Talk:Inductance/Archive 2

Archive 1

Archive 2

Archive 3

Archive 4

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 2000 Prof. 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. SpinningSpark 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 $V(t)=V_{0}cos(\omega t)$ be the voltage generated by the AC generator. It follows that the current $I(t)={\frac {V_{0}}{Z}}cos(\omega t-\delta )$, where the impedance $Z={\sqrt {R^{2}+(\omega L)^{2}}}$ and the phase constant $\delta =tan^{-1}({\frac {\omega L}{R}})$. The voltage drop across the inductor, $V_{L}={\frac {\omega LV_{0}}{Z}}sin(\omega t-\delta )$. 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)

My elderly Tipler "Physics" on pp. 889-890 says, in part,

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.

Advantages of this definition is that it doesn't talk about changing currents and voltages, it puts mutual inductance on the same level as self-inductance, it's a geometrical property and not something that only appears when we decide to change the current, and that it is referenced. Disadvantage is that it is too long for one sentence, and that it drags in the abstract notion of "magnetic flux", though if you buy into the existence of electric currents, an abstract notion like "flux" should not trouble you much more. --Wtshymanski (talk) 16:30, 6 May 2012 (UTC)

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) and any nearby circuits (mutual inductance). This effect derives from two fundamental observations of physics: First, that a steady current creates a steady magnetic field (Oersted's Law) ; second, that a time-varying magnetic field induces voltage in a nearby conductor (Faraday's law of induction). From Lenz's law, 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).

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

$L={\frac {\phi }{I}}\,$

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

${\mathcal {E}}={\frac {d\phi }{dt}}\,$

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

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

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 ${\mathcal {E}}={\frac {d(LI)}{dt}}=L{\frac {dI}{dt}}$, but ${\mathcal {E}}={\frac {d(LI)}{dt}}=L{\frac {dI}{dt}}+I{\frac {dL}{dt}}$. 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 $L=\phi /I\qquad \,$ 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)

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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)

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[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)

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)