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 For me cgs is obsolete.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)