Talk:Statcoulomb

Comments

This seems wrong but I do not have the expertise to confidently correct it: "The number 2997924580 is 10 times the value of the speed of light expressed in meters/second or, in other words, the speed of light in centimeters per second." That number is indeed 10 times the speed of light: 299792458 m/s. But then it is therefore in dm/s, because there are 100 cm in 1 m, not 10. Can someone clarify this for me or fix this? Thank you. — Preceding unsigned comment added by 86.143.159.70 (talk) 19:43, 3 January 2020 (UTC)

One Statcoulomb is NOT equal to 0.1/c (c expressed in cgs units). Try this: use the 0.1/c factor to convert the elementary charge from Coulomb to Statcoulomb. You will be off by a factor of 1/100. The appropriate correction factor is 10/c. —Preceding unsigned comment added by 75.13.69.16 (talk) 16:56, 14 March 2008 (UTC)

I agree with this, I worked through Coulomb's Law in detail. The article states that 1 C = 2997924580 statC, this IS correct. However I will correct where it says c expressed in cgs, it is in m/s. —Preceding unsigned comment added by 121.44.221.75 (talk) 11:32, 10 October 2008 (UTC)

I have changed this:

"Note that in order for the Coulomb's law formula to work using the electrostatic cgs system, the dimension of electrical charge must be [mass]^1/2 [length]^3/2 [time]^-2."

to this:

"Note that in order for the Coulomb's law formula to work using the electrostatic cgs system, the dimension of electrical charge must be [mass]^1/2 [length]^3/2 [time]^-1."

That is, I'm replacing a 1/(t^2) with just a 1/t because I think person who wrote the original version missed a square root when doing the algebra.

I corrected the hyperlink "electrostatic constant" to the article on permittivity, originally directed to "proportionality constant".Gp4rts (talk) 07:09, 22 September 2008 (UTC)

General incompatibility

Firstly I must admit that I know nothing about cgs units. I am a professional engineer, and adhere firmly to the SI system, in conform with with the world-wide scientific community. For me cgs is obsolete. However, I am intrigued by the comments in the article on the dimensions of the Coulomb & Statcoulomb. Since charge is defined conceptually & qualitatively in both systems in terms of Coulomb's law (the force between 'charges'), it seems improbable that the quantities can actually be different - reflected in their having different dimensions. Quantities with different dimensions are physically not the same, and I feel that this cannot be the case with something as fundamental as electric charge.

Here is what is probably a naive resolution... Since the omission of the factor epsilon0 in the cgs expression of Coulomb's law is the culprit, could it be that the permittivity of free space in the cgs system is numerically 1, but nevertheless has dimensions - the same as those of epsilon0 in the SI ? Andrew Smith g4oep. — Preceding unsigned comment added by 82.37.131.61 (talk) 09:50, 28 March 2017 (UTC)

Questions of this sort were much discussed in the final decades of the 1800s and the early decades of the 1900s. The prevailing view that emerged is that your statement, quantities with different dimensions are physically not the same, is not true in general. Here I assume that when we say that 'A and B are physically the same', we mean something like 'both A and B describe and quantify the same underlying physical phenomenon.'

Indeed, it is perfectly possible to have several different physical quantities (of different dimensions) that describe the same underlying physical phenomenon. This situation is not peculiar to electricity and magnetism. For example, time intervals can be equally well described by the quantity t, with dimensions of time, or by the quantity x₀=ct, with dimensions of length (here c is the speed of light in vacuum). The second description is particularly useful in relativistic settings, but it could, in principle, also be used in non-relativistic ones.

The general principle is clear: if the dimensionful physical quantity A describes and quantifies some physical phenomenon, then so does the physical quantity k A, where k is a constant whose magnitude and dimensions are completely arbitrary. In most cases, only for a limited class of k's will k A be a practically useful way to quantify the underlying physical phenomenon (the same that A quantifies on its own). But practical usefulness is a separate question. The fact remains that A and k A are 'physically the same' (meaning, they quantify the same underlying physical phenomenon) despite having different dimensions

The quantity of charge is a very good example on which to illustrate how it could happen that a multitude of different physical quantities could correspond to and describe the same underlying physical phenomenon.

The physical contents of Coulomb's and Ampere's laws (before choosing any particular system of units) are as follows:

If two point electric charges q₁ and q₂ are a distance r apart, then between them there is an electrostatic force F_elecstat such that $F_{\text{elecstat}}=k_{\text{e}}{\frac {q_{1}q_{2}}{r^{2}}}\,.$

If two thin, long, parallel conducting wires, each of diameter d and each of length L, carry steady currents I₁ and I₂ and are separated by a distance r such that d ≪ r ≪ L, then between them there is a magnetostatic force F_magnstat such that ${\frac {F_{\text{magnstat}}}{L}}=2k_{\text{m}}{\frac {I_{1}I_{2}}{r}}\,.$

Here k_e and k_m are constants of proportionality that depend on the choice of units. Further analysis shows that the following relation must hold: $k_{\text{e}}/k_{\text{m}}=c^{2}$, where c is the speed of light in vacuum (both in terms of its numerical value and in terms of its dimensions); thus, only one of the constants k_e and k_m can be chosen independently.

Now, one obvious choice is to declare k_e dimensionless and equal to unity, and this is what is done in the 'cgs electrostatic system of units', i.e. the 'cgs-esu' system of units. As a consequence, in cgs-esu, we have $F_{\text{elecstat}}={\frac {q_{1}q_{2}}{r^{2}}}$ and ${\frac {F_{\text{magnstat}}}{L}}={\frac {2}{c^{2}}}{\frac {I_{1}I_{2}}{r}}\,.$ Note that the esu charge has the dimensions of (force)^1/2(length) = (mass)^1/2(length)^3/2/(time); see e.g. here.

Another obvious choice is to declare k_m dimensionless and equal to unity, and this is what is done in the 'cgs electromagnetic system of units', i.e. the 'cgs-emu' system. As a consequence, in cgs-emu, we have $F_{\text{elecstat}}=c^{2}{\frac {q_{1}q_{2}}{r^{2}}}$ and ${\frac {F_{\text{magnstat}}}{L}}=2{\frac {I_{1}I_{2}}{r}}\,.$ Note that the emu charge has the dimensions of (force)^1/2(time) = (mass)^1/2(length)^1/2; see e.g. here.

Now look at the Coulomb law in the two systems. These two different equations describe the exact same physical situation. Moreover, the quantities F_elecstat, r, and c are purely mechanical. Thus, in any particular physical situation involving two electrical charges, F_elecstat, r, and c are the same in both systems, both as far as their numerical values and as far as their dimensions. The only way this is possible is if, in every particular physical situation, q₁ and q₂ in cgs-esu are equal (both as far as their numerical values and as far as their dimensions) to c q₁ and c q₂ in cgs-emu. In other words, we must always have $q_{\text{esu}}=c\,q_{\text{emu}}\,,$ where $q_{\text{esu}}$ is the quantity that enters in the numerator of Coulomb's law in the cgs-esu system, and $q_{\text{emu}}$ is the corresponding quantity that enters in the numerator of Coulomb's law in the cgs-emu system. The equation $q_{\text{esu}}=c\,q_{\text{emu}}$ must be a full-on physical equation, meaning that the two sides of the equation are equal both in terms of their numerical values and in terms of their physical dimensions; otherwise, in at least one of the two systems, the two sides of Coulomb's law would fail to have the same dimensions. Since $q_{\text{esu}}$ and $q_{\text{emu}}$ have different dimensions, they cannot be the same physical quantity. Nevertheless, they do describe the same underlying physical phenomenon, namely, electric charge, so in this sense, they are 'physically the same'.

In the article 'Relations among Systems of Electromagnetic Equations' (Am. J. Phys. 38, 421–424, 1970), C. H. Page described the situation as follows:

Since the corresponding equations in different systems are not identical, the symbols in them must represent (slightly) different quantities, i.e. different mathematical models of invariant physical phenomena.

And in the article 'On the History of Quantity Calculus and the International System' (Metrologia 31, 405-429, 1995), J. de Boer says the following about the currents in the Ampere's law in the emu and esu systems:

In these relations we compare two corresponding quantities, i.e. an e.s. quantity and the corresponding e.m. quantity, describing the same real physical situation. Thus, for example, the relation between the corresponding current quantities I_e and I_m can be easily found by writing down Ampère's force law between two parallel conductors in the e.s. and in the e.m. system: in the e.s. system this reads in vacuum $F/L=2\mu _{{\text{e}},0}\cdot I_{\text{e}}\cdot {I'}_{\text{e}}/r=2\cdot I_{\text{e}}\cdot {I'}_{\text{e}}/c^{2}r$… If we compare this with the corresponding equation … of the e.m. system we obtain $I_{\text{m}}=I_{\text{e}}/c$. This shows again that I_m and I_e are really different quantities differing by a factor c.

Thus, one and the same physical phenomenon can in principle be quantified and described using a variety of physical quantities. --Reuqr (talk) 02:44, 7 August 2020 (UTC)

statC

who did this calculation?

$1\;\mathrm {C} /{\sqrt {4\pi \epsilon _{0}}}=2997924580\;\mathrm {statC}$

As far as I can calculate:$1\;\mathrm {C} /{\sqrt {4\pi \epsilon _{0}}}=94802.6992620367$ m N^½. There seems rather some magic with speed of light (10 c) in those numbers ... The other conversion is similarly funny:

$1\;\mathrm {C} {\sqrt {4\pi /\epsilon _{0}}}=3.7673\times 10^{10}\;\mathrm {statC}$ (as unit of Φ_D)

by my calculation :$1\;\mathrm {C} {\sqrt {4\pi /\epsilon _{0}}}=1191325.854168388$ m N^½. Ra-raisch (talk) 22:29, 12 August 2017 (UTC)

so if I understand correctly, the conversions should be

$1\;\mathrm {C} {\sqrt {\tfrac {10^{9}}{4\pi \epsilon _{0}}}}=2997924580\;\mathrm {statC}$

$1\;\mathrm {C} {\sqrt {\tfrac {4\pi 10^{9}}{\epsilon _{0}}}}=3.7673\times 10^{10}\;\mathrm {statC}$ (as unit of Φ_D)

Ra-raisch (talk) 09:07, 13 August 2017 (UTC)

Conversion blahmanism

I wiped bollocks out, which originated from years of clueless editing. No prejudice against reinstating some old pieces by an expert editor, just note that [1] by Sbyrnes321 explicitly states that “C” (presumably coulomb) may be used as a unit of electric flux. Beware! Incnis Mrsi (talk) 07:05, 1 September 2019 (UTC)

The statement "A unit *must* be expressed via another unit using a numerical factor." is not true. E.g. https://www.google.de/books/edition/Encyclopaedia_of_Historical_Metrology_We/XnRVDwAAQBAJ?hl=en&gbpv=1&dq=statcoulomb+%22electric+flux%22+conversion&pg=PA29&printsec=frontcover contains conversion tables with electric flux density.--Debenben (talk) 13:56, 26 June 2021 (UTC)

Contradictory equations

@Quondum and other contributors: Would you please review the Statcoulomb § As a unit of flux of electric displacement field? The two equations/correspondences at the end of that section seem to contradict each other. I don't understand how they can both be true. And a recent edit removed a factor of 10⁹ from one equation. I can't determine if that change was correct. Indefatigable (talk) 16:32, 21 December 2024 (UTC)

The 9th SI Brochure says:

• electric flux density, electric displacement: coulomb per square metre | C m−2 | A s m−2

which makes sense to me a charge moving across an area. That is the meaning of a flux. It's hard to make sense of flux of a non-thing, the field.

The section in question has no sources we can use to learn more. So I deleted it. If someone has references then we would know the correct meaning and conversion. Johnjbarton (talk) 17:40, 21 December 2024 (UTC)

@Indefatigable: The removal of the factor 10⁹ appears to have been correct, and the correspondence and equation did not contradict each other (a correspondence is not an equation, and usually implies a context-dependent conversion). However, we should find a way of expressing it so that the intended meaning is crystal-clear.

@Johnjbarton: We cannot expect the SI to say anything about Gaussian quantities. With or without sources, the Gaussian system defines its quantities so that the electric charge contained within a closed surface differs from the total flux through that surface by a factor of 4π, and it makes sense to highlight the two different correspondences. More detail is given in Gaussian units. Here, lack of sourcing is a lesser eveil compared to failure to mention a counterintuitive point; it is implied by the preceding anyway. I will need to look around a bit to be sure that the unit statC or Fr was indeed used as a unit for electric flux. (I wish that modern physicists would just completely drop the Gaussian system, but as an encyclopaedia we do need to document this weirdness.) —Quondum 19:46, 21 December 2024 (UTC)

@Quondum Indeed SI need say nothing about historical units but someone must. Wikipedia should describe statcoulomb on its own terms first and foremost. If the statcoulomb is used for flux, which makes sense, then we should describe that use. That much should be sourceable if notable.

We could note similar SI units and source that. We don't need to derive a conversion which is, according to this article, dubious. An unsourced derivation with unclear limitations seems risky and unnecessary to me. Johnjbarton (talk) 19:56, 21 December 2024 (UTC)

See Electric flux and Gray. For the factor I removed, see the section statC above. Zophar (talk) 21:24, 21 December 2024 (UTC)

It is interesting that Gray (1954) uses "statcoulomb" for electric charge and "esu" for electric flux. Using distinct units would seem to be a sensible way to minimize confusion.

Johnjbarton, I think that you may be overestimating the risk, and underestimating the implications of consistently removing what was written in the section. From my perspective, the only aspect that might be in doubt is the actual name of the unit that was used. Why do you say that the article indicates that it is dubious? —Quondum 21:50, 21 December 2024 (UTC)

Jackson gives statcoulomb as a unit of charge and statcoulomb/cm² as the units of "Displacement". Berkeley Physics v2 claims that CGS unit is esu for charge and does not mention 'statcoulomb'. But for 'statvolt' is says 'stat' is for electrostatic.

RE: dubious: The article says "The conversion between the units coulomb and the statcoulomb depends on the context." and there is a whole section entitled "General incompatibility".

What does this questionable section do? As far as I can tell it claims that the units for "flux of the electric field", which is defined to be (page 63)

$$\Phi =\int \mathbf {E} \cdot d\mathbf {S} ,$$

can be selected by using Gauss' law. Closing the integral around a charge $Q$ gives $Q/\epsilon _{0}$ (page 8). (Pages in Panofsky, W. K. H., Phillips, M. (2012). Classical Electricity and Magnetism: Second Edition. United States: Dover Publications.)

The result, if true, is not related to SI vs CGS except that one can use two different units for $Q$ and get two different units for $\Phi$.

If we allow that this derivation is sensible without a reference, is that enough? Are there uses of "flux of the electric field" that require one to assign units? Are the units of "flux of the electric field" notable if we have no references? (To be sure, my references are theory oriented and old). Johnjbarton (talk) 23:10, 21 December 2024 (UTC)

Ah. Phrasing is everything. "depends on context", in this case, means a well-defined dependence on what quantity has "statcoulomb" as its unit. I hope my edit makes this clearer. There should be nothing to be interpreted as being vague or "dubious". Also, the "general incompatibility" is a badly phrased description of distinct systems of equations.

The equation that you give above applies only in the 'vacuum' convention (i.e. where no charges or currents are 'bound'), and so "flux of the electric field" is not a good concept to work with. The intuition behind this is that the constant ε₀ must be replaced by the location-dependent ε in the general case, at least when bound charges are treated as being hidden in the polarization of dielectric media. Consequently, it makes sense to find flux of the electric displacement field (⁠$\textstyle \Phi _{\text{D}}=\int \mathbf {D} \cdot d\mathbf {S}$⁠), not flux of the electric field strength (⁠$\textstyle \Phi _{\text{E}}=\int \mathbf {E} \cdot d\mathbf {S}$⁠). I presume that the source you are using is working in the context/convention that does not consider bound charge (what is misleadingly referred to as the "microscopic formulation" in Maxwell's equations), in which case it is correct, but I would not suggest assuming that convention here. [Side comment: I find it amazing that Electric field does not mention the correct SI term "electric field strength"!] I hope this makes sense as a response to your post, at least to work with. —Quondum 01:44, 22 December 2024 (UTC)

Your edits are very helpful, thanks!

Well my refs have what they have but nothing about flux of the electric displacement field. I can look in the library in a couple of weeks. Johnjbarton (talk) 02:03, 22 December 2024 (UTC)

One of the nasty things about conventions and terminology is that they are often not explicitly called out. I often find that a significant part of the work I do in trying to understand a physics or mathematics text is determining the underlying assumptions and conventions. From what you say, your source does not mention D (and presumably, it also uses B but not H). This convention collides with that in typical WP articles, unfortunately. Incidentally, your "unit-independent" approach above does not work with Gaussian quantities anyway: there is a factor of 4π needed (or in the Gaussian system, ε₀ = 1/4π), which makes it somewhat confusing. —Quondum 02:24, 22 December 2024 (UTC)

Here are more references. Zophar (talk) 20:50, 23 December 2024 (UTC)

References

Removed note

The removed footnote "As of the 2019 revision of the SI, the correspondence given is not exact, although it is very close." potentially has value. The fact that these are correspondences does not make them inexact. A better approach might be to use the exact conversion formula, though. The fact that the difference from exactness is about 10 decimal places in makes it subtle, but it helps a serious student to understand how the numbers are derived. —Quondum 02:03, 22 December 2024 (UTC)

I'm fine if the plain content says more like what you say. A footnote which waffles is not helpful; it says to the reader "psst, we have secrets but we are not telling". Johnjbarton (talk) 04:00, 22 December 2024 (UTC)

I've given the exact conversion, and trimmed the section of some waffle. I think that the entire section Statcoulomb § Dimensional relation between statcoulomb and coulomb, including its subsections, can be deleted, though we should see whether the reference in it should be retained. —Quondum 23:27, 24 December 2024 (UTC)