Tesla (unit)

tesla
Unit system	SI
Unit of	magnetic flux density
Symbol	T
Named after	Nikola Tesla
Conversions
1 T in ...	... is equal to ...
SI base units	1 kg⋅s −2⋅A −1
Gaussian units	≘ 104  G

The tesla (symbol: T) is the unit of magnetic flux density (also called magnetic B-field strength) in the International System of Units (SI).

One tesla is equal to one weber per square metre. The unit was announced during the General Conference on Weights and Measures in 1960 and is named ^[1] in honour of Serbian-American electrical and mechanical engineer Nikola Tesla, upon the proposal of the Slovenian electrical engineer France Avčin.

Definition

A particle, carrying a charge of one coulomb (C), and moving perpendicularly through a magnetic field of one tesla, at a speed of one metre per second (m/s), experiences a force with magnitude one newton (N), according to the Lorentz force law. That is,

$${\displaystyle \mathrm {T={\dfrac {N{\cdot }s}{C{\cdot }m}}} .}$$

As an SI derived unit, the tesla can also be expressed in terms of other units. For example, a magnetic flux of 1 weber (Wb) through a surface of one square meter is equal to a magnetic flux density of 1 tesla. ^[2] That is,

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

Expressed only in SI base units, 1 tesla is:

$${\displaystyle \mathrm {T={\dfrac {kg}{A{\cdot }s^{2}}}} ,}$$

where A is ampere, kg is kilogram, and s is second. ^[2]

Additional equivalences result from the derivation of coulombs from amperes (A), ${\displaystyle \mathrm {C=A{\cdot }s} }$:

$${\displaystyle \mathrm {T={\dfrac {N}{A{\cdot }m}}} ,}$$

the relationship between newtons and joules (J), ${\displaystyle \mathrm {J=N{\cdot }m} }$:

$${\displaystyle \mathrm {T={\dfrac {J}{A{\cdot }m^{2}}}} ,}$$

and the derivation of the weber from volts (V), ${\displaystyle \mathrm {Wb=V{\cdot }s} }$:

$${\displaystyle \mathrm {T={\dfrac {V{\cdot }{s}}{m^{2}}}} .}$$

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

Electric vs. magnetic field

In the production of the Lorentz force, the difference between electric fields and magnetic fields is that a force from a magnetic field on a charged particle is generally due to the charged particle's movement, ^[3] while the force imparted by an electric field on a charged particle is not due to the charged particle's movement. This may be appreciated by looking at the units for each. The unit of electric field in the MKS system of units is newtons per coulomb, N/C, while the magnetic field (in teslas) can be written as N/(C⋅m/s). The dividing factor between the two types of field is metres per second (m/s), which is velocity. This relationship immediately highlights the fact that whether a static electromagnetic field is seen as purely magnetic, or purely electric, or some combination of these, is dependent upon one's reference frame (that is, one's velocity relative to the field). ^{[4] [5]}

In ferromagnets, the movement creating the magnetic field is the electron spin ^[6] (and to a lesser extent electron orbital angular momentum). In a current-carrying wire (electromagnets) the movement is due to electrons moving through the wire (whether the wire is straight or circular).

Conversion to non-SI units

One tesla is equivalent to: ^{[7] [ page needed ]}

• 10,000 (or 10⁴) G (gauss), used in the CGS system. Thus, 1 G = 10⁻⁴ T = 100 μT (microtesla).
• 1,000,000,000 (or 10⁹) γ (gamma), used in geophysics. ^[8]

For the relation to the units of the magnetising field (ampere per metre or Oersted), see the article on permeability.

Examples

Main article: Orders of magnitude (magnetic field)

The following examples are listed in the ascending order of the magnetic-field strength.

• 3.2×10⁻⁵ T (31.869 μT) – strength of Earth's magnetic field at 0° latitude, 0° longitude
• 4×10⁻⁵ T (40 μT) – walking under a high-voltage power line ^[9]
• 5×10⁻³ T (5 mT) – the strength of a typical refrigerator magnet
• 0.3 T – the strength of solar sunspots
• 1 T to 2.4 T – coil gap of a typical loudspeaker magnet
• 1.5 T to 3 T – strength of medical magnetic resonance imaging systems in practice, experimentally up to 17 T ^[10]
• 4 T – strength of the superconducting magnet built around the CMS detector at CERN ^[11]
• 5.16 T – the strength of a specially designed room temperature Halbach array ^[12]
• 8 T – the strength of LHC magnets
• 11.75 T – the strength of INUMAC magnets, largest MRI scanner ^[13]
• 13 T – strength of the superconducting ITER magnet system ^[14]
• 14.5 T – highest magnetic field strength ever recorded for an accelerator steering magnet at Fermilab ^[15]
• 16 T – magnetic field strength required to levitate a frog ^[16] (by diamagnetic levitation of the water in its body tissues) according to the 2000 Ig Nobel Prize in Physics ^[17]
• 17.6 T – strongest field trapped in a superconductor in a lab as of July 2014 ^[18]
• 20 T - strength of the large scale high temperature superconducting magnet developed by MIT and Commonwealth Fusion Systems to be used in fusion reactors^{[ citation needed ]}
• 27 T – maximal field strengths of superconducting electromagnets at cryogenic temperatures
• 35.4 T – the current (2009) world record for a superconducting electromagnet in a background magnetic field ^[19]
• 45 T – the current (2015) world record for continuous field magnets ^[19]
• 97.4 T – strongest magnetic field produced by a "non-destructive" magnet ^[20]
• 100 T – approximate magnetic field strength of a typical white dwarf star
• 1200 T – the field, lasting for about 100 microseconds, formed using the electromagnetic flux-compression technique ^[21]
• 10⁹ T – Schwinger limit above which the electromagnetic field itself is expected to become nonlinear
• 10⁸ – 10¹¹ T (100 MT – 100 GT) – magnetic strength range of magnetar neutron stars

Notes and references

1. "Details of SI units". sizes.com. 2011-07-01. Retrieved 2011-10-04.
2. The International System of Units (SI), 8th edition, BIPM, eds. (2006), ISBN   92-822-2213-6, Table 3. Coherent derived units in the SI with special names and symbols Archived 2007-06-18 at the Wayback Machine
3. Gregory, Frederick (2003). History of Science 1700 to Present. The Teaching Company.
4. Parker, Eugene (2007). Conversations on electric and magnetic fields in the cosmos. Princeton University press. p. 65. ISBN   978-0691128412.
5. Kurt, Oughstun (2006). Electromagnetic and optical pulse propagation. Springer. p. 81. ISBN   9780387345994.
6. Herman, Stephen (2003). Delmar's standard textbook of electricity. Delmar Publishers. p. 97. ISBN   978-1401825652.
7. McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, ISBN   0-07-051400-3
8. "gamma definition". Oxford Reference. Retrieved 2 January 2024.
9. "EMF: 7. Extremely low frequency fields like those from power lines and household appliances". ec.europa.eu. Archived from the original on 2021-02-24. Retrieved 2022-05-13.
10. "Ultra-High Field". Bruker BioSpin. Archived from the original on 21 July 2012. Retrieved 4 October 2011.
11. "Superconducting Magnet in CMS" . Retrieved 9 February 2013.
12. "The Strongest Permanent Dipole Magnet" (PDF). Retrieved 2 May 2020.
13. "ISEULT – INUMAC" . Retrieved 17 February 2014.
14. "ITER – the way to new energy" . Retrieved 19 April 2012.
15. Hesla, Leah (13 July 2020). "Fermilab achieves 14.5-tesla field for accelerator magnet, setting new world record" . Retrieved 13 July 2020.
16. Berry, M. V.; Geim, A. K. (1997). "Of Flying Frogs and Levitrons" by M. V. Berry and A. K. Geim, European Journal of Physics, v. 18, 1997, p. 307–13" (PDF). European Journal of Physics. 18 (4): 307–313. doi:10.1088/0143-0807/18/4/012. S2CID   1499061. Archived from the original (PDF) on 8 October 2020. Retrieved 4 October 2020.
17. "The 2000 Ig Nobel Prize Winners". August 2006. Retrieved 12 May 2013.)
18. "Superconductor Traps The Strongest Magnetic Field Yet". 2 July 2014. Retrieved 2 July 2014.
19. "Mag Lab World Records". Media Center. National High Magnetic Field Laboratory, USA. 2008. Retrieved 24 October 2015.
20. "World record pulsed magnetic field". Physics World. 31 August 2011. Retrieved 26 January 2022.)
21. D. Nakamura, A. Ikeda, H. Sawabe, Y. H. Matsuda, and S. Takeyama (2018), Magnetic field milestone

External links

• Gauss ↔ Tesla Conversion Tool