# Gauss (unit)

The gauss, abbreviated as G or Gs, is the cgs unit of measurement of magnetic flux density (or "magnetic induction") (B). It is named after German mathematician and physicist Carl Friedrich Gauss.[1][2] One gauss is defined as one maxwell per square centimeter; the cgs system has been superseded by the International System of Units (SI), which uses the tesla (symbol T) as the unit of magnetic flux density.[3] One gauss equals 1×104 tesla (100 μT), so 1 tesla = 10,000 gauss.

## Unit name and convention

As with all units whose names are derived from a person's name, the first letter of its symbol is uppercase ("G"), but when the unit is spelled out, it should be written in lowercase ("gauss"), unless it begins a sentence.[4]

## Unit conversions

{\displaystyle {\begin{aligned}1\,{\rm {G}}&={\frac {\rm {Mx}}{{\rm {cm}}^{2}}}={\rm {cm}}^{-1/2}{\cdot }{\rm {g}}^{1/2}{\cdot }{\rm {s}}^{-1}\\&=10^{-4}\,{\rm {T}}=10^{-4}{\frac {\rm {kg}}{{\rm {A}}{\cdot }{\rm {s^{2}}}}}\end{aligned}}}

According to the system of Gaussian units (cgs), the gauss is the unit of magnetic flux density B and the equivalent of Mx/cm2, while the oersted is the unit of magnetizing field H. One tesla (T) is equal to 104 gauss, and one ampere (A) per meter is equal to 4π × 10−3 oersted.[5]

The units for magnetic flux Φ, which is the integral of magnetic field over an area, are the weber (Wb) in the SI and the maxwell (Mx) in the cgs system; the conversion factor is 108, since flux is the integral of field over an area, area having the units of the square of distance, thus 104 (magnetic field conversion factor) times the square of 102 (linear distance conversion factor, i.e., centimetres per meter). 108 = 104 × (102)2.

## References

1. ^ "Carl Friedrich Gauss | German mathematician". Encyclopedia Britannica. Retrieved 2018-03-27.
2. ^ W., Weisstein, Eric. "Gauss, Karl Friedrich (1777-1855) – from Eric Weisstein's World of Scientific Biography". scienceworld.wolfram.com. Retrieved 2018-03-27.
3. ^ NIST Special Publication 1038, Section 4.3.1
4. ^ Bureau International des Poids et Mesures (2006). "The International System of Units (SI)" (PDF). 8th ed. Retrieved 2009-05-20.
5. ^ Hayt, Jr., William H. (1974). Engineering Electromagnetics, Third Edition. McGraw-Hill. ISBN 0-07-027390-1
6. ^ Bruce A. Buffett (2010): "Tidal dissipation and the strength of the Earth’s internal magnetic field". Nature, volume 468, pages 952–954. doi:10.1038/nature09643
7. ^ Hoadley, Rick. "How strong are magnets?". www.coolmagnetman.com. Retrieved 2017-01-26.
8. ^ Juha Pyrhönen; Tapani Jokinen; Valéria Hrabovcová (2009). Design of Rotating Electrical Machines. John Wiley and Sons. p. 232. ISBN 0-470-69516-1.
9. ^ Laughton, M. A.; Warne, D. F., eds. (2003). "8". Electrical Engineer's Reference Book (Sixteenth ed.). Newnes. ISBN 0-7506-4637-3.
10. ^ "How strong are magnets?". Experiments with magnets and our surroundings. Magcraft. Retrieved 2007-12-14.
11. ^ a b "Magnetars, Soft Gamma Repeaters and Very Strong Magnetic Fields". Robert C. Duncan, University of Texas at Austin. March 2003. Archived from the original on 2007-06-11. Retrieved 2007-05-23.