Difference between revisions of "Emu system"

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The '''emu system''' was a system of units for measuring electrical and magnetic quantities based on the [[CGS system|centimetre–gram–second (CGS) system]]. They were developed by the [[British Association for the Advancement of Science]] (B.A.) from 1862 to 1873,<ref>{{citation | first = Fleeming | last = Jenkin | authorlink = Fleeming Jenkin | title = Reports of the Committee on Electrical Standards | location = London | year = 1873}}.</ref><ref name="EB11">{{citation | contribution = Units, Physical | title = Encyclopædia Britannica | volume = 27 | year = 1911 | edition = 11th | pages = 738–45}}.</ref> based on an original idea by [[Wilhelm Weber|Weber]],<ref group="Note">Weber's original proposal was based on a millimetre–milligram–second system of units.</ref> and rendered obsolete by the introduction of electrical and magnetic units into the [[International System of Units]] (SI) in 1948.<ref>{{SIbrochure8th|page=144}}.</ref>
 
The '''emu system''' was a system of units for measuring electrical and magnetic quantities based on the [[CGS system|centimetre–gram–second (CGS) system]]. They were developed by the [[British Association for the Advancement of Science]] (B.A.) from 1862 to 1873,<ref>{{citation | first = Fleeming | last = Jenkin | authorlink = Fleeming Jenkin | title = Reports of the Committee on Electrical Standards | location = London | year = 1873}}.</ref><ref name="EB11">{{citation | contribution = Units, Physical | title = Encyclopædia Britannica | volume = 27 | year = 1911 | edition = 11th | pages = 738–45}}.</ref> based on an original idea by [[Wilhelm Weber|Weber]],<ref group="Note">Weber's original proposal was based on a millimetre–milligram–second system of units.</ref> and rendered obsolete by the introduction of electrical and magnetic units into the [[International System of Units]] (SI) in 1948.<ref>{{SIbrochure8th|page=144}}.</ref>
  
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The emu system was usually treated as a non-rationalized three-quantity system in which [[electric current]], for example, had the [[dimension]] [[force]]<sup>½</sup>. The [[magnetic constant]] (known at the time as the "permeability of free space") was literally ignored: in modern terms, it was set as dimensionless and with a value of 1. For these reasons, the form of [[quantity equation]]s intended for use with the emu system is often different from that of the corresponding equations in the four-quantity rationalized [[International System of Quantities]].<ref>{{GreenBook2nd|pages=117–23}}.</ref>
+
The emu system was usually treated as a non-rationalized three-quantity system in which [[electric current]], for example, had the [[dimension]] [[force]]<sup>½</sup>. The [[magnetic constant]] (known at the time as the "permeability of free space") was literally ignored: in modern terms, it was set as dimensionless and with a value of 1. For these reasons, the form of [[quantity equation]]s intended for use with the emu system is often different from that of the corresponding equations in the four-quantity rationalized [[International System of Quantities]].<ref name="IUPAC">{{GreenBook2nd|pages=117–23}}.</ref>
  
 
==Units==
 
==Units==
−
{| class="wikitable"
+
{| class="wikitable" align=right style="margin:0 0 0 0.5em;"
 
|-
 
|-
 
!
 
!
 
! Name
 
! Name
 
! SI equivalent
 
! SI equivalent
 +
! [[Dimension]]s
 
|-
 
|-
 
| emu of [[electric current]]
 
| emu of [[electric current]]
 
| [[abampere]]<br/>[[biot]]
 
| [[abampere]]<br/>[[biot]]
 
| 10 [[Ampere|A]]
 
| 10 [[Ampere|A]]
 +
| '''L'''<sup>½</sup>'''M'''<sup>½</sup>'''T'''<sup>−1</sup>'''μ'''<sup>−½</sup>
 
|-
 
|-
 
| emu of [[electric charge]]
 
| emu of [[electric charge]]
 
| [[abcoulomb]]
 
| [[abcoulomb]]
 
| 10 [[Coulomb|C]]
 
| 10 [[Coulomb|C]]
 +
| '''L'''<sup>½</sup>'''M'''<sup>½</sup>'''μ'''<sup>−½</sup>
 
|-
 
|-
 
| emu of [[capacitance]]
 
| emu of [[capacitance]]
 
| [[abfarad]]
 
| [[abfarad]]
 
| 10<sup>9</sup> [[Farad|F]]
 
| 10<sup>9</sup> [[Farad|F]]
 +
| '''L'''<sup>−1</sup>'''T'''<sup>2</sup>'''μ'''<sup>−1</sup>
 
|-
 
|-
 
| emu of [[inductance]]
 
| emu of [[inductance]]
 
| [[abhenry]]
 
| [[abhenry]]
 
| 10<sup>−9</sup> [[Henry|H]]
 
| 10<sup>−9</sup> [[Henry|H]]
 +
| '''Lμ'''
 
|-
 
|-
 
| emu of [[electric conductance]]
 
| emu of [[electric conductance]]
 
| [[abmho]]
 
| [[abmho]]
 
| 10<sup>9</sup> [[Siemens|S]]
 
| 10<sup>9</sup> [[Siemens|S]]
 +
| '''L'''<sup>−1</sup>'''Tμ'''<sup>−1</sup>
 
|-
 
|-
 
| emu of [[electric resistance]]
 
| emu of [[electric resistance]]
 
| [[abohm]]
 
| [[abohm]]
 
| 10<sup>−9</sup> [[Ohm|Ω]]
 
| 10<sup>−9</sup> [[Ohm|Ω]]
 +
| '''LT'''<sup>−1</sup>'''μ'''
 
|-
 
|-
 
| emu of [[electromotive force]]
 
| emu of [[electromotive force]]
 
| [[abvolt]]
 
| [[abvolt]]
 
| 10<sup>−8</sup> [[Volt|V]]
 
| 10<sup>−8</sup> [[Volt|V]]
 +
| '''L'''<sup>{{frac|3|2}}</sup>'''M'''<sup>½</sup>'''T'''<sup>−2</sup>'''μ'''<sup>½</sup>
 +
|-
 +
| emu of [[magnetic flux density]]
 +
| [[gauss]]
 +
| 10<sup>−4</sup> [[Tesla|T]]
 +
| '''L'''<sup>−½</sup>'''M'''<sup>½</sup>'''T'''<sup>−1</sup>'''μ'''<sup>½</sup>
 +
|-
 +
| emu of [[magnetomotive force]]
 +
| [[gilbert]]
 +
| {{frac|10|4π}} [[Ampere|A]]<ref group="Note">The [[MKS system|MKS unit]] of magnetomotive force was the [[ampere-turn]], which is numerically equal to the [[ampere]].</ref>
 +
| '''L'''<sup>½</sup>'''M'''<sup>½</sup>'''T'''<sup>−1</sup>'''μ'''<sup>−½</sup>
 +
|-
 +
| emu of [[magnetic flux]]
 +
| [[maxwell]]
 +
| 10<sup>−8</sup> [[Weber|Wb]]
 +
| '''L'''<sup>{{frac|3|2}}</sup>'''M'''<sup>½</sup>'''T'''<sup>−1</sup>'''μ'''<sup>½</sup>
 +
|-
 +
| emu of [[magnetic field strength]]
 +
| [[oersted]]
 +
| {{frac|1000|4π}} [[Ampere|A]] [[Metre|m<sup>−1</sup>]]
 +
| '''L'''<sup>−½</sup>'''M'''<sup>½</sup>'''T'''<sup>−1</sup>'''μ'''<sup>−½</sup>
 
|-
 
|-
 
|}
 
|}
 +
The names of the different units never received widespread usage (except the [[gauss]] in the Unitd States), and it was always common to refer to "the emu of capacitance" or "an inductance of 100&nbsp;emu" (emu&nbsp;= "electromagnetic unit"). The prefix "ab-" in many of the names serves to distinguish the units from the corresponding [[International System of Electrical and Magnetic Units|"international practical units"]] (without prefix) and the corresponding units in the [[esu system]] (with the prefix "stat-").
 +
 +
==The three-quantity emu system==
 +
===Dimensional analysis===
 +
 +
===Quantity equations===
 +
The quantity equations is the three-quantity emu system can be derived from the corresponding equations in the four-quantity [[International System of Quantities]] by the following substitutions:<ref name="IUPAC"/>
 +
:''μ''<sub>0</sub> = 4π
 +
:''μ'' = 4π''μ''<sub>r</sub>
 +
:''ε''<sub>0</sub> = 1/4π''c''<sub>0</sub><sup>2</sup>
 +
:'''''H''''' = '''''H'''''<sup>(ir)</sup>/4π
 +
:''χ'' = 4π''χ''<sup>(ir)</sup>
 +
where '''''H'''''<sup>(ir)</sup> and ''χ''<sup>(ir)</sup> are the irrational [[magnetic field strength]] and the irrational [[magnetic susceptibility]] respectively.
 +
;force between current elements in vacuum:'''''F''''' = [''I''d'''''ℓ'''''<sub>1</sub> × (''I''d'''''ℓ'''''<sub>2</sub> × '''''r''''')]/''r''<sup>3</sup>
 +
;force on a current element in a field:'''''F''''' = ''I''d'''''ℓ''''' × '''''B'''''
 +
;potential due to a current element in vacuum:'''''A''''' = ''I''d'''''ℓ'''''/r
 +
;relation between field and potential:'''''B''''' = curl '''''A'''''
 +
;field due to a current element in vacuum:'''''B''''' = (''I''d'''''ℓ''''' × '''''r''''')/''r''<sup>3</sup>
 +
;field due to a current density '''''j''''' in vacuum:curl '''''B''''' = 4π'''''j'''''
 +
;magnetic dipole of a current loop of area d'''''A''''':'''''m''''' = ''I''d'''''A'''''
 +
;potential around a magnetic dipole in vacuum:'''''A''''' = ('''''m''''' × '''''r''''')/''r''<sup>3</sup>
 +
;energy of a magntic dipole in a field:''E''<sub>p</sub> = −'''''m'''''·'''''B'''''
 +
;magnetic dipole induced by a field:'''''m''''' = ''ξ'''B'''''
 +
;relative permeability:''μ''<sub>r</sub> = 1 + 4π''χ''<sup>(ir)</sup>
 +
;magnetic susceptibility:'''''M''''' = ''χ''<sup>(ir)</sup>'''''B'''''
 +
;Curie relation:''χ''{{su|p=(ir)|b=m}} = ''V''<sub>m</sub>''χ''<sup>(ir)</sup> = ''Lm''<sup>2</sup>/3''kT''
  
 
==Notes and references==
 
==Notes and references==

Latest revision as of 08:22, 12 August 2010

The emu system was a system of units for measuring electrical and magnetic quantities based on the centimetre–gram–second (CGS) system. They were developed by the British Association for the Advancement of Science (B.A.) from 1862 to 1873,[1][2] based on an original idea by Weber,[Note 1] and rendered obsolete by the introduction of electrical and magnetic units into the International System of Units (SI) in 1948.[3]

The emu system was usually treated as a non-rationalized three-quantity system in which electric current, for example, had the dimension force½. The magnetic constant (known at the time as the "permeability of free space") was literally ignored: in modern terms, it was set as dimensionless and with a value of 1. For these reasons, the form of quantity equations intended for use with the emu system is often different from that of the corresponding equations in the four-quantity rationalized International System of Quantities.[4]

Units

Name SI equivalent Dimensions
emu of electric current abampere
biot 		10 A L½M½T−1μ−½
emu of electric charge abcoulomb 10 C L½M½μ−½
emu of capacitance abfarad 109 F L−1T2μ−1
emu of inductance abhenry 10−9 H Lμ
emu of electric conductance abmho 109 S L−1Tμ−1
emu of electric resistance abohm 10−9 Ω LT−1μ
emu of electromotive force abvolt 10−8 V L3⁄2M½T−2μ½
emu of magnetic flux density gauss 10−4 T L−½M½T−1μ½
emu of magnetomotive force gilbert 10⁄4π A[Note 2] L½M½T−1μ−½
emu of magnetic flux maxwell 10−8 Wb L3⁄2M½T−1μ½
emu of magnetic field strength oersted 1000⁄4π A m−1 L−½M½T−1μ−½

The names of the different units never received widespread usage (except the gauss in the Unitd States), and it was always common to refer to "the emu of capacitance" or "an inductance of 100 emu" (emu = "electromagnetic unit"). The prefix "ab-" in many of the names serves to distinguish the units from the corresponding "international practical units" (without prefix) and the corresponding units in the esu system (with the prefix "stat-").

The three-quantity emu system

Dimensional analysis

Quantity equations

The quantity equations is the three-quantity emu system can be derived from the corresponding equations in the four-quantity International System of Quantities by the following substitutions:[4]

μ0 = 4π
μ = 4πμr
ε0 = 1/4πc02
H = H(ir)/4π
χ = 4πχ(ir)

where H(ir) and χ(ir) are the irrational magnetic field strength and the irrational magnetic susceptibility respectively.

force between current elements in vacuum
F = [Idℓ1 × (Idℓ2 × r)]/r3
force on a current element in a field
F = Idℓ × B
potential due to a current element in vacuum
A = Idℓ/r
relation between field and potential
B = curl A
field due to a current element in vacuum
B = (Idℓ × r)/r3
field due to a current density j in vacuum
curl B = 4πj
magnetic dipole of a current loop of area dA
m = IdA
potential around a magnetic dipole in vacuum
A = (m × r)/r3
energy of a magntic dipole in a field
Ep = −m·B
magnetic dipole induced by a field
m = ξB
relative permeability
μr = 1 + 4πχ(ir)
magnetic susceptibility
M = χ(ir)B
Curie relation
χ(ir)m = Vmχ(ir) = Lm2/3kT

Notes and references

Notes

  1. ↑ Weber's original proposal was based on a millimetre–milligram–second system of units.
  2. ↑ The MKS unit of magnetomotive force was the ampere-turn, which is numerically equal to the ampere.

References

  1. ↑ Jenkin, Fleeming Reports of the Committee on Electrical Standards; London, 1873.
  2. ↑ Units, Physical. In Encyclopædia Britannica, 11th ed., 1911; Vol. 27, pp 738–45.
  3. ↑ The International System of Units (SI), 8th ed.; International Bureau of Weights and Measures: Sèvres, France, 2006; p 144. ISBN 92-822-2213-6, <http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf>.
  4. ↑ 4.0 4.1 Quantities, Units and Symbols in Physical Chemistry, 2nd ed.; Blackwell Science: Oxford, 1993; pp 117–23. ISBN 0-63203-5838, <http://old.iupac.org/publications/books/gbook/green_book_2ed.pdf>.

External links

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