# Talk:Gaussian units

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## Finger error in a formula

Thanks for this useful article. Please, correct a "finger error" in the formula relating B and H. The correct equation is B = "mu" H. --189.231.190.214 (talk) 17:00, 16 November 2009 (UTC)

Yes, thank you, I have now changed it! --Steve (talk) 20:49, 16 November 2009 (UTC)

## Gaussian or CGS?

If, as the article states, the term "cgs units" is deprecated, why is it used several times, with no further qualification, in the text? For those who know, would it be safe to change existing unqualified references in this article from "cgs units" to "Gaussian units"?

Fixed! :-) --Steve (talk) 22:40, 14 April 2012 (UTC)

## Why?

This article does a pretty comprehensive job of describing how Gaussian units differ from SI ones, but offers no explanation for why factors of 4pi, epsilon_zero etc. differ between the two systems. There's some (not very clear) discussion at Centimetre_gram_second_system_of_units#Derivation_of_CGS_units_in_electromagnetism, but this article doesn't mention that and only links to it in passing in the lead. There needs to be a brief description of why these factors disappear, and a clear link to the relevant place for more information. I'd fix it myself, but frankly I don't follow the reasoning (despite having a degree in physics and working in a field where Gaussian units are still used), so I doubt I could write anything that was correct. Modest Genius talk 00:35, 27 December 2012 (UTC)π

About the 4pi: It's not clear to me exactly what question you're looking to answer:
• "Why is it that if Coulomb's law has an explicit 4pi then Gauss's law does not have an explicit 4pi, and vice-versa?" I think the article answers that well: "The quantity 4π appears because 4πr2 is the surface area of the sphere of radius r. For details, see the articles Relation between Gauss's law and Coulomb's law and Inverse-square law."
• "What are the advantages and disadvantages of rationalized versus non-rationalized units?" This is a subjective question. One person might think that something is an advantage, someone else with different preferences might think the same thing is a disadvantage. It's not impossible to discuss subjective questions in a wikipedia article, but it is difficult. You need to fairly summarize all the major points of view, and find references for them. The latter is very difficult; even if lots of physicists say to each other over coffee "Gaussian units make XYZ unnecessarily complicated", they rarely would write that into a publication that we can reference.
• "What are the historical circumstances that caused SI to be rationalized while Gaussian is not?" It looks like Reference 5 discusses the history and I'm sure you can find the information you're looking for there. If you want to add better historical information to the article, that would be great, and I'm happy to help as I can.
About epsilon0: The main thing is that in Gaussian units,
1 statC = 1 g1/2 cm3/2 s−1
while in SI, there is no analogous relation between Coulombs and the "mechanical" units (length, mass, time). This difference leads to a wide variety of formula differences, especially when epsilon0 and mu0 are involved.
Again, maybe you're wondering what the advantages and disadvantages are to defining charge in terms of mechanical units. Or maybe you're wondering why, theoretically, people have a choice in the matter at all. Or maybe you're wondering why, historically, different systems developed in different ways. Which is it? --Steve (talk) 18:15, 27 December 2012 (UTC)
The analogous relation in SI comes from Ampere's law with the constant 10-7 N/A2. If you define that constant to be unity, then A^2=10^7 N, or
1 A = 107/2 N1/2.
I suspect that the 107/2 discourages its use.Gah4 (talk) 15:04, 25 October 2015 (UTC)

Rationalization just moves the 4π around. It has to go somewhere so that surface integrals work. Other than that, Gaussian units are electrostatic, SI are magnetostatic. Gah4 (talk) 23:38, 20 October 2015 (UTC)

There is a basic idea that isn't well covered here. That electromagnetic units are based either on the force between charges (electrostatic) or force between currents (magnetostatic). Maxwell's equations (and special relativity) connect electricity and magnetism, such that you can't (or shouldn't) specify the units separately. The claim that Gaussian units don't have ε0 isn't quite right. Gaussian units defines the charge unit (ESU) such that ε0 has the value 1/(4π). SI instead defines the charge unit as the ampere second, (with ampere based on the force between currents). That is, the ampere is defined in terms of mechanical units, and the coulomb derived from the ampere. The definition of ampere is strange enough that ampere is always used instead of the mechanical units. Gah4 (talk) 23:38, 20 October 2015 (UTC)

An ampere is indeed "defined in terms of mechanical units" (at the moment; it will eventually be defined as a certain number of electrons per second). But it is not expressible purely in terms of mechanical units, i.e. there is no SI equation for ampere that looks like the gaussian-units equation
1 statC = 1 g1/2cm3/2s−1.
Do you agree? Experienced physicists might dismiss this as a triviality, but for people first learning about different unit systems it is extremely important and often confusing. People expect the "number of independent base units" (mass, length, time, etc.) to have some profound meaning, and are therefore confused by the fact that SI has an extra base unit for electromagnetism but gaussian does not.
The statement "ε0 does not even exist in Gaussian units" is true in the following sense: People who use gaussian units do not have a quantity called ε0 that they put into electromagnetism formulas. I guess you're saying "Well, they don't use the notation "ε0", but they do have "1/(4π)" which plays the same role." But I think the context makes it clear that we are remarking on the fact that ε0 is a dimensionful constant in SI, and gaussian units definitely does not have any dimensionful constant at all analogous to that. (Perhaps the wording in the article could be improved.)
It seems to me that the choice of "C is my base unit and A = C/s" versus "A is my base unit and C = A*s" is not at all important in understanding or using SI. It's in the fine print, something that only super-high-precision physics labs have any reason to care about. Similarly, today amp is defined in terms of forces on wires, and in 2018 it will be defined as a certain number of electrons per second. This is important to some precision physicists but I don't see why the rest of us should care, or why it should affect the basic way we understand SI.
Sorry if I'm misunderstanding your point. --Steve (talk) 16:29, 23 October 2015 (UTC)

Well, for one, the meter is now a derived unit, not a base unit. There is work to make the kilogram a derived unit, though not quite ready yet. (Either from hbar or avogadro's number.) And the ampere is also a derived unit, by defining the force between two current carrying wires. The important difference is that gaussian units are derived through electrostatic, and SI derived through magnetostatics. That difference is important for those learning E&M to know. Gah4 (talk) 00:30, 24 October 2015 (UTC)

What do you mean by "base unit" and "derived unit"? You should use different words, because in the context of SI, "base unit" and "derived unit" have specific universally-agreed-upon definitions (see for example SI base unit and SI derived unit), and according to those definitions the ampere and meter are base units, not derived units. You must be talking about something else and I don't know what. --Steve (talk) 00:44, 24 October 2015 (UTC)
From SI base unit However, in a given realization in these units they may well be interdependent, i.e. defined in terms of each other. For some reason, there is no Derived unit separate from SI derived unit. A base unit should be one that isn't defined in term of other units, but SI cheats. Also, note the fourth paragraph in Dimensional_analysis#Definition Gah4 (talk) 06:05, 24 October 2015 (UTC)
Will SI cease to be "derived through magnetostatics" in 2018, assuming that ampere is redefined as a certain number of electrons per second?
You say gaussian electromagnetic units are defined in terms of electric forces on charges. You can define them that way if you want, there's nothing wrong with that. But I can equally well define gaussian electromagnetic units in terms of magnetic forces on currents. Or heck, I could say that the definition of statC is
1 statC = 1 g1/2cm3/2s−1.
which has no relation to electric forces or magnetic forces. (I actually prefer this last definition if I had to pick one.) So to summarize, I don't believe your statement that gaussian electromagnetic units are defined in terms of electrostatics. --Steve (talk) 14:04, 24 October 2015 (UTC)
Those units come from setting the constant in Coulomb's law to 1. SI units set the constant in Ampère's_force_law from Magnetostatics to ${\displaystyle 10^{-7}}$ N / A2. In both cases, the corresponding constant in the other equation has the appropriate value required by Maxwell's_equations. Gah4 (talk) 14:22, 25 October 2015 (UTC)
And no, if the proposed 2018 changes define the kilogram in terms of e, they are still "derived through magnetostatics", but in the other direction. Instead of defining the electromagnetic units from mechanical units, the mechanical units will be defined through magnetostatics and quantum mechanics.[1] Gah4 (talk) 15:28, 25 October 2015 (UTC)
See Proposed redefinition of SI base units. You say "the mechanical units will be defined through magnetostatics and quantum mechanics", but I think you are mistaken. The mechanical units will be defined through the the hyperfine energy splitting of cesium atoms, the speed of light, and Planck's constant. How is magnetostatics involved in any of those? You linked to a PDF, but that PDF does not mention magnetostatics either. (Indeed, under the proposal, we will not know the exact numerical value of μ0; it will have experimental error bars.)
You say: "[Gaussian electromagnetic] units come from setting the constant in Coulomb's law to 1." OK, well I say: "Gaussian electromagnetic units come from setting the constant in Ampere's force law to 1/c2". There, I just defined gaussian units in terms of magnetostatics. I don't see what rational basis there could be for saying that my definition is wrong and yours is right. The two definitions lead to the exact same system of units, right?
Similarly, the SI authority says: "the ampere is the constant current that will produce an attractive force of 2e−7 N/m between two parallel wires 1m apart in vacuum". But it would be 100% equivalent to say: The ampere is defined so that the electric permittivity of vacuum is exactly 10000000 / (4*pi* 2997924582) A2⋅s4⋅kg−1⋅m−3. If they had used that definition, everything about SI would be exactly the same, but now things would be based around electric permittivity, with no mention of magnetostatics.
So we see in both cases that you can swap electric-based definitions for magnetostatic-based definitions without changing anything whatsoever about the unit system. It's wise (for pedagogical reasons) to pick a definition and stick to it, and some definitions are pedagogically better than others, but they don't reflect any profound truth or understanding of the unit system.
So I continue to think that "SI is based on magnetostatics, gaussian on electrostatics" is not really true and definitely not a profound truth that is worth emphasizing or even mentioning. --Steve (talk) 02:15, 27 October 2015 (UTC)

I am not so sure by now which units will be defined in terms of which. The Watt_balance is used to define the kilogram in terms of electronic units, instead of the other way around. Since 1983, when c was defined as 299792458 m/s, yes, you could as easily define through Coulomb's law as through Ampere's law, but BIPM didn't do that. They could have changed it in 1983, but didn't. I suspect the reason is that it is easier to physically measure current instead of charge. Yes, the difference isn't as profound as before 1983, but it is still the way the units are defined. The CGS units include both stat units, based on Coulomb's law, and ab units based on Ampere's law, and both defined before 1983. The important part is that you choose a consistent set, such that each unit has only one definition. For many years, c was not so well known. In the early years of spectroscopy, wavelength could be measured with smaller relative error than c. It was, then, usual to do physics with wavenumber (inverse wavelength) instead of frequency, avoiding the uncertainty in c. Gah4 (talk) 08:30, 27 October 2015 (UTC)

I think there is a contradiction between the articles on cgs unit system http://en.wikipedia.org/wiki/Centimetre_gram_second_system_of_units#Electrostatic_units_.28ESU.29 and the one on the Gaussian unit system http://en.wikipedia.org/wiki/Gaussian_units.

In the Table Electromagnetic units in various CGS systems of http://en.wikipedia.org/wiki/Centimetre_gram_second_system_of_units#Electrostatic_units_.28ESU.29 the conversion of magnetic field units between SI unit system (i.e. Tesla) and ESU unit system is give as 10^4 statT/c. This conversion is quite consistent when one begins with the Lorentz force equation in SI units and converts it to ESU. In this way the additional (1/c) term in the denominator of the corresponding equation in ESU is automatically obtained. In the same table the conversion between Tesla and Gauss is 1 T = 10^4 G. In the light of the conversion between SI and USU this implies that whenever one replaces 1 T in the Lorentz equation in SI units by 10^4 G one obtains the corresponding equation in Gaussian units. On the other hand in the table Electromagnetic unit names of http://en.wikipedia.org/wiki/Gaussian_units the conversion between SI and Gaussian units is given as 1 T = 10^4 Gauss. Probably this does not mean that whenever one replaces 1 T in the Lorentz equation in SI units by 10^4 Gauss one obtains the corresponding equation in Gaussian units. I think this point requires clarification. — Preceding unsigned comment added by 193.140.249.2 (talk) 14:11, 2 April 2013 (UTC)

ESU is not the same as Gaussian. But anyway, you're correct that you cannot replace "1 T" in an SI equation by "10^4 G" in a gaussian or ESU equation. There is already some text about this in the article: " The symbol "↔" was used instead of "=" as a reminder that the SI and Gaussian units are corresponding but not equal because they have incompatible dimensions. For example, according to the top row of the table, something with a charge of 1 C also has a charge of (10^−1 c) Fr, but it is usually incorrect to replace "1 C" with "(10−1 c) Fr" within an equation or formula...". There is similar text in the statcoulomb article. I have just now copied the exact same text and notation to the table in Cgs units#Electromagnetic units in various CGS systems. Does that help? --Steve (talk) 17:49, 2 April 2013 (UTC)
It is correct to use = rather than a double-arrow, because a statement like e = 4.802E-10 Fr, is something that does not imply the construction of the franklin from any given theory. A franklin is equal to a charge of 1E10/4.802 electrons, and can be directly related to that. Whether you choose to suppose the franklin is a mechanical unit dyn^½ cm, or a base unit (1947 standard), is irrelevant. Wendy.krieger (talk) 11:54, 22 December 2016 (UTC)
Do you think that "↔" is technically incorrect? You didn't say that, and I definitely don't think so, because "↔" does not have any strict technical definition in this context that we could be violating. Now, an abundance of personal experience and talk-page comments suggests that people will definitely substitute "1C" with "3e9 Fr" unless they are told not to (and then reminded over and over). Even if the "=" were technically correct, so is "↔", and since the latter is pedagogically better, we should stick with it.
But I actually don't think that "=" is technically correct. How do I know? When two things are equal, you can substitute one for the other in an equation, but you can't substitute "1C" with "3e9 Fr" in an equation. It's as simple as that!
Here's an analogy. Suppose that everyone talks about spheres all the time, but Europeans traditionally specify a sphere by stating its radius, and Africans traditionally specify a sphere by stating its volume. A "3cm sphere" in Europe is the same sphere as a "12π cm^3 sphere" in Africa. But it's wrong to say "3cm = 12π cm^3", and it's right to say "3cm ↔ 12π cm^3 when specifying spheres". The descriptions correspond to each other—they are describing the same sphere—but the descriptions are not equal to each other. Similarly, "1C of charge" and "3e9 Fr of charge" are two descriptions with the same referent. But it's wrong to say "1C = 3e9 Fr", and it's right to say "1C ↔ 3e9 Fr when describing amounts of electric charge". --Steve (talk) 13:46, 22 December 2016 (UTC)

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The link doesn't exist at internet archive either, so I deleted it altogether. --Steve (talk) 22:02, 28 February 2016 (UTC)