Difference between revisions of "CGS versus SI"

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(Split out the constants into their own table.)
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{{Warning|If hard core NMR or physics theory is not to your taste, please do not read any further!}}
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The [https://en.wikipedia.org/wiki/International_System_of_Units SI or International System of Units] versus the [https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units CGS or Centimetre–gram–second] system of units is a constant source of confusion in the field of NMR.  Both are based on the metric system, however the differences can result in quite different forms of the fundamental NMR equations.  An example of this is Tesla versus Gauss units for the magnetic field strength.
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== CGS flavours ==
 +
 
 +
Note that in the CGS system, that there are different sets of units for electromagnetism.  The major systems are [https://en.wikipedia.org/wiki/Centimetre_gram_second_system_of_units#Electrostatic_units_.28ESU.29 ESU], [https://en.wikipedia.org/wiki/Centimetre_gram_second_system_of_units#Electromagnetic_units_.28EMU.29 EMU], [https://en.wikipedia.org/wiki/Gaussian_units Gaussian units], and [https://en.wikipedia.org/wiki/Lorentz%E2%80%93Heaviside_units Lorentz-Heaviside units].  In NMR papers not using SI units, the EMU system is most commonly used.
  
The [https://en.wikipedia.org/wiki/International_System_of_Units SI or International System of Units] versus the [https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units CGS or Centimetre–gram–second] system of units is a constant source of confusion in the field of NMR.  Both are based on the metric system, however the differences can result in quite different forms of the fundamental NMR equations.  An example of this is Tesla versus Gauss units for the magnetic field strength.
 
  
 
== Units of measurement ==
 
== Units of measurement ==
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! Symbol
 
! Symbol
 
! colspan="3" | SI unit
 
! colspan="3" | SI unit
! colspan="3" | CGS unit
+
! colspan="3" | CGS unit (EMU)
 
! SI to CGS conversion factor
 
! SI to CGS conversion factor
 
|-
 
|-
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! Name
 
! Name
 
! Symbol
 
! Symbol
! Base unit
+
! [https://en.wikipedia.org/wiki/SI_base_unit Base units]
 
! Name
 
! Name
 
! Symbol
 
! Symbol
! Base unit
+
! Base units
 
!
 
!
 
|-
 
|-
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|| ''L''
 
|| ''L''
 
|style="text-align:left;"| metre
 
|style="text-align:left;"| metre
||  
+
|| m
 
|| m
 
|| m
 
|style="text-align:left;"| centimetre
 
|style="text-align:left;"| centimetre
||  
+
|| cm
 
|| cm
 
|| cm
 
|| 10<sup>−2</sup>
 
|| 10<sup>−2</sup>
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|| ''m''
 
|| ''m''
 
|style="text-align:left;"| kilogram
 
|style="text-align:left;"| kilogram
||  
+
|| kg
 
|| kg
 
|| kg
 
|style="text-align:left;"| gram
 
|style="text-align:left;"| gram
||  
+
|| g
 
|| g
 
|| g
 
|| 10<sup>−3</sup>
 
|| 10<sup>−3</sup>
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|| ''t''
 
|| ''t''
 
|style="text-align:left;"| second
 
|style="text-align:left;"| second
||  
+
|| s
 
|| s
 
|| s
 
|style="text-align:left;"| second
 
|style="text-align:left;"| second
||  
+
|| s
 
|| s
 
|| s
 
|| 1
 
|| 1
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! acceleration  
 
! acceleration  
 
|| ''a''
 
|| ''a''
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Metre_per_second_squared Metre per second squared]
+
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Metre_per_second_squared metre per second squared]
 
||  
 
||  
 
|| m⋅s<sup>−2</sup>
 
|| m⋅s<sup>−2</sup>
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Gal_%28unit%29 Gal]
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|style="text-align:left;"| [https://en.wikipedia.org/wiki/Gal_%28unit%29 galileo]
|| gal
+
|| Gal
 
|| cm⋅s<sup>−2</sup>
 
|| cm⋅s<sup>−2</sup>
 
|| 10<sup>−2</sup>
 
|| 10<sup>−2</sup>
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|| kg⋅m<sup>2</sup>·s<sup>−3</sup>
 
|| kg⋅m<sup>2</sup>·s<sup>−3</sup>
 
|style="text-align:left;"| erg per second
 
|style="text-align:left;"| erg per second
|| erg⋅s<sup>−1</sup>
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||
 
|| g·cm<sup>2</sup>·s<sup>−3</sup>
 
|| g·cm<sup>2</sup>·s<sup>−3</sup>
 
|| 10<sup>−7</sup>
 
|| 10<sup>−7</sup>
 
|-
 
|-
! magnetic flux density
+
! magnetic dipole moment
 +
|| ''μ''
 +
|style="text-align:left;"| Newton-meters per Tesla
 +
||
 +
|| A·m<sup>2</sup>
 +
|style="text-align:left;"| electromagnetic unit
 +
|| emu
 +
|| abA·cm<sup>2</sup>
 +
|| 10<sup>−3</sup>
 +
|-
 +
! magnetic flux density (B-field)
 
|| ''B''
 
|| ''B''
 
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Tesla_%28unit%29 Tesla]
 
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Tesla_%28unit%29 Tesla]
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|style="text-align:left;"| [https://en.wikipedia.org/wiki/Gauss_%28unit%29 Gauss]
 
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Gauss_%28unit%29 Gauss]
 
|| Gs
 
|| Gs
|| esu·cm<sup>−2</sup>
+
|| Mx·cm<sup>−2</sup>
 
|| 10<sup>−4</sup>
 
|| 10<sup>−4</sup>
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|-
 +
! magnetic flux density (H-field)
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|| ''H''
 +
|style="text-align:left;"| Amperes per metre
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||
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|| A·m<sup>−1</sup>
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|style="text-align:left;"| [https://en.wikipedia.org/wiki/Oersted Oersted]
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|| Oe
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|| g·cm·s<sup>−2</sup>
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|| 4π·10<sup>−3</sup>
 
|-
 
|-
 
! magnetic flux
 
! magnetic flux
|| ''H''
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|| ''Φ<sub>B</sub>''
 
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Weber_%28unit%29 Weber]
 
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Weber_%28unit%29 Weber]
 
|| Wb
 
|| Wb
 
|| kg·m<sup>2</sup>·s<sup>−2</sup>·A<sup>−1</sup>
 
|| kg·m<sup>2</sup>·s<sup>−2</sup>·A<sup>−1</sup>
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Oersted Oersted]
+
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Maxwell_%28unit%29 Maxwell]
|| Oe
+
|| Mx
|| g·cm·s<sup>−2</sup>
+
|| Mx
|| 1000/4π
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|| 10<sup>−8</sup>
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|-
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! magnetic susceptibility
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|| ''χ<sub>m</sub>''
 +
|style="text-align:left;"|
 +
||
 +
|| -
 +
|style="text-align:left;"|
 +
||
 +
|| -
 +
|| ()<sup>−1</sup>
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|-
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! electric current
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|| ''I''
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|style="text-align:left;"| [https://en.wikipedia.org/wiki/Ampere ampere]
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|| A
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|| A
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|style="text-align:left;"| [https://en.wikipedia.org/wiki/Abampere abampere] (or biot)
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|| abA (or Bi)
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|| abA (or Bi)
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|| 10<sup>−1</sup>
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|-
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! electric charge
 +
|| ''Q''
 +
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Coulomb coulomb]
 +
|| C
 +
|| A·s
 +
|style="text-align:left;"| [https://en.wikipedia.org/wiki/Abcoulomb abcoulomb]
 +
|| abC
 +
|| abA·s
 +
|| 10<sup>−1</sup>
 
|}
 
|}
  
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! Symbol
 
! Symbol
 
! colspan="3" | SI unit
 
! colspan="3" | SI unit
! colspan="3" | CGS unit
+
! colspan="3" | CGS unit (EMU)
 
! SI to CGS conversion factor
 
! SI to CGS conversion factor
 
|-
 
|-
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! Definition
 
! Definition
 
! Value
 
! Value
! Base units
+
! [https://en.wikipedia.org/wiki/SI_base_unit Base units]
 
! Definition
 
! Definition
 
! Value
 
! Value
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|| ''µ<sub>0</sub>''·(4π)<sup>−1</sup>
 
|| ''µ<sub>0</sub>''·(4π)<sup>−1</sup>
 
|| 10<sup>−7</sup>
 
|| 10<sup>−7</sup>
|| kg⋅m·s<sup>−2</sup>·A<sup>−3</sup>
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|| kg⋅m·s<sup>−2</sup>·A<sup>−2</sup>
||
+
|| Unity
 
|| 1
 
|| 1
 
||  
 
||  
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|| ''µ<sub>0</sub>''
 
|| ''µ<sub>0</sub>''
 
|| 4π·10<sup>−7</sup>
 
|| 4π·10<sup>−7</sup>
|| kg·m·s<sup>−2</sup>·A<sup>−3</sup>
+
|| kg·m·s<sup>−2</sup>·A<sup>−2</sup>
||
+
|| Unity
 
|| 1
 
|| 1
 
||  
 
||  
 
|| ''µ<sub>0</sub>''<sup>−1</sup>
 
|| ''µ<sub>0</sub>''<sup>−1</sup>
 
|}
 
|}
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== See also ==
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 +
[[Category:Theory]]

Latest revision as of 15:55, 6 November 2015

This article is a stub. Please help to improve the relax wiki by expanding the article.

The SI or International System of Units versus the CGS or Centimetre–gram–second system of units is a constant source of confusion in the field of NMR. Both are based on the metric system, however the differences can result in quite different forms of the fundamental NMR equations. An example of this is Tesla versus Gauss units for the magnetic field strength.

CGS flavours

Note that in the CGS system, that there are different sets of units for electromagnetism. The major systems are ESU, EMU, Gaussian units, and Lorentz-Heaviside units. In NMR papers not using SI units, the EMU system is most commonly used.


Units of measurement

Quantity Symbol SI unit CGS unit (EMU) SI to CGS conversion factor
Name Symbol Base units Name Symbol Base units
length L metre m m centimetre cm cm 10−2
mass m kilogram kg kg gram g g 10−3
time t second s s second s s 1
velocity v metre per second m⋅s−1 centimetre per second cm⋅s−1 10−2
acceleration a metre per second squared m⋅s−2 galileo Gal cm⋅s−2 10−2
force F Newton N kg⋅m⋅s−2 dyne dyn g·cm·s−2 10−5
energy E Joule J kg⋅m2·s−2 erg erg g·cm2·s2 10−7
power P Watt W kg⋅m2·s−3 erg per second g·cm2·s−3 10−7
magnetic dipole moment μ Newton-meters per Tesla A·m2 electromagnetic unit emu abA·cm2 10−3
magnetic flux density (B-field) B Tesla T kg·s−2·A−1 Gauss Gs Mx·cm−2 10−4
magnetic flux density (H-field) H Amperes per metre A·m−1 Oersted Oe g·cm·s−2 4π·10−3
magnetic flux ΦB Weber Wb kg·m2·s−2·A−1 Maxwell Mx Mx 10−8
magnetic susceptibility χm - - (4π)−1
electric current I ampere A A abampere (or biot) abA (or Bi) abA (or Bi) 10−1
electric charge Q coulomb C A·s abcoulomb abC abA·s 10−1

Constants

Constant Symbol SI unit CGS unit (EMU) SI to CGS conversion factor
Definition Value Base units Definition Value Base units
magnetic force constant kA µ0·(4π)−1 10−7 kg⋅m·s−2·A−2 Unity 1 4π·µ0−1
magnetic constant µ0 µ0 4π·10−7 kg·m·s−2·A−2 Unity 1 µ0−1

See also