# Talk:Permeability (electromagnetism)

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## From PNA/Physics

• Permittivity, permeability - these should be explained more thoroughly; in particular, it's unclear what any of these mean. --[[User:Eequor|ᓛᖁ]] 14:36, 6 Nov 2004 (UTC)

## Numerical Value of Permeability in Free Space

Does somebody understand where 4 * pi * 10 ^ -7 comes from? 4 * pi is obviously the standard expansion factor of an eculidian universe, but the 10 ^ -7 is unexpected.

Here's my guess: the 4 * pi shows up whenever you try to do spherically or cylindrically symmetric surface integrals in 3 dimensions, and where it appears is a matter of convention. It shows up in the permeability so some other expression will appear cleaner. The 10^-7 arises through the old SI definitions which make the ampere be the amount of current such that two parallel wires carrying it, spaced at 1 meter, will feel a force of 1 newton/meter length. The ampere is inconviently large (because the coulomb is); the 10^-7 is needed to match up these large currents with the smallish magnetic force.
--Vortmeester
I saw this and had to comment on the phrase "has the exact value 4π×10−7 N·A−2." This is not true. The permeability of free space has the aproximate value 4π×10−7 H·m−1 (Henries per meter being equivalent to Newtons per square Ampere), but the exact value is 1.25663706143... H·m−1. Similarly the permittivity of free space is approximately (36π×109)−1, or exactly 8.854187... F·m−1. The convenient upshot of these approximations is 1) they are highly (but not exactly) accurate, 2) the intrinsic impedance of free space becomes approximately 120π, 3) the speed of light in a vacuum becomes 3×108 m·s−1. Obviously, as the meter is now defined so as to make most measurements of the twentieth century exactly accurate (that is, so that the vacuum speed of light is exactly 299,792,458 m·s−1), these values for permittivity and permeability in free space cannot be exact. They are, however, very convenient for engineering work. -- Charles Robertson; no User page on wikipedia. —The preceding unsigned comment was added by 72.177.69.176 (talk) 01:14, 3 April 2007 (UTC).
Well then according to your logic if we by definition make the meter, Newton, and Amp exactly these values than the given values for permittivity and permeability are by definition exact. -134.50.3.138 (talk) 00:19, 8 February 2008 (UTC)
The value 4π×10−7 N·A−2 is exact. There is only really one experimentally determined constant in electromagnetism, that being the speed of light. The permeability of free space is fixed at exactly 4π×10−7 N·A−2 and any uncertainty is carried by the permittivity of free space.70.253.89.209 (talk) 16:45, 17 September 2008 (UTC)
The Ampere is older than SI and even CGS. Specifically, the Ohm is the decade-emu closest to the Siemens Unit (a resistor, 1 mm² by 1 m of Hg), the Volt being closest decade-emu to the Daniels Cell. By Ohm's law, V=IR defines the Ampere. Maxwell showed in 1873, that the practical volt-ohm-second system are the emu of a system where the length is a quadrant (10,000 km), the mass unit is 10 picograms, and the second. The value of the constant is 1 henry per quadrant, and is thus 10-7 henry/metre because the metre is 10-7 quadrants.
The ampere, having a definition outside of the SI, for being incorporated into SI, comes with a decade value because the SI itself is a decade-multiple of the quadrant 10-11gram second system. The value of 4 pi comes from a kind of rationalisation that preserves charge and current. A different rationalisation, which gives the same formulae, but preserves the permeability and permittivity, is used in the heaviside-lorentz system. --Wendy.krieger (talk) 08:02, 4 October 2011 (UTC)

It comes from the definition of the ampere. The current definition of the ampere is based on a formula that involves the permeability of free space. Because the result of that formula is defined to be a fixed number (2 x 10-7 Newtons, in order to define the amp), it makes the permeability of free space a fixed number as well. The 4 pi comes from that formula also. The 10-7 in that formula is just the choice they made historically for setting the size of the amp; like when they defined the g, they foolishly made it 10-3 times anything useful at the time, which is why we now use kg instead.

The current definition of the ampere is really just a stupidly convoluted way of defining the amp by fixing the value of the permeability of free space. It would be better to do that directly, instead of invoking a complicated experimental setup to generate a formula that involves it.

The proposed new definition of the ampere is based on assuming a fixed value for e (the electric charge), instead of for the result of that formula. If they use that definition instead, the permeability of free space is no longer involved in the definition, and so is no longer forced to be a constant. This is because there is no formula for e that just involves the permeability of free space and defined constants; there is no known formula for the fine-structure constant that doesn't include e, and its value must therefore be found by experiment. — Preceding unsigned comment added by 94.196.243.2 (talk) 11:33, 13 March 2016 (UTC)

## History of the Ampere

History of the Ampere

The factor of 10^-7 arises mainly because of the transition from CGS to SI units.

10^-5 going from a dyne to a newton of force.
10^-2 going from an abampere to an ampere (because it flows in both conductors).

Or something like that.

The "practical units of electricity" have nothing to do with cgs (since they are older than cgs in any case). The practical electrical units displaced older ones like 'a geographic mile of no. 6 copper wire', and various cells of particular construction. The new system did not prevent the old constructions, but stated that the results should be expressed in terms of a particular decade-multiple of the metric-electrostatic system. The system in use at the time was Metre-gram-second.

The size of the resistance unit (ohm) was selected to be as near that of the siemens unit (a column of mercury, 1 mm² in section, and 1 metre long), and the potential that nearest the daniels cell. Maxwell showed that the required system to make this happen was to have a length of 10,000 km, and a mass of 10 picograms, along with the second. The value of 10-7 comes, because the henry (in emu, a length of 10,000 metres), gives 1 henry/(10,000 km), or 10-7 henry (ie 10,000 km) / metre.

The 'practical' bit was because they were intended to be used in practical use, like wiring up houses etc. They were always intended to be perfect multiples of the theoretical EMU. It's much like the practical unit of speed is km/h or mph, while the theoretical unit is m/s or f/s. The former is practical for driving cars, the latter is the 'coherent unit'.

The 'international' bit is to deal with the constructions outside of the definition. This has nothing to do with the intended size of the unit, but what is the 'best way' of creating measures that could be used for calibration etc. In much the same way, one hears talk of 'conventional', which refers to the most exact way of producing units. The errors in the CODATA tables is due to the inexactutde in reproducing the theoretical definitions from the implementations, not from the implementation themselves.

A proposal exists to redefine the ampere as x electrons per second, and the kilogram in terms of planck's constant. Under such a definition, the size of the permittivity constant comes to errors in the fine structure constant, since the resistance unit will become h/e², which is 137.036 times the current resistance of 29.9792458 (ie 10-7 c). The permeability will then have an error equal to that of that of the fine structure constant. 08:36, 4 October 2011 (UTC)Wendy.krieger (talk)

## Definition of Absolute Permeability

I'm concerned about the definition of 'absolute permeability' being given synonymously with mu0. Absolute permeability is sometimes used in the SI, but not in the CGS system. All text books that I have read, eg Cheng's 'Fundamentals of Engineering Electromagnetics' define absolute permeability as the ratio of B to H in any medium you care to choose (a vacuum included). It's purpose is to reinforce the distinction with 'relative permeability' by which it differs by the factor 4 pi 10^-7.

In short, mu0 is an absolute permeability, but not all absolute permeabilities are mu0. Absolute permeability is a synonym for 'permeability', at least in the SI.

Bright Engineering > Physics

RAClarke 10:02, 2 October 2005 (UTC)

mu0 is the permeability in vacuum. In gaussian, heaviside lorentz and electromagnetic systems, this is defined to unity, and may be ommitted from the formulae. mur is dimensionless in all cases, is a relative permeability, relative to vacuum. mu = murmu0 is like density = s.g × water. Still.
The value of 10-7 comes from the fact that metre, kg, second and ampere were all previously defined as decade-multiples of an electromagnetic system, and the decade appropriate is 10-7. The 4pi comes from a change of formulae from flux from a radiant source (which is what coulomb's inverse law is), to flux measured by Gauss's law (flux = charge). When charge and current are preserved (as would happen here), then a 4pi pops up in the permeability system.
Wendy.krieger (talk) 08:45, 4 October 2011 (UTC)

i shall assume by the two units given ( mu0 and 10-7 ) that here is where i shall put the comment. this is in regards to the two columns. i would like to state that the two are so simular that they are the same (for those who dont know). i found that for many, the difference is that one is 800,000x the other - but if the vacuum figures are the benchmark then the number is 795,774.691x. the H/m uses more digits accuracy. nickel is the odd one out (out of the ones i tested), the mu0 is 700, not 100-600 (may be due to different test field strengths?). Charlieb000 (talk) 08:56, 17 April 2012 (UTC)

## μ vs µ

I don’t know what difference it makes, but μ and µ are two different characters. The only difference I see (and only in some fonts) is that µ is slanted and μ isn’t. In the Unicode character palette, µ (0x00B5) was found under Symbols > Letterlike Symbols, and μ (0x03BC) under European Scripts > Greek. I changed all the mus in the article to the former, which is the one I can type (option-M on a Mac). If it makes any difference and I’m in the wrong, change them all to the other μ. —Frungi 06:58, 29 September 2006 (UTC)

U+00B5 is "MICRO SIGN", so I think when you say "μ = 1.26 µN A-2", the first μ should be U+03BC because it's the Greek letter being used as a variable, but the second µ should be U+00B5 because it stands for 10−6. —Keenan Pepper 06:31, 30 September 2006 (UTC)

## Usage of the word "resulting" in the following

If one puts the ferromagnetic material into an externally applied magnetic field, the domains tend to line up, so that the sum of the fields from the ferromagnet and the resulting magnetic field is higher in magnitude than the applied magnetic field alone.

I suggest that the word "applied" would make more sense, otherwise it could be read that the ferromagnet field is included twice. Alternatively, it could be rewritten "so that the resulting magnetic field is higher in magnitude than the externally applied magnetic field alone." I have not made the change as this needs to be confirmed by an academic who should make the change. Just Maybe 23:27, 27 May 2007 (UTC)

## Table values listed

Never mind, that was a stupid idea. Sorry.

## No Estimation of Error

Just before the explanation for why there is no error in the figures comes reasons why there should be. I see nothing in SI units and mathematic definitions that keep error out of real-world experimental results. Brewhaha@edmc.net 06:17, 17 July 2007 (UTC)

## Units problem

According to the definition of the auxiliary field, H

B=μ(H+M)

where

μ is the material's permeability, measured in henries per meter. B is the magnetic field (also called the magnetic flux density or the magnetic induction) in the material, measured in teslas H is the auxiliary magnetic field, measured in amperes per metre M is the magnetic moment per unit of volume or magnetization, measured in teslas

How can you add H and M in the parenthesis if they have different units? (H has A/m, M has teslas).

This doesn't look right. —Preceding unsigned comment added by 77.49.235.14 (talk) 16:47, 30 October 2007 (UTC)

Most textbooks I have seen, and most web pages (e.g. http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Quantifying.htm ) say that ‘Magnetization carries the same units as a magnetic field: amperes/meter.’

There was something called ‘Intensity of magnetization’ in the defunct Kennelly variant of the SI, which had units of teslas.

RAClarke 23:11, 4 November 2007 (UTC)

## Proposal: merge Permeability (electromagnetism) with magnetic susceptibility

I propose to merge this article (Permeability (electromagnetism)) with magnetic susceptibility because both quantities are trivially related to each other; they are just two different ways of expressing the same physical ideas. The articles overlap to a large extent; the slow down in the edit histories shows that we do not have the manpower to maintain both of them. The rules on Wikipedia:Merging are also clearly in favor: Overlap is a good reason for merging two or more pages on related subjects: »Wikipedia is not a dictionary; there does not need to be a separate entry for every concept in the universe. For example, "Flammable" and "Non-flammable" can both be explained in an article on Flammability.«

A year ago, I did a similar merger for the electric counterparts electric susceptibility and permittivity. This merger has recently been reverted, which I strongly oppose. I suggest that we continue the discussion for both cases, electric and magnetic, at this place. -- Marie Poise (talk) 23:23, 6 November 2010 (UTC)

Something needs to be done and somehow made to stick. For example, I am currently trying to find a home for a lot of information on the constitutive relations that is currently in Maxwell's equations. One thing to be aware of is that permeability is used by magnetitians in magnetic circuits while magnetic susceptibility is used more often I think by theorists. The situation is worse in the electric side with Dielectric constant moved to static relative permittivity which is then moved to relative permittivity. This is made even worse since the index of refraction is usually dependent on the square root of the relative permittivity (at the frequency of the light).
I will support any solution that sticks provided it doesn't end up with an article that is unwieldy and there are ways for people only looking for a subset of the information to not be swamped. I propose that you merge into permeability (electromagnetism) then add sections in that article titled 'magnetic susceptibility', 'relative permeability', and 'permeability (magnetic circuit)' and then do redirects to the section from those three articles, magnetic susceptibility, relative permeability, and permeability (magnetic circuit). I hope that merging to section will stick better. If it doesn't stick then it will be worse in the end then if you never made the merge, in my opinion. TStein (talk) 21:13, 10 November 2010 (UTC)
Oppose. I understand the beauty of simplifying Wikipedia into relatively few articles. However, in this case, there is actually very little overlap. The way these two notions (related by simply adding 1) are used is different: they serve two different communities. Just look at the corresponding example tables. Permeability folks are using large numbers, mostly for ferromagnetic cores of transformers and coils. For them adding 1 is almost as good as adding 0. On the other hand, there is a long history of using susceptibility for precision measurements such as NMR. Unfortunately, there is a huge confusion in the literature about susceptibility definitions and units (because of loose interpretations of CGS). They need to be addressed in an article dedicated to susceptibility, otherwise the scope of this discussion will be lost. I wouldn't worry about the lack of manpower to edit and maintain two articles, since the user communities overlap as little as the articles themselves, in my opinion. Xenonice (talk) 00:40, 16 November 2010 (UTC)
I agree with you on the final goal. Where we disagree is how to get there. (To be completely honest my feeling in the matter aren't that strong, though.) Right now both articles are a mess each having stuff that probably belongs in the other. In my opinion it would be easier to organize in one article. Then if there was enough stuff we can split out relatively trivially the appropriate sections. I also think that there is a third audience and that are students and people studying E&M in general. They are more likely to be interested in how the permeability fits into Ampere's law for H. In the end there probably should be three articles to cover each of these topics.
Further even if we fix the articles to reflect their appropriate community, they won't remain fixed for long. We are going to need to use all of the tools at our disposal in order to keep the appropriate material in the appropriate location. That means using different navigation panels and using template:about templates to get the user quickly to the right article. TStein (talk) 17:29, 16 November 2010 (UTC)
Oppose per Xenonice. And those arguments do not influence the situation with electric susceptibility and permittivity. /Pieter Kuiper (talk) 09:23, 6 February 2011 (UTC)
Oppose These have entirely different definitions. These are two entirely different quantities, which are brought into apposition by rationalisation. Susceptability is the ratio of induced polarisation density to the inducing field. In cgs, the polarisation density is Bi/cm, while the inducing field is in Oe, or Gb/cm. The ratio of Bi/Gb is 4pi Gb = 1 Bi. This is why in CGS, one sees epsilon = epsilon-0 + 4 pi × susceptability. Wendy.krieger (talk) 08:53, 4 October 2011 (UTC)

## Max frequency for ferrites

http://www.ti.com/lit/ml/slup124/slup124.pdf suggests that while the figure we quote for manganese-zinc ferrites is about right, nickel-zinc ferrites are suitable for somewhat higher frequency use. Could somebody who knows more about this stuff than me see if this makes sense? 212.159.69.4 (talk) 11:20, 5 February 2012 (UTC)

## Metglas and Nanoperm Claims

The values of applied field at which these permeabilities are supposedly measured seem extremely suspicious, considering that metglas datasheets (e.g. [[1]]) suggest the material has a saturation flux density just over half a Tesla. The 1,000,000 relative perm claimed on the site doesn't specify the field, and probably refers to 0.5A/m, which is a very small fraction of a Tesla. Someone more familiar with metglas should really verify this one, since nearly everything I know of starts going into saturation well below half a Tesla. 66.108.191.72 (talk) 10:07, 5 September 2012 (UTC)

## Amumetal?

Can someone add the characteristics of amumetal to the table? That's amumetal, not mu-metal. Thanks. — Preceding unsigned comment added by 150.195.9.61 (talk) 22:01, 31 January 2013 (UTC)

## Relative permeablity, µ/µ0

relative permeability (µr) is =µ/µ0 So if i take it litterally : µ=µr*µ0

BUT, if i take Carbon steel : µ=100*4pi*10^-7= 1.2566*10^-4, and not "8.75×10−4", So , did i missed something or just an error ?

Thanks — Preceding unsigned comment added by 213.139.124.12 (talk) 14:55, 21 November 2013 (UTC)