Talk:Inductance/Archive 4

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Archive 4

dL/dt

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.

$v=L{di(t) \over dt}.$ 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:

$v={dL(t)i(t) \over dt}.$ 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.

$v={dL(t) \over dt}.{di(t) \over dt}.$ 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:

$v=L(t){di(t) \over dt}.$ (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)

I said chain rule above, but it is actually product rule. That page explains it pretty well. And while $v=L(t){di(t) \over dt}.$ 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.

${\frac {d(L\cdot i)}{dt}}=(L\cdot i)'={\overset {\bullet }{(L\cdot i)}}=L\cdot i'+L'\cdot i=L\cdot {\dot {i}}+{\dot {L}}\cdot i=\;...$

A second $T^{-1}$ would result from $L'\cdot i',$ which was never proposed.

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 $v={d \over dt}(Li)$ is unnecessary in the introduction, and the more familiar equation for linear inductance $v=L{di \over dt}$ 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

$v={d\phi \over dt}={d \over dt}(Li)=i{dL \over dt}+L{di \over dt}=(i{dL \over di}+L){di \over dt}$

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 $v=L{di \over dt}$ 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)

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 $L(t,i)$ with $i=i(t)$?), 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)

Inductance of elementary objects

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 ($0\cdot \infty$) 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)

Actual physical explanation? The article has none.

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. 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

sign

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 $i$ and voltage $v$ 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 $v$ created in an inductor with $di/dt>0$ it is positive according to the PSC, so in order for the inductance $L$ to come out positive, the constitutive equation must have a plus sign ($v=L[di/dt]$). 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)

U

A recent edit has the summary (Changed from "U" to "E" in formulas for magnetic energy stored in Inductance. Reason: Not to mix energy up with voltage (commonly written with U) also E is most common for energy.). As well as I know, E is used for voltage more often that U, but I don't know either enough to cause the confusion indicated. U is common for energy in thermodynamics, but otherwise E gets confused with electric field. Was it really that confusing before? Gah4 (talk) 13:59, 8 October 2019 (UTC)

The Feynman Lectures uses upper case U. Haliday, Resnick and Walker, 6th ed uses upper case U. Jackson 3rd ed uses lower case u and upper case E on the same page, Hayt in Engineering Electromagnetics uses upper case W and in Engineering Circuit Analysis uses lower case w. Griffiths uses upper case W. Kraus in Electromagnetics uses upper case W. I guess I would stick with upper case U since that is what is in the article, but I could support changing to upper case W (for work). Constant314 (talk) 22:02, 8 October 2019 (UTC)

We've had this before on other articles with European editors trying to change to U for voltage. U seems to be common in Continental sources, but it is rare in English sources. English Wikipedia should stick to common English notations. I don't support a change to W. That is most commonly used for "work done", which is clearly inappropriate in this case since no work is being done. SpinningSpark 22:28, 8 October 2019 (UTC)

Hat note distinguish

I find the hat note "Not to be confused with electromagnetic induction," produced by template distinguish inappropriate, because that term is in fact closely related to the subject at hand, while certainly not the same. The lede already has a link to that topic and explains it as one of the causes of inductance. So the reader ought not to be directed away from the article prematurely. The template does not appear helpful for casual or novice readers of physics or electronics, rather it appeals to people fond of hair splitting or similar attitudes. Other terms could as well be tagged in the same unhelpful manner. It appears more helpful to let readers read two or three sentences to be informed better. The template ought to be only used when there is danger of confusion because of subtle spelling differences of unrelated topics. Kbrose (talk) 15:39, 29 July 2020 (UTC)

Agree. The distinguish is inappropriate and should be removed. Constant314 (talk) 17:34, 29 July 2020 (UTC)

Agree. --Chetvorno^TALK 18:29, 29 July 2020 (UTC)