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. 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 The cgs system has been superseded by the International System of Units (SI), which uses the tesla (unit T) as the unit of magnetic flux density.^[1] One gauss equals 1×10⁻⁴ tesla (100 μT), so 1 tesla = 10000 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.^[2]

Unit conversions

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

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

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

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 X (10²)².

Typical values

• 10⁻⁹–10⁻⁸ gauss – the magnetic field of the human brain
• 10⁻⁶–10⁻³ gauss – the magnetic field of Galactic molecular clouds
• 0.25–0.60 gauss – the Earth's magnetic field at its surface
• 25 gauss – the Earth's magnetic field in its core^[4]
• 50 gauss – a typical refrigerator magnet
• 100 gauss – an iron magnet
• 10000 to 13000 gauss – remanence of a neodymium-iron-boron (NIB) magnet^[5]
• 16000 to 22000 gauss - saturation of high permeability iron alloys used in transformers^[6]
• 600–70,000 gauss – a medical magnetic resonance imaging machine
• 10¹²–10¹³ gauss – the surface of a neutron star^[7]
• 4×10¹³ gauss – the quantum electrodynamic threshold
• 10¹⁵ gauss – the magnetic field of some newly created magnetars^[8]
• 10¹⁷ gauss – the upper limit to neutron star magnetism^[8]

See also

• Centimetre gram second system of units
• Gaussian units
• Carl Friedrich Gauss
• Magnetic field

References

1. NIST Special Publication 1038, Section 4.3.1
2. Bureau International des Poids et Mesures (2006). "The International System of Units (SI)" (PDF). 8th ed. Retrieved 2009-05-20.
3. Hayt, Jr., William H. (1974). Engineering Electromagnetics, Third Edition. McGraw-Hill. ISBN 0-07-027390-1
4. "Medical Daily: First measurement of magnetic field in Earth's core". First measurement of magnetic field in Earth's core. Medical Daily. Retrieved 2010-12-17.
5. Juha Pyrhönen; Tapani Jokinen; Valéria Hrabovcová (2009). Design of Rotating Electrical Machines. John Wiley and Sons. p. 232. ISBN 0-470-69516-1.
6. Laughton, M. A.; Warne, D. F., eds. (2003). "8". Electrical Engineer's Reference Book (Sixteenth ed.). Newnes. ISBN 0-7506-4637-3.
7. "How strong are magnets?". Experiments with magnets and our surroundings. Magcraft. Retrieved 2007-12-14.
8. "Magnetars, Soft Gamma Repeaters and Very Strong Magnetic Fields". Robert C. Duncan, University of Texas at Austin. March 2003. Retrieved 2007-05-23.