-1 - Identical LHS and RHS therefore valid equation.

Your equation:

${\displaystyle v=\frac{dL(t)i(t)}{dt}.}$ gives.

M L² T^-3 I^-1 = M L² T^-3 I^-2 * I T^-1

= M L² T^-3 I^-1 = M L² T^-4 I^-1 - LHS and RHS do not balance therefore equation impossible. This is because the differentiation of the L term (WRT time) introduces another T^-1 term in the RHS. Either your broken link is wrong or you have misinterpreted it. Which, I could not say.

In any case, why is the inductance changing? 86.158.241.195 (talk) 17:21, 8 March 2019 (UTC)

I can't figure out your math, but the equation is right. Moving terms into, or out of, the derivative does not change the units. Expanded using the chain rule it is v=L di/dt + i dL/dt, check the units on that one. Gah4 (talk) 18:34, 8 March 2019 (UTC)

I first knew about this from the story of someone who had to fix the design of a product that failed when the designers forgot about the dL/dt term. Specifically in the case of solenoid actuators, which are inductors with a moving iron core. According to one book, another case is a rail gun. (Always a favorite for physics E&M class, not so popular in actual use.) Probably this can go down to the solenoid section near the end, which I noticed after making the edit in the first place. A note about the assumption that L is constant, would be nice, though. Otherwise, L can change if the wires move due to the magnetic force. This is where the hum comes from in transformers and lamp ballasts. It is also the source of the back EMF in some motors. (A rail gun is, pretty much, a linear motor.) The convenient part about Leibniz derivative notation is that the units work if you ignore the d's (or just don't give them any units). Works for integrals, too. Using Newton's dots, or (I don't know who) primes doesn't have this advantage. Gah4 (talk) 18:34, 8 March 2019 (UTC)

See page 11-42, Table 11.11 for reasons L might change. Most books ignore these, but that doesn't mean that they are wrong. Gah4 (talk) 18:44, 8 March 2019 (UTC)

I first knew about this from the story of someone who had to fix the design of a product that failed when the designers forgot about the dL/dt term. Specifically in the case of solenoid actuators, which are inductors with a moving iron core. According to one book, another case is a rail gun. (Always a favorite for physics E&M class, not so popular in actual use.) Probably this can go down to the solenoid section near the end, which I noticed after making the edit in the first place. A note about the assumption that L is constant, would be nice, though. Otherwise, L can change if the wires move due to the magnetic force. This is where the hum comes from in transformers and lamp ballasts. It is also the source of the back EMF in some motors. (A rail gun is, pretty much, a linear motor.) The convenient part about Leibniz derivative notation is that the units work if you ignore the d's (or just don't give them any units). Works for integrals, too. Using Newton's dots, or (I don't know who) primes doesn't have this advantage. Gah4 (talk) 18:34, 8 March 2019 (UTC)

See page 11-42, Table 11.11 for reasons L might change. Most books ignore these, but that doesn't mean that they are wrong. Gah4 (talk) 18:44, 8 March 2019 (UTC)

No. The expanded equation is.

${\displaystyle v=\frac{dL(t)}{dt}.\frac{di(t)}{dt}.}$ because the divisor dt is common to both (multiplied) dividend terms above the line.

You have declared L to be a time varying quantity. This and your explanation is far too complex to introduce so early in an article.

Did you mean:

${\displaystyle v=L(t)\frac{di(t)}{dt}.}$ (valid equation)

But this still declares L to be time varying.

dL/dt is mathematical notation for rate of change of inductance and introduces an extra T^-1. 86.158.241.195 (talk) 18:49, 8 March 2019 (UTC)

Coil Inductance Calculation Formulas

I said chain rule above, but it is actually product rule. That page explains it pretty well. And while ${\displaystyle v=L(t)\frac{di(t)}{dt}.}$ may be a valid equation, it is not valid physics. Gah4 (talk) 19:05, 8 March 2019 (UTC)

┌─────────────────────────┘

Gah4 has it right, except for the Lagrangian primes and Newtonian dot notation.

A second ${\displaystyle T^{-1}}$ would result from which was never proposed. Bose 102 ea amplifier manual download.

People should know when they exceed their competence, as also for inductance and capacitance, too!

I agree to shifting down the time-variable inductance, I'd remove the formula from the lead, but it is ridiculous against my opinon to call it 'too long'. BTW, I oppose also to this edit, that is no essential improvement to my measures.

BTW, one might research the spelling of 'lede' vs 'lead' and find that 'lede' results from an over-the-top desire to be correct, and was used formerly, based on a mistake.I apologized already for my non-native English, I won't do it again, but I strongly suspect that my mastering of my second language is better than the IPs (if he speaks one at all).

I won't take care anymore of this article, as long as ignorance prevails. revised 07:39, 9 March 2019 (UTC)Purgy (talk) 19:43, 8 March 2019 (UTC)

I agree with Gah4 and Purgy about the equation for nonlinear inductance. I think it should be put in the 'Source of inductance' section, but it seems to me that the equation ${\displaystyle v=\frac{d}{dt}(Li)}$ is unnecessary in the introduction, and the more familiar equation for linear inductance ${\displaystyle v=L\frac{di}{dt}}$ should be there. --Chetvorno^TALK 20:11, 8 March 2019 (UTC)

Thanks all. I thought I asked about it here earlier, but it seems to have been archived. Since it mostly goes with solenoids, the later sections which discuss solenoids would be appropriate. Gah4 (talk) 07:33, 9 March 2019 (UTC)

@Purgy Purgatorio:@Gah4: Thank you for bringing up this important point which is missing from the article. I just wanted to clarify that I think this issue, and Purgy's equation, should definitely be in the article. It is not only important in solenoids with moveable cores, but also in inductors which operate in the nonlinear portion of the ferromagnetic BH curve, like magnetic amplifiers. A form used with these inductors is

${\displaystyle v=\frac{d\varphi }{dt}=\frac{d}{dt}(Li)=i\frac{dL}{dt}+L\frac{di}{dt}=(i\frac{dL}{di}+L)\frac{di}{dt}}$

It is just that if we include the nonlinear equation in the introduction, it is going to contradict our definition that inductance is the ratio between induced voltage and rate of change of current, which is valid in the vast majority of cases. Maybe when we give the linear equation ${\displaystyle v=L\frac{di}{dt}}$ in the introduction, we could add a mention that this equation is not valid in some ferromagnetic inductors in which the inductance is not constant with current. --Chetvorno^TALK 07:47, 10 March 2019 (UTC)

Cable Inductance Calculation

To my understanding, variations of inductance in a setting are caused (in all mentioned cases), either by a change in geometry (relay), or by a change in material properties (ferromagnetics). They do not depend immediately on effects of induction. E.g., the inductance of an activated relay changes in the same way, whether it is deactivated electrically or dropped by hand. The relay has different inductance, depending on the position of the relay armature, not on a current flowing or not. Magnetizability, and thus inductance, may change by temperature, also independently of currents and other flows. This brings me back to the fundamental confusion of inductance and induction, sadly by some even extended to the dual notion of 'capacitance' (which is also just a property, fully determined by geometry and material), and which must be repaired in the current lead. I won't try to do this again.

I think it is fully appropriate to mention both a generally time-dependent and a current dependent inductance (now we have the chain rule too ;) ; as an aside: who dares to talk consistently about an explicit time dependence ${\displaystyle L(t,i)}$ with ${\displaystyle i=i(t)}$?), however, I insist on claiming the inductance not conceptionally depending on EM-quantities, leaving it safely as proportional factor (may be not a constant one).

I also agree to the vast majority of cases being those where the notion of inductance is especially handy for dealing with discrete, concentrated, not moving components (wires, coils, transformers, ..) at low frequencies. I am not briefed in a treatment of inductance in the context of radiation. The above, imho useful quote, was also removed recently. Purgy (talk) 14:17, 10 March 2019 (UTC)

Actual physical explanation? The article has none.[edit]

The article does not even mention how inductance emerges from a bunch of electrons and protons. It seems to be stuck in outdated oversimplified and incomplete models from two centuries ago, before relativity and quantum physics were a thing. And it talks about laws, leaving it at that, and expects readers to blindly accept those like ”magic“ rules, not to think about.

Nowadays, everyone learns relativity and basic quantum physics in school. And inductance is really not hard to actually explain. On that level!
I would at least have expected the reasoning to include how a magnetic field is just an electric field under relativistic motion. But … nothing of that kind is even mentioned.

What a sad joke state this article is in … — 109.40.66.25 (talk) 11:43, 6 May 2019 (UTC)

Everyone learns relativity and basic QM, but most not to the point to explain inductance. Note that magnetism itself is completely due to special relativity, yet that is rarely explained. Well, not quite two centuries, but back close to Maxwell and his equations. One book that well explains the connection between magnetism and relativity is Purcell.^[1] That is the 3rd edition, which uses SI units. The connections of relativity are a little more obvious in Gaussian units, though. If you can find a 2nd edition, that might also be nice. Otherwise, yes, blindly accept the rules is usual. Gah4 (talk) 09:20, 3 July 2019 (UTC)

References

1. ^Purcell, Edward (January 21, 2013). Electricity and Magnetism (3rd ed.). Cambridge University Press. ISBN978-1107014022.

sign[edit]

I reverted a sign change, as it didn't change the sign in the equations that come before and after. It seems that the sign is related to Lenz's law. More obvious to me, the sign should be the same as the sign of a positive resistor in place of the inductor. Gah4 (talk) 17:53, 2 July 2019 (UTC)

No comments on this one. As well as I know, either sign works as well as the other. It just depends on the way you define voltage and current. In other words, which meter lead you hook up to which end. Gah4 (talk) 09:22, 3 July 2019 (UTC)

The rationale for the negative sign is to remind that the emf is opposing the change of current (as stated by Lenz's law). However, this has never made much sense to me from a circuit analysis perspective; the voltage across passive components is always defined in the direction that opposes the current. The negative sign can be read as meaning that the voltage arrow should be drawn in the same direction as the current when the current is increasing – which is clearly wrong. We don't put a negative sign in Ohm's law so putting one here makes the constitutive relations incompatible with each other in a circuit analysis of a complete circuit. That generates more confusion than elightenment. SpinningSpark 16:46, 3 July 2019 (UTC)

Sorry, was away from Wikipedia. @Gah4: I personally like your idea of defining the variables to give the constitutive equation a negative sign, to represent Lenz's law. However, that is not consistent with the equation in most textbooks. The reason, and the reason I changed the sign, is that I believe the sign in the constitutive equation is determined by the passive sign convention. According to the passive sign convention, the direction of the current ${\displaystyle i}$ and voltage ${\displaystyle v}$ variables in a component must be defined so positive current enters the terminal designated as positive voltage. If you look at the direction of back EMF ${\displaystyle v}$ created in an inductor with ${\displaystyle di/dt>0}$ it is positive according to the PSC, so in order for the inductance ${\displaystyle L}$ to come out positive, the constitutive equation must have a plus sign (${\displaystyle v=L[di/dt]}$). The inductance of a passive component must always be positive (negative inductance is possible but requires an active circuit). I believe Spinningspark's argument is equivalent to this. --Chetvorno^TALK 23:07, 3 July 2019 (UTC)

That's absolutely right. The negative sign is using the active sign convention in which positive current flows out of the positive end of the voltage. Since current is not actually flowing in that direction then the sign has to be negative. If we want to use that convention, then the voltage should be designated e(t) rather than v(t) to show that we consider it an emf of a source, not a voltage drop across a passive component. On Gah4's argument that the article has to be consistent, the body of the article 100% consistently uses a positive sign for L di/dt terms. Chetvorno's edit actually made the lead consistent with this and Gah4's reversion restored the inconsistency. The only place a negative sign is used for dφ/dt terms is when it is first introduced. It is subsequently dropped in 100% of cases. In light of that, I am in favour of restoring Chetvorno's edit and removing any other inconsistencies. SpinningSpark 17:54, 4 July 2019 (UTC)

My concern at the revert, was that there were three equations together in the section, but only one was changed. As the equations are connected, they have to change consistently. I suppose they should also be consistent across the article, but I hadn't got that far. Eventually, the inductance and capacitance equations have to be consistent, which I think means opposite sign. Even more, the sign of an RLC circuit has to be consistent with Lenz's law. Without a complete circuit, the signs are somewhat arbitrary. Gah4 (talk) 20:34, 4 July 2019 (UTC)

What three equations? There is only one equation line in the lead. It has two minus signs, both of which were changed in Chetvorno's edit. I also support the simplification of the form of the defining equation – using an inverse power makes it unnecessarily harder to understand.

Eventually, the inductance and capacitance equations have to be consistent, which I think means opposite sign. No it doesn't. SpinningSpark 21:34, 4 July 2019 (UTC)

OK, the one with three equations is: Inductance#Source_of_inductance. Which ones does this have to agree with? Gah4 (talk) 23:43, 4 July 2019 (UTC)

There are two different things there as I pointed out in my previous post. Obviously, the expression for v(t) in the lead should be consistent with the v(t) expressions in the body, ALL of which are positive. The expression with the dφ/dt term does not involve voltage so is irrelevant. I'm still thinking about that one, but as I also pointed out above, that one is inconsistent with the rest of the dφ/dt terms in the article, being the only one that is negative. SpinningSpark 20:59, 5 July 2019 (UTC)

Inductance Calculation Formula