Loading AI tools
From Wikipedia, the free encyclopedia
This article is written in British English, which has its own spelling conventions (colour, travelled, centre, defence, artefact, analyse) and some terms that are used in it may be different or absent from other varieties of English. According to the relevant style guide, this should not be changed without broad consensus. |
This level-5 vital article is rated C-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||
|
Archives: 1 |
|
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)
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:
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:
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)
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:
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
In free space these become
From these we may derive Coulomb's law and the Biot-Savart law using the usual mathematical arguments. The results are
whence it follows that the rationalization constants are equal to one. Zophar (talk) 04:58, 18 December 2017 (UTC)
Gavo atoms (talk) 07:08, 28 February 2020 (UTC)can you help me to have question and answers of EMFD unit
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.