-: The Unified Electric System :-

Wendy's: Home Nines Magnet UES

The UES describes the manner in which electromagnetic systems are derived from the mechanical units.
      Kennerley described a set of prefixes ab- for EMU and stat for ESU. Holding the Gaussian system to be a mixture of ab- EMU and stat ESU, one sees that the choice of the correct ESU, EMU and Gaussian unit is a matter of a prefix rule.
      In the same manner, one might hold the unrationalised system to be a mix of units from several rationalised systems. Although not suggested, this might be handled by suffix rules.
      In the following table, we see how the primary rules are allocated. Rules N and R have very little intersection with the GU rules, and are mostly entirely new units. N is central to E and M, and R to I and Y.
      In the UES, a unit has a particular size. So the permittivity of free space, for example is 1 statfaradero per centimetre. The coherent measure under a different rules may give a different name, and hence a different conversion-factor. The ER rule amounts to fixing every prefix to stat and every suffix to , giving a statfaradero: ie leaving the measure unchanged. Rule MI would give abfarad, a much larger and different unit.
- elec magn U I R Y
- - - - - -ero -ade
- - - -ade - -ero -ade
G stat- ab- Gaussian HDU HLU -
E stat- stat- ESU CGSFr (r) CGSHe(r) -
M ab- ab- EMU CGSBi (r) CGSLo(r) CGSUp(r)
H - ab- Hansen - - -
N nen- nen- NNU NNA NNB -
- - - - SI
mksa MI
fpsc NR
Professor Hallen suggested using the CGSFr and CGSBi in a rationalised mode, similar to SI. Stephen Dresner combined these into a Gaussian-like system, which he called HLU.
      The HLU units have different units. Although the system did not see a lot of use, in practice, it can be regarded as a mixture of electric and magnetic unts too.
      The Hansen system is a mixture of GGS emu for magnetic, and Practical for electric. The prefix rule corresponds to suppressing stat- in the Gaussian units, rather than making it ab-, as
      The Nines systems (Rule N) was actually implemented on rule MI with both c and N set to 1e9. The idea of setting N=c, and using 1/c for ε and μ is an fpsc invention.
      The CGSUp(r) system was never used, because the notion of magnetic charge was largely gone before rationalisation. But such a system is potentially possible, and it falls here. Most of the quantities that change size under I-rationalisation belong to a matching Y rule.
If one wants to create a measurement system without the trouble of studying electromagnetics or its history, the easiest way is to replace the value of 2/10**7 in the definition of the Ampere by 2/N, where N is some power of the desired base, or some number that works neatly.
      If one wants the size of the charge unit, etc to be rational, then the product of N and the density of metric water should be a square.
      Because SI corresponds to the UES rules MI=10**7, the derived system would be UES MI=N, eg UES MI=120**4.
      By rule MI, we find that, where c is the speed of light:
        Permeability of free-space = μ = 4π/N
        Permittivity of free space = ε = N/4πc²
UES Naming Rule
A convension on setting β=η=κ=1, for the purpose of naming units. The different measures are based on prefix and suffix rules. The scale is given some generality by Prefix Suffix = Value
      β: When β=1, the flux exiting a shell is equal to the net charge inside the shell. Because a flux drop corresponds to a displacement of charge divided by β, setting this to 1, allows the two quantities to be merged or rationalised into one.
      γ: When γ=4πβ=1, the system is defined in terms of radiance: that is, unit flux at unit distance from a unit source. Such are described as unrationalised
      η: When η=1, the system is symmetric: that is, 'electric' and 'magnetic' can be interchanged in the definitions.
      κ: When κ=1, the electric and magnetic definitions of the same quantity lead to the same unit: eg Ampere = Ampere-turn.
      In the UES, a unit name may apply across all β,η,κ, as if they were unity. That is, it is correct to call a unit-pole a Franklin, but incorrect to call the unrationalised unit of flux derived from a coulomb as a Coulomb.
UES Prefix
The origins of the prefix-rule can be seen in the use of Kennerley's ab- and stat- prefixes in the Gaussian [or mixed] system. To find the corresonding ESU, convert the mixed prefix to stat-, the EMU is by using ab-.
      From this derives the notion that a unit like abvolt is a particular size, and that one selects from the available voltage-units, one that the prefix rule indicates is appropriate for that measure.
      The rules are more complex in later forms, but largely affects the distribution of a largish numerical value, representing the notional value of the speed of light.
      Ignoring the distribution of the factor 4π, the prefix rules are as follows.
Rule Electric Magnetic Linkage Examples
formula F=eQQ/KR² F/L=2I/KmL
I=Q/κT emκ²=c²
G_ N N c/N Gaussian, HLU
E_ N c²/N 1 ESU, CGSFr (r)
M_ c²/N N 1 EMU, SI, CGSBi(r)
N_ c c 1 Nines, FPSC

Linkage corresponds here to '1/turn' in the notion of Ampere-turn.
Ignoring the factor 4π, which is handled by the suffix rule, one can use any of these rules, with N set to a suitable value.
      There are two magnetic equations shown, reflecting the former and current definitions of magnetism, by the notions of magnetic charge and vortex current. Note that the definition by poles (the second equation), parallels Coulomb's equation.
UES Suffix
The role of the Suffix is to handle the value of 4π in equations, and roughly corresponds to the notion of rationalisation.
      The prototype of electromagnetism is the radiant laws as found in gravity. When this is set to points in empty space, this leads to the inverse square law, as in Coulomb's or the gravity equation.
      Electrical and magnetic charges occur also in bulk distributions, and it is more suitable to regard the sum of sources inside a surface as equal to the net charge flowing out.
Rule ε μ γ  preserves Examples
_U 1/e 1/m 1 all Gaussian, any 'unrationalised'
_R 1/e 1/m ε,μ HLU, FPSC
_I 1/4πe 4π/m charge SI, any usu. rationalised
_Y 4π/e 1/4πm magn pole cgs-Up
What this table shows is the relative sizes of the permitivity and permeability of space, as well as the flux radiating from a charge, in terms of the numbers e and m derived in terms of the prefix-rule.
      For example, the SI has e=c²/N, and m=N. We see then that for N=1e7 and c = 299792458, rule MI gives:
        ε = N/4πc² = 8.854187817620E-12 F/m
        μ = 4π/N = 1.256637061435917E-6 H/m

© 2003-2004 Wendy Krieger