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Weber (unit)

From Wikipedia, the free encyclopedia
SI derived unit of magnetic flux
weber
Unit systemSI
Unit ofmagnetic flux
SymbolWb
Named afterWilhelm Eduard Weber
Conversions
1 Wbin ...... is equal to ...
   SI base units   1kg⋅m2⋅s−2⋅A−1
   Gaussian units   1×108 Mx

Inphysics, theweber (/ˈveɪb-,ˈwɛb.ər/VAY-,WEH-bər;[1][2] symbol:Wb) is the unit ofmagnetic flux in theInternational System of Units (SI). The unit is derived (throughFaraday's law of induction) from the relationship1 Wb = 1 V⋅s (volt-second). Amagnetic flux density of 1 Wb/m2 (one weber persquare metre) is onetesla.

The weber is named after the German physicistWilhelm Eduard Weber (1804–1891).

Definition

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The weber may be defined in terms ofFaraday's law, which relates a changingmagnetic flux through a loop to theelectric field around the loop. A change in flux of one weber persecond will induce anelectromotive force of onevolt (produce an electricpotential difference of one volt across two open-circuited terminals).

Officially:

Weber (unit of magnetic flux) — The weber is the magnetic flux that, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second.[3]

That is:Wb=V⋅s.{\displaystyle \mathrm {Wb} =\mathrm {V} {\cdot }\mathrm {s} .}

One weber is also the total magnetic flux across a surface of one square meter perpendicular to a magnetic flux density of one tesla; that is,Wb=T⋅m2.{\displaystyle \mathrm {Wb} =\mathrm {T} {\cdot }\mathrm {m} ^{2}.}

Expressed only inSI base units, 1 weber is:Wb=kg⋅m2s2⋅A.{\displaystyle \mathrm {Wb} ={\dfrac {\mathrm {kg} {\cdot }\mathrm {m} ^{2}}{\mathrm {s} ^{2}{\cdot }\mathrm {A} }}.}

The weber is used in the definition of thehenry as 1 weber perampere, and consequently can be expressed as the product of those units:Wb=H⋅A.{\displaystyle \mathrm {Wb} =\mathrm {H} {\cdot }\mathrm {A} .}

The weber is commonly expressed in a multitude of other units[citation needed]:Wb=Ω⋅C=JA=N⋅mA,{\displaystyle \mathrm {Wb} =\Omega {\cdot }{\text{C}}={\dfrac {\mathrm {J} }{\mathrm {A} }}={\dfrac {\mathrm {N} {\cdot }\mathrm {m} }{\mathrm {A} }},}

where Ω isohm, C iscoulomb, J isjoule, and N isnewton.

The weber is named afterWilhelm Eduard Weber. As with everySI unit named after a person, its symbol starts with anupper case letter (Wb), but when written in full, it follows the rules for capitalisation of acommon noun; i.e.,weber becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.

History

[edit]

In 1861, theBritish Association for the Advancement of Science (known as "The BA"[4]) established a committee under William Thomson (laterLord Kelvin) to study electrical units.[5] In a February 1902 manuscript, with handwritten notes ofOliver Heaviside,Giovanni Giorgi proposed a set of rational units ofelectromagnetism including the weber, noting that "the product of the volt into the second has been called theweber by the B. A."[6]

TheInternational Electrotechnical Commission began work on terminology in 1909 and established Technical Committee 1 in 1911, its oldest established committee,[7] "to sanction the terms and definitions used in the different electrotechnical fields and to determine the equivalence of the terms used in the different languages."[8]

It was not until 1927 that TC1 dealt with the study of various outstanding problems concerning electrical and magnetic quantities and units. Discussions of a theoretical nature were opened at which eminent electrical engineers and physicists considered whether magnetic field strength and magnetic flux density were in fact quantities of the same nature. As disagreement continued, the IEC decided on an effort to remedy the situation. It instructed a task force to study the question in readiness for the next meeting.[9]

In 1930, TC1 decided that the magneticfield strength (H) is of a different nature from the magnetic flux density (B),[9] and took up the question of naming the units for these fields and related quantities, among them the integral of magnetic flux density.[citation needed]

In 1935, TC 1 recommended names for several electrical units, including the weber for the practical unit of magnetic flux (and themaxwell for theCGS unit).[9][10]

It was decided to extend the existing series of practical units into a complete comprehensive system of physical units, the recommendation being adopted in 1935 "that the system with four fundamental units proposed by Professor Giorgi be adopted subject to the fourth fundamental unit being eventually selected". This system was given the designation of "Giorgi system".[11]

Also in 1935, TC1 passed responsibility for "electric and magnetic magnitudes and units" to the new TC24. This "led eventually to the universal adoption of the Giorgi system, which unified electromagnetic units with theMKS dimensional system of units, the whole now known simply as theSI system (Système International d'unités)."[12]

In 1938, TC24 "recommended as a connecting link [from mechanical to electrical units] thepermeability of free space with the value ofμ0 = 4π×10−7 H/m". This group also recognized that any one of the practical units already in use (ohm, ampere, volt, henry,farad, coulomb, and weber), could equally serve as the fourth fundamental unit.[9] "After consultation, the ampere was adopted as the fourth unit of the Giorgi system in Paris in 1950."[11]

Multiples

[edit]

Like other SI units, the weber can be modified by adding aprefix that multiplies it by apower of 10.

SI multiples of weber (Wb)
SubmultiplesMultiples
ValueSI symbolNameValueSI symbolName
10−1 WbdWbdeciweber101 WbdaWbdecaweber
10−2 WbcWbcentiweber102 WbhWbhectoweber
10−3 WbmWbmilliweber103 WbkWbkiloweber
10−6 WbμWbmicroweber106 WbMWbmegaweber
10−9 WbnWbnanoweber109 WbGWbgigaweber
10−12 WbpWbpicoweber1012 WbTWbteraweber
10−15 WbfWbfemtoweber1015 WbPWbpetaweber
10−18 WbaWbattoweber1018 WbEWbexaweber
10−21 WbzWbzeptoweber1021 WbZWbzettaweber
10−24 WbyWbyoctoweber1024 WbYWbyottaweber
10−27 WbrWbrontoweber1027 WbRWbronnaweber
10−30 WbqWbquectoweber1030 WbQWbquettaweber
Common multiples are in bold face.

Conversions

[edit]
  • Onemaxwell (Mx), theCGS unit of magnetic flux, equals 10−8 Wb

Notes and references

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  1. ^Wells, John (3 April 2008).Longman Pronunciation Dictionary (3rd ed.). Pearson Longman.ISBN 978-1-4058-8118-0.
  2. ^"weber (main entry is American English, Collins World English (further down) is British)".Dictionary.com.
  3. ^"CIPM, 1946: Resolution 2 / Definitions of Electrical Units".International Committee for Weights and Measures (CIPM) Resolutions.International Bureau of Weights and Measures (BIPM). 1946. Archived fromthe original on 2020-11-25. Retrieved2008-04-29.
  4. ^"The BA (British Association for the Advancement of Science)".
  5. ^Frary, Mark."In the beginning...The world of electricity: 1820-1904". International Electrotechnical Commission. Archived fromthe original on 2018-04-18. Retrieved2018-04-19.
  6. ^Giorgi, Giovanni (February 1902)."Rational Units of Electromagnetism". p. 9. Archived fromthe original(Manuscript with handwritten notes byOliver Heaviside) on 2019-10-29. Retrieved2014-02-21.
  7. ^"Strategic Policy Statement, IEC Technical Committee on Terminology"(PDF). International Electrotechnical Commission. Archived fromthe original(PDF) on 2006-09-04. Retrieved2008-04-29.
  8. ^"IEC Technical Committee 1". International Electrotechnical Commission. Retrieved2018-04-19.
  9. ^abcd"The role of the IEC / Work on quantities and units".History of the SI. International Electrotechnical Commission. Archived fromthe original on 11 June 2007. Retrieved2018-04-19.
  10. ^"Summary: Electrical Units".IEC History. International Electrotechnical Commission. Archived fromthe original on 2018-04-20. Retrieved2018-04-19.
    This page incorrectly states that the units were established in 1930, since that year, TC 1 decided "that the question of names to be allocated to magnetic units should not be considered until general agreement had been reached on their definitions"[1]Archived 2007-06-11 at theWayback Machine
  11. ^abRuppert, Louis (1956).Brief History of the International Electrotechnical Commission(PDF). International Electrotechnical Commission. p. 5. Archived fromthe original(PDF) on 2016-12-24. Retrieved2018-04-19.
  12. ^Raeburn, Anthony."Overview: IEC technical committee creation: the first half-century (1906-1949)". International Electrotechnical Commission. Retrieved2018-04-19.[permanent dead link]
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