Definitions

# Weber (unit)

In physics, the weber (symbol: Wb; ) is the SI unit of magnetic flux. It 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.

Officially,

Weber (unit of magnetic flux) — The weber is the magnetic flux which, 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.

In SI base units, the dimensions of the weber are $dfrac\left\{mbox\left\{kg\right\} cdot mbox\left\{m\right\}^2\right\}\left\{mbox\left\{s\right\}^2 cdot mbox\left\{A\right\}\right\}$. In derived units, they are volt-seconds $\left(mbox\left\{V\right\} cdot mbox\left\{s\right\}\right)$, or joules per amp $dfrac\left\{mbox\left\{J\right\}\right\}\left\{mbox\left\{A\right\}\right\}$.

The weber is a large unit, equal to 1 T m2 = 108 maxwells.

A flux density of one Wb/m2 (one weber per square meter) is one tesla.

## History

In 1861, the British Association for the Advancement of Science (known as "The BA) established a committee under William Thomson (later Lord Kelvin) to study electrical units. 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.”. The International Electrotechnical Commission begain 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 magnetic field strength (H) is of a different nature than 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 the maxwell for the CGS unit).

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 the MKS dimensional system of units, the whole now known simply as the SI system (Système International d’unités).″

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.” It 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.”`

## References

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