Talk:Inductance/Archive 3

Archive 1

Archive 2

Archive 3

Archive 4

Units

where v(t) denotes the voltage in volts across the circuit, and i(t) the current in amperes through the circuit. The formula implicitly states that a voltage is induced across an inductor, equal to the product of the inductor's inductance, and current's rate of change through the inductor.

Seems to me that the equation should be true independent of the units for voltage and current. One could, for example, use statvolts for voltage or abamperes for current. Does it need to specify the units for v(t) and i(t)? Gah4 (talk) 21:11, 12 August 2015 (UTC)

That's true. Kbrose (talk) 22:08, 12 August 2015 (UTC)

Same point. It is misleading impressive noise. radical_in_all_things (talk) 14:59, 21 August 2015 (UTC)

Per unit length

It should be "per length" instead of "per unit length" everywhere in the article. The unit doesn't matter. It has been argued that "per unit length" would imply the derivative, but "per unit length" simply doesn't say this and unnecessarily restricts the imagination. When you calculate a quantity per length you can take any length, say an infinitesimal if you like. This is much more straightforward. Even if "per unit length" somehow would imply the derivative, the article talks of transmission lines and cylinders. radical_in_all_things (talk) 15:17, 21 August 2015 (UTC)

It is a commonly-used idiom which clarifies the math. If you divide a quantity by a length, you get the amount of that quantity in a unit length. --Chetvorno^TALK 17:42, 21 August 2015 (UTC)

There are about 14 times as many google hits for "inductance per unit length" as for "inductance per length", as, yes, that is the idiom for it. Which imagination is restricted by "per unit length"? I don't understand that part. You can use any length unit you want, that is the whole point. Gah4 (talk) 21:05, 21 August 2015 (UTC)

Mentioning a unit is superfluous ("You can use any length unit you want"). It is the type of dimension that matters (lenght). A google count is irrelevant here, if this were an argument there wouldn't be any change ever. Think of defining density as "mass per unit volume" or speed as "meter per unit time". Why not "unit meter per time" or "unit meter per unit time??"? Speed is "lenght per time". The rest is done automatically by the unit system, which luckily we have. It is illogical, superfluous and obsolete to mention units in definitions. A similar point is in the discussion above. radical_in_all_things (talk) 10:08, 22 August 2015 (UTC)

I do not think that it is superfluous. The meaning of per in an English sentence is for each. So, stating capacitance for each length is not clear and rather awkward, as it would be to say driving at 60 miles per time. Instead one uses 60 miles per hour, or equivalently 60 miles per unit time. Capacitance per length is a dimension, not a measurement. Alternately, the statement of capacitance per length is an extensive property, it depends on the length of the lines, while capacitance per unit length is intensive, meaning independent of the total length of the line. Kbrose (talk) 03:14, 23 August 2015 (UTC)

Regardless of the semantics, "per unit length" is the proper English form. SpinningSpark 23:48, 4 September 2015 (UTC)

Alternately, the statement of capacitance per length is an extensive property, it depends on the length of the lines, while capacitance per unit length is intensive, meaning independent of the total length of the line. This is the important part that I was not explaining well above. It isn't just the length divided by the capacitance, which some might call capacitance per length, but the capacitance divided by the length, at each position, in the limit that the length goes to zero. Gah4 (talk) 18:27, 9 September 2015 (UTC)

Even if it varies continuously, distributed capacitance is still measured by the amount of capacitance a unit length of the line would have, in whatever system of units is being used. For example, in SI, the units that distributed capacitance is measured in are farads per meter. Since the meter is the unit of length in SI, the generic name for distributed capacitance is capacitance per unit length. --Chetvorno^TALK 20:37, 9 September 2015 (UTC)

Negative mutual inductance/coupling coefficient?

When reading the section Mutual inductance of two wire loops, I would say that, depending on the definition of the direction of the contours, L may be positive or negative. Indeed, this corresponds with my memory (this answer to Q15.6).

If self-inductances can only be positive (this answer to Q15.14), then the coupling coefficient k can be, generally negative (from -1 to +1, I'd say). Am I mistaken?

If not, I suggest we change that: k -1 ≤ k ≤ +1.

Should we make other edits too, to keep the article consistent? Sjoerdoptland (talk) 17:54, 16 November 2015 (UTC)

Constant

The coefficients of inductance are constant, as long as no magnetizable material with nonlinear characteristics is involved. They can also be not constant if parts of the circuit move. We don't tend to think about that, as it isn't the usual way to build circuits, but should we say it here? Gah4 (talk) 16:33, 12 March 2016 (UTC)

If you can understand this article, you don't need to be reading it

This article is a prime example of the Wikipedia Paradox, to wit: If you can understand the article, you don't need to be reading it. Articles like this one may be technically correct, but are not written at a level that the layperson can understand. rowley (talk) 19:26, 2 May 2012 (UTC)

A common problem. Could you give some for-instances of where it goes off into the deep grass? --Wtshymanski (talk) 20:42, 2 May 2012 (UTC)

Never mind, whoever wrote "Inductance here is a symmetric matrix. The diagonal coefficients Lm,m are called coefficients of self inductance, the off-diagonal elements are called coefficients of mutual inductance. The coefficients of inductance are constant as long as no magnetizable material with nonlinear characteristics is involved." is far too clever to be wasting his time writing encyclopedia articles. In the lead, forsooth. --Wtshymanski (talk) 20:46, 2 May 2012 (UTC)

They are describing the mathematical formula above what is written. The fact that your understanding of mathematics does not extend to the level presented, comes as no surprise. In fact your understanding of everything engineering related falls far short of what is required to even think about editing an encyclopedia (as you continually demonstrate - but would never admit).

Jmrowland has a very legitimate point. While the the equation was described, they did not explain it. Equations describe relationships and those relationships can be described in common language without referring to an equation. Us unwashed non academic morons come here to understand things. I did not come here for a test answer but to understand the interaction of electricity and magnetic fields. I understand the equations and can work with them but this is a poor article for anyone trying to understand the subject matter.

Any reader who is not interested in, or unable to comprehend the more advanced material is free to skip it and move on to the next bit. 109.145.22.224 (talk) 14:54, 3 May 2012 (UTC)

The concept of Inductance is not advanced material but offers opportunities for acedemics to make themselves look smart by not explaining simple relationships in common language. Of course the equations are essential for an encyclopedia article but should not replace an explanation of the concept.

Assuming, arguendo, that I am such an ignoramus, then why isn't this article more accessible to me as presumably an ill-educated person in search of knowledge? The extreme of this position is to redirect everything to Maxwell's Equations - implicit in those chilly lines of runic symbols is everything that can be known about electromagetism. (Instead of spending four years to get an electrical engineering degree, we could instead just hand each new postulatant a business card with Maxwell on one side and his degree on the other! Think of the savings!)

However, for us lesser intellects not blessed with God-like mathmatical intuition, we must make do with approximate explanations in words. That's why we come to an encyclopedia, instead of dropping in on an underaduate level physics course half-way through the term. --Wtshymanski (talk) 15:04, 3 May 2012 (UTC)

I made no assumptions whatsoever on your level of understanding. It is an established fact from your continued disruptive editing and your attitude to others and your erroneous belief that you are right and every one else wrong.

"Most editors are here to hurt the encyclopedia, not to help it."

- Wtshymanski

If I want to check up on (say) the Derivation from Faraday's law of inductance, I know where to go. The fact that you were probably unaware that there even was a Faraday's law of inductance, or can't understand the derivation is no reason to remove it from an article. If you don't understand it, and you are not interested, skip over it, and move to something that you can understand (which I would imagine is the date and time the page was last modified). — Preceding unsigned comment added by 109.145.22.224 (talk) 15:21, 3 May 2012 (UTC)

I agree. I'm learning about inductance from a textbook (Gibilisco). I looked at this article to maybe pick up some different perspective, as another source. I was disappointed. Maybe the article is helpful to someone, somewhere. But for the most part, I would call it pretty badly written. BTW, I have a strong math, science, and writing background. wikipedia is great with various kinds of current cultural trivia. But there is something about wikipedia that can lead to bad results, especially with technical topics. 71.212.122.165 (talk) 03:29, 15 July 2012 (UTC)

The personal attacks need to stop. --Chetvorno^TALK 06:07, 15 July 2012 (UTC)

Even an expert can use a refresher from time to time. Even if the article is incomprehensible to the average reader, if it contains good equations and techniques in a readily readable form, it has great value. The goal of educating the ignorant is an ideal but perhaps beyond the scope of an encyclopedia. — Preceding unsigned comment added by RDXelectric (talk • contribs) 03:25, 4 November 2016 (UTC)

It is true that experts need a reference, and this should be that reference. But it also needs to have enough for beginners to understand. Beginners should know that they won't understand the whole thing at first. Even so, there are some prerequisites. Gah4 (talk) 06:00, 4 November 2016 (UTC)

Inductance of a Solenoid

Two dramatically different equations for the inductance of a solenoid are given in this article. In the section Inductance of a Solenoid the equation: $\displaystyle L=\mu _{0}N^{2}A/l.$ is given. This is the typical equation which is given in any freshman physics course, and what anyone who just wants a quick approximation of the inductance of a solenoid will use. In the section Self Inductance of Simple Electrical Circuits in air the much more complicated equation:

${\frac {r^{2}N^{2}}{3l}}\left\{-8w+4{\frac {\sqrt {1+m}}{m}}\left(K\left({\sqrt {\frac {m}{1+m}}}\right)-\left(1-m\right)E\left({\sqrt {\frac {m}{1+m}}}\right)\right)\right\}$ $={\frac {r^{2}N^{2}\pi }{l}}\left\{1-{\frac {8w}{3\pi }}+\sum _{n=1}^{\infty }{\frac {\left(2n\right)!^{2}}{n!^{4}\left(n+1\right)\left(2n-1\right)2^{2n}}}\left(-1\right)^{n+1}w^{2n}\right\}$
$={\frac {r^{2}N^{2}\pi }{l}}\left(1-{\frac {8w}{3\pi }}+{\frac {w^{2}}{2}}-{\frac {w^{4}}{4}}+{\frac {5w^{6}}{16}}-{\frac {35w^{8}}{64}}+...\right)$ for w << 1
$=rN^{2}\left\{\left(1+{\frac {1}{32w^{2}}}+O({\frac {1}{w^{4}}})\right)\ln {8w}-1/2+{\frac {1}{128w^{2}}}+O({\frac {1}{w^{4}}})\right\}$ for w >> 1

is given. This is an equation which is more accurate, but is enough more complicated that it seems beyond the typical scope of an encyclopedia article. Either one of these equations should be deleted, or the differences between the equations should be better explained in the article. — Preceding unsigned comment added by 155.13.48.129 (talk) 22:25, 25 January 2013 (UTC)

Here's something strange--if this is correct: "Ignoring end effects the total magnetic flux through the coil is obtained by multiplying the flux density B by the cross-section area A and the number of turns N," then wouldn't resulting equation have N squared? — Preceding unsigned comment added by 76.126.255.148 (talk • contribs) 05:19, 10 June 2013 (UTC)

The above formula does not work out to an accurate value of inductance but seems to be way off for some constructions as compared to several other formulas that have been used in electronic work for years. It does not even produce the same value as the formula that follows next. The original author should get back here and post a source for this one and possibly look at it again and try to correct it using the original source as reference, possibly after tracing that back to it's origins also.

A second problem is that the form of E(x) is not given, and there are two different forms, one is E(k) and the other is E(m) where m=k^2, and we should know which form is being used in order to get the right results. — Preceding unsigned comment added by 74.105.23.56 (talk) 09:58, 20 April 2017 (UTC)

Definition

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

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

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

Inductance [lead]

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

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

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

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

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

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

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

Geometry of inductance

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

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

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

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

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

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

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

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

Maxwell's equations

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

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

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

$\mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\int _{C}{\frac {Id{\boldsymbol {\ell }}\times \mathbf {r'} }{|\mathbf {r'} |^{3}}}$

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

Mutual inductance of two wire loops

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

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

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

Oh, I forgot, the final setup is a

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

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

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

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

'azimuthal'? What's that?

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

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

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

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

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

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

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

Mutual inductance: Equivalent circuits: π-circuit

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

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

sum

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

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

$dW=\sum \limits _{m}^{K}i_{m}v_{m}dt=\sum \limits _{m=1}^{K}\sum \limits _{n=1}^{K}i_{m}L_{m,n}di_{n}$

$W(i)=\int {1 \over 2}\sum \limits _{m=1}^{K}\sum \limits _{n=1}^{K}i_{m}L_{m,n}di_{n}={1 \over 2}\sum \limits _{m=1}^{K}\sum \limits _{n=1}^{K}\int i_{m}L_{m,n}di_{n}={1 \over 2}\sum \limits _{m=1}^{K}\sum \limits _{n=1}^{K}i_{m}L_{m,n}i_{n}$

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

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

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

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

Self-inductance of a wire loop

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

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

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

I just saw a source that underlined the double integral, and stated that its dimension was length, and it's magnitude, $l$. I had already surmised that the integral must collapse to some function of length or perimeter of the loop if length >> radius of conductor. Magnetic field strength declines as the square of the distance from current source, right? Is that still true for a point-to-point vector? The integral sums point-to-point vectors and treats the decline as linear (x -x'); the resulting integrated quantity is logarithmic. What happens when the loops are "infinitely close"? The transverse distance between loops is meaningless, constant or not. So the integration is constrained by another condition, |s-s'|>a/2 which in the original text was erroneously stated as |x-x'|>a/2. s is an axial separation, not transverse, because the vector can't get too short or we have the infinity problem all over. So "arcs" of the integrand are missing. Therefore, we need to add back in some function of length to fix it. That's ${\frac {\mu _{0}}{4\pi }}lY$ it seems. Ostensibly, this must represent the flux inside the wire, because when there is no current inside the wire, there is no flux, and the length term disappears. When the current is uniformly distributed over the cross-section of the wire, the term is ${\frac {\mu _{0}}{4\pi }}l/2$. This term isn't ignorable, or we wouldn't need it; the cited source doesn't mention any bounding conditions, so may we assume that in the limit, this length term is the whole integrand? Now, what is that limit?

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

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

Shielding Back EMF

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

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

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

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

Self-inductance of thin wire shapes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Mutual inductance of two parallel straight wires

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

Notes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

@Sbalfour: Here are my feelings about the above points:

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

--Chetvorno^TALK 22:02, 12 December 2017 (UTC)

Ok, lets whack the matrix math, and restructure the mutual inductance stuff down into a section following the main article. I like that idea. I'm buying time here to determine where to put my effort, so do whatever you can. Sbalfour (talk) 23:38, 12 December 2017 (UTC)

May as well plug in your 2 intro sections, to give the revamped article a foundation. I'll figure out how to merge the rest of my lead into it later. You replicated a chunk of history that would be the start of a History section, so could structure it into a third section following your intro. Sbalfour (talk) 23:53, 12 December 2017 (UTC)

Done. --Chetvorno^TALK 23:41, 13 December 2017 (UTC)

Is it really necessary to remove the matrix representation section? I feel like it's just a small, unobtrusive section which clearly mentions in which context it is useful (2-port parameters), so that the uninterested can skip ahead onward. If you understand 2-port parameters, the z-parameter representation of mutual inductance really helps the reader to understand it in a very concise and clear way. At least for me, that's how I finally understood how mutual inductance "behaves". I suggest to bring it back. Nijoakim (talk) 11:33, 5 July 2018 (UTC)

Since noone objected, I re-added the short section for the matrix representation for mutual inductance. If you don't agree with this change, feel free to discuss it here. Nijoakim (talk) 09:50, 12 September 2018 (UTC)

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

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

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

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

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

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

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

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

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

big or small

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

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

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

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

Relation between inductance and capacitance

For high-frequency transmission lines, $\displaystyle L'C'={\varepsilon \mu }.$ where ε and µ denote the dielectric constant and magnetic permeability of air.

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

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

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

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

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

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

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

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

Unitism

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

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

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

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

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

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

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

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

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

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

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

Inductance vs induction

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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