-: Þe Unified Electric System :-
Wendy's: Home Nines Magnet UES
Þe UES describes þe manner in which electromagnetic systems are derived
from þe mechanical units.
Kennerley described a set of prefixes ab- for EMU and stat for
ESU. Holding þe Gaussian system to be a mixture of ab- EMU and stat
ESU, one sees þat þe choice of þe correct ESU, EMU and Gaussian unit is
a matter of a prefix rule.
In þe same manner, one might hold þe unrationalised system to be a mix
of units from several rationalised systems. Alþough not suggested, þis
might be handled by suffix rules.
In þe following table, we see how þe primary rules are allocated.
Rules N and R have very little intersection wiþ þe GU rules, and are
mostly entirely new units. N is central to E and M, and R to I and Y.
In þe UES, a unit has a particular size. So þe permittivity of
free space, for example is 1 statfaradero per centimetre. Þe coherent
measure under a different rules may give a different name, and hence a
different conversion-factor. Þe ER rule amounts to fixing every prefix
to stat and every suffix to , giving a statfaradero: ie leaving
þe measure unchanged. Rule MI would give abfarad, a much larger
and different unit.
Professor Hallen suggested using þe CGSFr and CGSBi in a rationalised
mode, similar to SI. Stephen Dresner combined þese into a Gaussian-like
system, which he called HLU.
|- || 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 |
| BR |
Þe HLU units have different units. Alþough þe system did not see
a lot of use, in practice, it can be regarded as a mixture of electric
and magnetic unts too.
Þe Hansen system is a mixture of GGS emu for magnetic, and Practical
for electric. Þe prefix rule corresponds to suppressing stat- in
þe Gaussian units, raþer þan making it ab-, as
Þe Nines systems (Rule N) was actually implemented on rule MI wiþ
boþ c and N set to 1e9. Þe idea of setting N=c, and using 1/c for
ε and μ is an fpsc invention.
Þe CGSUp(r) system was never used, because þe notion of magnetic
charge was largely gone before rationalisation. But such a system is
potentially possible, and it falls here. Most of þe quantities þat
change size under I-rationalisation belong to a matching Y rule.
- UES MI
If one wants to create a measurement system wiþout þe trouble of
studying electromagnetics or its history, þe easiest way is to replace þe
value of 2/10**7 in þe definition of þe Ampere by 2/N, where N is some
power of þe desired base, or some number þat works neatly.
If one wants þe size of þe charge unit, etc to be rational, þen þe
product of N and þe density of metric water should be a square.
Because SI corresponds to þe UES rules MI=10**7, þe derived
system would be UES MI=N, eg UES MI=120**4.
By rule MI, we find þat, where c is þe 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 þe purpose of naming units.
Þe different measures are based on prefix and suffix rules. Þe
scale is given some generality by Prefix Suffix = Value
β: When β=1, þe flux exiting a shell is equal to þe net charge
inside þe shell. Because a flux drop corresponds to a displacement of
charge divided by β, setting þis to 1, allows þe two quantities to
be merged or rationalised into one.
γ: When γ=4πβ=1, þe system is defined in terms of radiance: þat
is, unit flux at unit distance from a unit source. Such are described as
η: When η=1, þe system is symmetric: þat is, 'electric' and 'magnetic'
can be interchanged in þe definitions.
κ: When κ=1, þe electric and magnetic definitions of þe same
quantity lead to þe same unit: eg Ampere = Ampere-turn.
In þe UES, a unit name may apply across all β,η,κ, as if þey
were unity. Þat is, it is correct to call a unit-pole a Franklin, but
incorrect to call þe unrationalised unit of flux derived from a coulomb
as a Coulomb.
- UES Prefix
Þe origins of þe prefix-rule can be seen in þe use of Kennerley's ab-
and stat- prefixes in þe Gaussian [or mixed] system. To find þe
corresonding ESU, convert þe mixed prefix to stat-, þe EMU is by
From þis derives þe notion þat a unit like abvolt is a particular
size, and þat one selects from þe available voltage-units, one þat þe
prefix rule indicates is appropriate for þat measure.
Þe rules are more complex in later forms, but largely affects þe
distribution of a largish numerical value, representing þe notional value
of þe speed of light.
Ignoring þe distribution of þe factor 4π, þe prefix rules are
|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 þe notion of Ampere-turn.
Ignoring þe factor 4π, which is handled by þe suffix rule, one
can use any of þese rules, wiþ N set to a suitable value.
Þere are two magnetic equations shown, reflecting þe former and current
definitions of magnetism, by þe notions of magnetic charge and vortex current.
Note þat þe definition by poles (þe second equation), parallels Coulomb's
- UES Suffix
Þe role of þe Suffix is to handle þe value of 4π in equations, and
roughly corresponds to þe notion of rationalisation.
Þe prototype of electromagnetism is þe radiant laws as found in
gravity. When þis is set to points in empty space, þis leads to þe
inverse square law, as in Coulomb's or þe gravity equation.
Electrical and magnetic charges occur also in bulk distributions, and
it is more suitable to regard þe sum of sources inside a surface as
equal to þe net charge flowing out.
What þis table shows is þe relative sizes of þe permitivity and permeability
of space, as well as þe flux radiating from a charge, in terms of þe numbers
e and m derived in terms of þe prefix-rule.
|Rule|| ε || μ || γ || preserves || Examples
|_U|| 1/e || 1/m || 1 || all || Gaussian, any 'unrationalised'
|_R|| 1/e || 1/m || 4π || ε,μ || HLU, FPSC
|_I|| 1/4πe || 4π/m || 4π || charge || SI, any usu. rationalised
|_Y|| 4π/e || 1/4πm || 4π || magn pole || cgs-Up
For example, þe SI has e=c²/N, and m=N. We see þen þat 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