Weber (unit)

Inphysics,theweber(/ˈveɪb-,ˈwɛb.ər/VAY-,WEH-bər;symbol:Wb) is the unit ofmagnetic fluxin 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 densityof 1 Wb/m²(one weber persquare metre) is onetesla.

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

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

Definition

The weber may be defined in terms ofFaraday's law,which relates a changingmagnetic fluxthrough a loop to theelectric fieldaround the loop. A change in flux of one weber persecondwill induce anelectromotive forceof onevolt(produce an electricpotential differenceof 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.

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

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

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

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

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

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

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

History

In 1861, theBritish Association for the Advancement of Science(known as "The BA") established a committee under William Thomson (laterLord Kelvin) to study electrical units.In a February 1902 manuscript, with handwritten notes ofOliver Heaviside,Giovanni Giorgiproposed a set of rational units ofelectromagnetismincluding the weber, noting that "the product of the volt into the second has been called theweberby the B. A. "

TheInternational Electrotechnical Commissionbegan work on terminology in 1909 and established Technical Committee 1 in 1911, its oldest established committee,"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."

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.

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

In 1935, TC 1 recommended names for several electrical units, including the weber for the practical unit of magnetic flux (and themaxwellfor theCGSunit).

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".

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 theMKSdimensional system of units, the whole now known simply as theSIsystem (Système International d'unités). "

In 1938, TC24 "recommended as a connecting link [from mechanical to electrical units] thepermeability of free spacewith the value ofμ₀= 4π×10⁻⁷H/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."After consultation, the ampere was adopted as the fourth unit of the Giorgi system in Paris in 1950."

Multiples

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

SI multiples of weber (Wb)

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

Conversions

• Onemaxwell(Mx), theCGSunit of magnetic flux, equals 10⁻⁸Wb