emu system
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
- ↑ Weber's original proposal was based on a millimetre–milligram–second system of units.
- ↑ The MKS unit of magnetomotive force was the ampere-turn, which is numerically equal to the ampere.
References
- ↑ Jenkin, Fleeming Reports of the Committee on Electrical Standards; London, 1873.
- ↑ Units, Physical. In Encyclopædia Britannica, 11th ed., 1911; Vol. 27, pp 738–45.
- ↑ 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>.
- ↑ 4.0 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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