Talk:Centimetre–gram–second system of units

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Values of parameters in different systems of units[edit]

The table of parameters in the section "Various extensions of the CGS system to electromagnetism" has incorrect entries in the columns for ε0, μ0, λ, and λ′ that contradict the text of the article and other articles. According to the text ESU and Gaussian are not rationalized, and so, according to the text, λ = λ′ = 4π in these systems. Whence it follows from the formula for λ in the table that ε0 = 1 in these systems.

The table assumes that ε0μ0 = 1/c2 in all systems, but this is incorrect, the correct formula being ε0μ0 = 1/αL2/c2. Hence, μ0 = 1/c2 in ESU, and μ0 = 1 in Gaussian and Lorentz–Heaviside.

The same conclusions can be reached in another way. According to the text, D = ε0E and B = μ0H in free space in all systems. But according to the articles Gaussian units and Lorentz–Heaviside units D = E and B = H in free space in Gaussian and Lorentz–Heaviside. Therefore, ε0 = μ0 = 1 in these systems. The formulas for D and B in these articles also plainly show that λ and λ′ are 4π in Gaussian and 1 in Lorentz–Heaviside.

Accordingly, the quadruple (ε0, μ0, λ, λ′) should be changed to (1, 1/c2, 4π, 4π) for ESU, to (1, 1, 4π, 4π) for Gaussian, and to (1, 1, 1, 1) for Lorentz–Heaviside. 72.251.58.64 (talk) 02:05, 14 November 2017 (UTC)

This is quite a long series of posts, so I'll start by noting that the values for ε0 and μ0 are in complete agreement with Table 2 of the Appendix on Units and Dimensions in the Jackson reference, while (with the conversions given below the table) the various k constants agree with Table 1. In Wikipedia, the references are paramount. Contrary to the statement by the IP editor, the column for λ does agree with those for kC and ε0 through the formula λ = 4 π kCε0. RockMagnetist(talk) 16:42, 15 December 2017 (UTC)
I have belatedly realized that the table is correct because the IP editor changed it. Thank you! RockMagnetist(talk) 17:44, 15 December 2017 (UTC)

The following pertains to the section "Alternate derivations of CGS units in electromagnetism."

Theorem. λ = 4πε0kC and λ′ = 4παB/(μ0αL).

Corollary. If λ = λ′, then c2 = 1/(ε0μ0αL2).

Proof. Begin with the equations in SI. Let λ, λ′, σ, τ be independent variables. Define β = λστ and β′ = λ′στ. Perform the following multiplications:

B by σ/β′ and D by τ/β
E by σ and H by τ
M by β′/σ and Q, ρ, I, J, P by λτ/β
μ by λ′σ2/β′2 and ε by λτ2/β2

Notice that the cross products P × E and M × B are invariant under this transformation since they represent torque densities. After eliminating σ and τ from the resulting equations, we obtain the most general system subject to the usual constraints. It may be seen that λ and λ′ have the meanings given them in the text. That the formulas in the theorem are valid in the general system can be verified directly. For λ this is obvious by inspection; for λ′ use the fact that λ/β = λ′/β′.

The corollary follows from the theorem and the formulas kC/kA = c2 and kA = αLαB given in the text. 72.251.58.81 (talk) 02:28, 12 December 2017 (UTC)

The general system has six parameters, λ, λ′, β, β′, ε0, μ0, subject to two constraints, λ/β = λ′/β′ and c2 = ββ′/(ε0μ0). It therefore has four degrees of freedom in the choice of units. It may be thought of as having seven base units, including the three mechanical units. The units of P and M, however, are directly derived from those of E and B, respectively.

In terms of these parameters the constants defined in the text have the following values:

αL = 1/β′
kC = λ/(4πε0)
αB = λμ0/(4πβ)
kA = λμ0/(4πββ′)

72.251.58.233 (talk) 04:22, 13 December 2017 (UTC)

The text states that 4πε0kC is a dimensionless quantity, but since ε0 is arbitrary, including its unit, this is not necessarily so. In general both ε0 and μ0 may be selected at will, but if it is required that λ = λ′, then the only limitation is that indicated in the corollary. It would be very convenient to assign a unit to λ and λ′ (if they are equal) in order to facilitate conversion from one system to another. The unit that seems most appropriate is that of a solid angle. The difference between unrationalized and rationalized systems would be that the former use the steradian as the unit of solid angle whereas the latter use the sphere. 72.251.62.29 (talk) 03:02, 14 December 2017 (UTC)

The proof of the theorem refers to the "usual constraints." These are conditions and equations that are invariant under the transformation in the proof. They include the equation of continuity, the formulas D = εE and B = μH, and the definitions of electric and magnetic moments as torques per units of E and B, respectively. There are, however, systems that violate the constraints. The most notorious offenders are variants of the Gaussian system. One such measures charge in ESU and current in EMU; this system violates the equation of continuity. The standard Gaussian system was carefully constructed to satisfy the constraints. For example, the magnetic moment of a small current loop is defined as m = IA/c. The c is inserted here to ensure that M is measured in EMU, as are B and H. If it is omitted, then M is measured in ESU and λ′ = 4π/c. If electric and magnetic dipole moments are defined by p = 4πQd and m = 4πIA/c, respectively, then λ = λ′ = 1. This in no way, however, makes the system rationalized. The way to rationalize the standard Gaussian system (without changing the units of E, B, P, M) is to choose ε0 = 1/(4π) and μ0 = 4π.

Rationalization, as the word is ordinarily understood, requires that ε0 and μ0 be so chosen that kC = 1/(4πε0) and αB = μ0αL/(4π). 72.251.59.120 (talk) 03:39, 15 December 2017 (UTC)

Can anyone summarize the issue? Also, it would help if you make a wiki user. MaoGo (talk) 13:32, 15 December 2017 (UTC)

The IP editor was correct about the table, and I would encourage them to add the other material to the article. However, they should be aware of the core Wikipedia policy of verifiability and provide citations of a reliable source for anything they add. RockMagnetist(talk) 17:55, 15 December 2017 (UTC)
This all seems reasonable and I would encourage 72.251 (who was also very helpful at Talk:Gaussian units last month) to feel welcome and encouraged to edit the text yourself.
My only gripe about the table is that I wish the ε0 and μ0 columns were named something else, ideally meaningless symbols with no prior associations, like "k_2" and "k_3" for example. For example, the statement "ε0=1 in Gaussian units" is I think prone to being misunderstood ... for example I worry that a reader will see that and then feel entitled to replace ε0 with 1 in translating random formulas (like Coulomb's law) from SI to Gaussian. That statement is really supposed to be "ε0=1 in Gaussian units, where ε0 is by definition the ratio D/E in free space". That statement is correct, but it would still be equally correct if we used a different symbol besides ε0. Just my opinion, and I don't think it's a huge deal. --Steve (talk) 20:24, 15 December 2017 (UTC)

I am the IP editor. There are three problems with the text as currently written. (1) It implies that λ and λ′ may be chosen independently of ε0 and μ0; I hold that this is only possible if P and M have unusual units. (2) It states that 4πε0kC is a dimensionless quantity; I hold that this is not necessarily so. (3) It states that rationalization depends upon the values of λ and λ′; I hold that, if the formulas of the theorem do not hold, then it depends, rather, on the values of ε0 and μ0.

I cannot cite any sources, since I do not have access to any books that discuss these issues in sufficient detail. But the statements of the text ought themselves to be verifiable if they are to stand. The only reference in the text that seems to be relevant is to Jackson, whose discussion of the subject is wholly inadequate. The text seems to draw unwarranted inferences from what he does say (or doesn't say). (1) Jackson says nothing about the relationships between λ and λ′, on the one hand, and ε0 and μ0, on the other; the text infers that there are no necessary relationships. (2) Jackson says, "λ and λ′ are chosen as pure numbers"; the text infers that they must be so chosen. (3) Jackson says, "λ = λ′ = 1 in rationalized systems"; the text infers that this is the definition of "rationalization," and it calls λ and λ′ "rationalization constants."

I propose that the text "The factors … be 'rationalized'" be replaced with the following:

The units of P and M are usually so chosen that the factors λ and λ′ are equal to the "rationalization constants" and , respectively. If the rationalization constants are equal, then . If they are equal to one, then the system is said to be "rationalized"

Zophar (talk) 04:44, 17 December 2017 (UTC)

Here is a direct proof that rationalization means that what I call the rationalization constants are equal to one. Rationalization means that Maxwell's equations in material media for static fields have the form

∇·D = ρ and ∇×E = 0
∇·B = 0 and ∇×H = αLJ

In free space these become

∇·E = ρ/ε0 and ∇×E = 0
∇·B = 0 and ∇×B = μ0αLJ

From these we may derive Coulomb's law and the Biot-Savart law using the usual mathematical arguments. The results are

kC = 1/(4πε0) and αB = μ0αL/(4π)

whence it follows that the rationalization constants are equal to one. Zophar (talk) 04:58, 18 December 2017 (UTC)

emfd[edit]

Gavo atoms (talk) 07:08, 28 February 2020 (UTC)can you help me to have question and answers of EMFD unit

As others have noted, the talk page is for discussing the article, or improvements to the article. If there is an EMFD unit that should be included, then we can discuss that. (As far as I know, there is no such unit, at least in the CGS contexts.) I try to be a little flexible, and give people the benefit of the doubt, that the question might have some use for improving the article. But deleting this posts doesn't even allow discussion of the relevance to the article. (Though I agree, that I suspect that there isn't any.) Gah4 (talk) 01:44, 29 February 2020 (UTC)
What is an EMFD unit? Dondervogel 2 (talk) 09:29, 29 February 2020 (UTC)

Method of reconciling systems[edit]

I am uncomfortable with Centimetre–gram–second system of units § Various extensions of the CGS system to electromagnetism. I know it is referenced, but there are other completely different ways to reconcile metrological systems (I can't access the two references, but the one is just a response to the other). This approach seems to be to insert various constants into equations so that the equations end up constructed as for each of the systems when the constants are chosen for the system, but removes the understanding that the quantities (e.g. "charge") are different in each of the systems and does not help intuition. This leads to misunderstandings such as the idea that 104 G = 1 T. They correspond, but equality is mathematical nonsense, and quickly produces confusion and contradictions. I have seen too much OR on WP that is based on this misunderstanding. I suggest simply deleting this section. —Quondum 16:56, 7 June 2020 (UTC)

I agree it is strange, but it is also useful and important. It looks to me that the distinction is well explained, but maybe it can be explained better. Yes one has to be careful with units but if, for example, I buy a magnet that says 1T, I can replace that value with 10000gauss, and if I have a gaussmeter, I know what it should say. But yes, one has to be careful with equations when doing that. Deleting the section does not reduce confusion, people will just find it somewhere else. The only way people will know about the possible misunderstanding is to explain it. Gah4 (talk) 19:38, 7 June 2020 (UTC)
The current explanation does not distinguish the definition of charge in the different systems (these are different quantities, like the radius and circumference of a circle being different quantities, but both giving the same information); it just emphasizes that the units are different. Expressing things in different units is familiar, e.g. the circumference of a circle being expressed in feet and metres. This is not what is happening in the difference between CGS and SI. Yes, explanation is necessary, and it seems I might need to write one, but what we have at the moment is worse than an explanation: it is effectively incorrect, hence my suggestion to delete it. —Quondum 20:31, 7 June 2020 (UTC)
One can make a connection between tesla and gauss. One can also connect coulomb and Gaussian ESU, the latter being confusing, as it is also the name of a unit system. This isn't completely unrelated to the problems that one might have between feet and meters. It gets more interesting when you get to pound(mass) and pound(force), or kilogram(mass) and kilogram(force) where, as you note, quantities are being compared that shouldn't be. But I do understand what you are trying to say, in that the equations use in the different systems are different. You can't put coulombs into the Gaussian equations, and can't put ESU into the SI equations. But note that gauss is commonly (if incorrectly) often used for magnetic field, even when everything else is SI. Sounds much better than centicentitesla. Using these units will require users to learn and understand the differences in their definitions, and also in the distinction between electrostatic based and magnetostatic based unit systems. Gah4 (talk) 13:40, 8 June 2020 (UTC)
Note also, or maybe you are already noting, the convenience of the Gaussian units for B and E in the electromagnetic tensor. E and B directly transform through the Lorentz transformation, where a c is needed in SI. But that already comes from using different units for distance and time, which confuses special relativity. Next you find mass quoted in eV (an energy unit). Special relativity is much nicer in c=1 units, and quantum mechanics in ħ=1 units. Special relativity is, then, much nicer to study in Gaussian units than SI units, and electrodynamics is very closely related to special relativity. If you haven't thought about this, read the earlier Purcell[1] E&M books which, among others, consider the current in a wire, in a frame moving along with the moving charge, at some reasonable fraction of c. The most recent Purcell seems to have converted to SI. Gah4 (talk) 13:40, 8 June 2020 (UTC)
To be sure, I do understand what you are asking, but see it differently. Understanding the differences in the definitions of the units means learning more about the origins of them, and the physics behind them, and especially that electrostatic and magnetostatic units are not independent. If you ignore special relativity, and only work at low speeds, you can think of them as independent, but they aren't. Learning about that is important, and the different unit systems emphasizes that connection. When you understand it, it makes problem easier, not harder. Gah4 (talk) 13:49, 8 June 2020 (UTC)
Thinking about this again, and especially the noted problem of putting values into the wrong equation, there are two things to consider. One is rationalized vs. unrationalized. That is a little complicated, but usually not so bad. One can avoid it by using SI units along with Heaviside-Lorentz units. The other is factors of c. It is usually pretty obvious if one gets an answer wrong by a factor of c. Like other things, doing it right improves with practice. Don't wait until the night before the final to cram all the equations into your brain! Gah4 (talk) 22:39, 10 June 2020 (UTC)


References

  1. ^ Purcell, Edward. Electricity and Magnetism (1 ed.). McGraw Hill. ISBN 978-0070048591. Retrieved 8 June 2020.

prefactor[edit]

In some places, or maybe in edit summaries, there is mention of no prefactor. I think this isn't quite right. In some cases, a prefactor is defined for convenience, and not for units. For example, it might be a power of 10, or might have a 4pi in it. The important point is that it is dimensionless. Gah4 (talk) 19:41, 7 June 2020 (UTC)

I don't see how you see that. It is not dimensionless as used in this article. In any event, where it is used it seem to be tied in with the thread above, and needs rewriting. —Quondum 20:36, 7 June 2020 (UTC)
So what would you call a dimensionless power of 10 that was in an equation? Gah4 (talk) 03:42, 8 June 2020 (UTC)
Maybe I misunderstood our comment. As far as I see it, the term "prefactor" has been used to mean any multiplier that is not dimensionless 1. I see only one instance where it is dimensionless: "Ampère's force law simply contains 2 as an explicit prefactor", which seems to result from the ratio of a 4π (from the spherically symmetric Coulomb force law) with a 2π (from a cylindrically symmetric Ampère's force law). I am still in the dark about what point you are trying to make, but this may be moot since all these references to the nonstandard term "prefactor" should be rewritten. —Quondum 10:54, 8 June 2020 (UTC)
I was taking it as any term in front of the appropriate physical variables, which would include the 2 you mention. Partly this comes from recent (last few days) interest in the definition of the volt, convenient sized for common electrochemistry, and otherwise for common usage. It took getting powers of 10 in the right place to make that work. Note also the significance of using units scaled by powers of 10, such as the centimeter in CGS, and the kilogram in SI. Gah4 (talk) 13:12, 8 June 2020 (UTC)
I don't believe that such scaling factors (the powers of 10 to get units of convenient size) are applied to the equations that relate the defined quantities (and thus affect coherence), not those that define unit scaling. Do you have an example of the use of "prefactor" in this scaling sense that concerns you? —Quondum 14:09, 8 June 2020 (UTC)
I was recently reading this one as suggested by someone else, to understand the origins of units like the volt. It seemed like it wasn't an accident that common electrochemical cells come out about one volt. The article shows how powers of 10 were moved around to make it come out that way. But the question original came from an edit summary on a previous edit. Gah4 (talk) 14:40, 8 June 2020 (UTC)

Vacuum_permeability[edit]

The article mentions vacuum permittivity as part of the SI definition of Ampere, but I think it should be Vacuum_permeability. Now, since there is a connection between the two, maybe it isn't so obvious. Gah4 (talk) 04:53, 10 June 2020 (UTC)

I've changed the link. —Quondum 11:56, 10 June 2020 (UTC)

units and equations[edit]

I always try to give at least a little benefit of the doubt when something might not be so obviously toward improving the article, and at least mention why (someone) thinks it isn't a possible contribution to the article before deleting it. But it seems that some don't believe in that. OK, so an actual question which might go to the article. Is gauss allowed in otherwise SI problems? Gah4 (talk) 04:41, 19 June 2020 (UTC)

IMO, never without an explicit conversion between quantities (Gaussian magnetic flux density and SI magnetic flux density are distinct and dimensionally incompatible quantities, albeit related by a constant of proportionality). And then only when for some reason the source data is unavoidably given in units of gauss. Not sure how this related to CGS, though, which is not an SI article. —Quondum 11:18, 19 June 2020 (UTC)
The question came up somewhere, maybe here, about how often CGS units are used. I mentioned gauss and oersted being often used, and the claim from someone was that it wasn't really CGS units. It seems that some use gauss where centicentitesla should be used. That is, as an appropriatly scaled SI unit. They are, for example, commonly used in measurements for magnetic tape. This table is one example. (Web search for tape coercivity and see what you find.) On the other hand, I suspect that tape equipment measures head current in SI amps, not statamps or abamps. There is some history that I don't know about. Gah4 (talk) 12:25, 19 June 2020 (UTC)
Or just look here: Compact_Cassette_tape_types_and_formulations Gah4 (talk) 12:32, 19 June 2020 (UTC)
Nothing stands out for me to suggest that G or Oe are being used as SI units; other than that, typically there is little emphasis on the distinction of the quantities between the systems. It all just looks like an industry that is migrating from one system to another. I see enough use of mT and kA⋅m−1. We should be writing the WP articles to use SI units; where source material is given in Oe, for example, we should be giving the corresponding A⋅m−1 values. —Quondum 13:21, 19 June 2020 (UTC)
There has to be some connection between the amps in the tape head, and the gauss in the tape. There are some tape data sheets with both, but only very recently. I believe that they are used for permanent magnets other than tape, too. Gah4 (talk) 19:07, 19 June 2020 (UTC)
I do not see where you are heading with this – there just does not seem to be anything new here. Niche groups are slow to switch to SI, so we see the use of older quantity and unit systems in certain specialities, and this is what we are seeing: people still using older units. In the case of Gaussian units, we can directly convert to SI quantities and units: as long as we know what the original quantity is (not always clear from the units), we can convert through a suitable multiplier to the corresponding SI units. Since Gaussian units give special names to distinguish the quantity even though the quantities might not be dimensionally distinct, this is made easier. We translate Oe to A⋅m−1 and G to T with little or no ambiguity. I see no benefit in retaining Gaussian units in WP articles except where we are directly referring to what is given by references. To your point of Gaussian units being used recently, I do not see that this should keep WP with the old system. Since the mag tape industry is using the new units, we can use them. We do not use Gaussian units in particle physics articles, even if the majority of particle physicist were still using these units. It is just too confusing to the reader. —Quondum 19:57, 19 June 2020 (UTC)
Well, one question is, should this be mentioned in the article? I believe gauss is still commonly used in describing electromagnets and such. As well as I know, more generally than just tape, Oersted for coercivity of permanent magnets. WP, and especially WP:COMMONNAME is supposed to follow actual usage. (Not that I always agree with it.) It would seem that this page could mention the use, even if just to claim that it is deprecated. It does seem that using Gaussian units makes sense in a page on Gaussian units, though. Gah4 (talk) 21:22, 19 June 2020 (UTC)
A section detailing where Gaussian units are still used at present would make sense in this article. I expect that modern "actual usage" has SI units strongly dominating in electromagnetic applications. —Quondum 21:48, 19 June 2020 (UTC)
Well, that would still allow for magnetostatics which mostly describes permanent magnets. Maybe that is why they stay around. Coercivity does come up in degaussing, which it should connect to currents. It seems that people are not bothered by the connection between amperes in a degaussing circuit and coercivity in oersteds. Gah4 (talk) 22:13, 19 June 2020 (UTC)
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