Weber (unit)

In physics, the weber (/ˈveɪb-, ˈwɛb.ər/ VAY-, WEH-bər;^[1][2] symbol: Wb) is the unit of magnetic flux in the International System of Units (SI). The unit is derived (through Faraday's law of induction) from the relationship 1 Wb = 1 V⋅s (volt-second). A magnetic flux density of 1 Wb/m² (one weber per square metre) is one tesla.

weber
Unit system	SI
Unit of	magnetic flux
Symbol	Wb
Named after	Wilhelm Eduard Weber
Conversions
1 Wb in ...	... is equal to ...
SI base units	1 kg⋅m2⋅s−2⋅A−1
Gaussian units	1×108 Mx

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

Definition

The weber may be defined in terms of Faraday's law, which relates a changing magnetic flux through a loop to the electric field around the loop. A change in flux of one weber per second will induce an electromotive force of one volt (produce an electric potential 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: $${\displaystyle \mathrm {Wb} =\mathrm {V} {\cdot }\mathrm {s} .}$$

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, $${\displaystyle \mathrm {Wb} =\mathrm {T} {\cdot }\mathrm {m} ^{2}.}$$

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

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

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

where Ω is ohm, C is coulomb, J is joule, and N is newton.

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

History

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

The International 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 magnetic field 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 the maxwell for the CGS 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 the MKS dimensional system of units, the whole now known simply as the SI system (Système International d'unités)."^[12]

In 1938, TC24 "recommended as a connecting link [from mechanical to electrical units] the permeability of free space with the value of μ₀ = 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

Like other SI units, the weber can modified by adding a prefix that multiplies it by a power of 10.

SI multiples of weber (Wb)

Submultiples			Multiples
Value	SI symbol	Name	Value	SI symbol	Name
10−1 Wb	dWb	deciweber	101 Wb	daWb	decaweber
10−2 Wb	cWb	centiweber	102 Wb	hWb	hectoweber
10−3 Wb	mWb	milliweber	103 Wb	kWb	kiloweber
10−6 Wb	μWb	microweber	106 Wb	MWb	megaweber
10−9 Wb	nWb	nanoweber	109 Wb	GWb	gigaweber
10−12 Wb	pWb	picoweber	1012 Wb	TWb	teraweber
10−15 Wb	fWb	femtoweber	1015 Wb	PWb	petaweber
10−18 Wb	aWb	attoweber	1018 Wb	EWb	exaweber
10−21 Wb	zWb	zeptoweber	1021 Wb	ZWb	zettaweber
10−24 Wb	yWb	yoctoweber	1024 Wb	YWb	yottaweber
10−27 Wb	rWb	rontoweber	1027 Wb	RWb	ronnaweber
10−30 Wb	qWb	quectoweber	1030 Wb	QWb	quettaweber
Common multiples are in bold face.

Conversions

• One maxwell (Mx), the CGS unit of magnetic flux, equals 10⁻⁸ Wb

Notes and references

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. Retrieved 2008-04-29.
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. Retrieved 2018-04-19.
6. Giorgi, Giovanni (February 1902). "Rational Units of Electromagnetism" (Manuscript with handwritten notes by Oliver Heaviside). p. 9. Retrieved 2014-02-21.
7. "Strategic Policy Statement, IEC Technical Committee on Terminology" (PDF). International Electrotechnical Commission. Archived from the original (PDF) on 2006-09-04. Retrieved 2008-04-29.
8. "IEC Technical Committee 1". International Electrotechnical Commission. Retrieved 2018-04-19.
9. "The role of the IEC / Work on quantities and units". History of the SI. International Electrotechnical Commission. Archived from the original on 11 June 2007. Retrieved 2018-04-19.
10. "Summary: Electrical Units". IEC History. International Electrotechnical Commission. Retrieved 2018-04-19.

    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"

11. Ruppert, Louis (1956). Brief History of the International Electrotechnical Commission (PDF). International Electrotechnical Commission. p. 5. Retrieved 2018-04-19.
12. Raeburn, Anthony. "Overview: IEC technical committee creation: the first half-century (1906-1949)". International Electrotechnical Commission. Retrieved 2018-04-19.