Tesla (unit)

Tesla
The tesla definition T = Wb/m^2 is prominently depicted on the 100 Serbian dinars banknote, along with the picture of Nikola Tesla.
Unit information
Unit system	SI derived unit
Unit of	Magnetic field strength
Symbol	T
Named after	Nikola Tesla
In SI base units:	kg⋅s^-2⋅A^-1

The tesla (symbol T) is a unit of measurement of the strength of a magnetic field. It is a derived unit of the International System of Units, the modern form of the metric system.

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 Nikola Tesla.

The strongest fields encountered from permanent magnets are from Halbach spheres which can be over 4.5 T. The strongest field trapped in a laboratory superconductor as of July 2014 is 17.6 T.^[2] The record magnetic field has been produced by scientists at the Los Alamos National Laboratory campus of the National High Magnetic Field Laboratory, the world's first 100-tesla, non-destructive magnetic field.^[3]

Definition

A particle, carrying a charge of one coulomb, and passing through a magnetic field of one tesla, at a speed of one metre per second, perpendicular to said field, experiences a force with magnitude one newton, according to the Lorentz force law. As an SI derived unit, the tesla can also be expressed as

$\mathrm{T} = \dfrac{\mathrm{V}\cdot{\mathrm{s}}}{\mathrm{m}^2} = \dfrac{\mathrm{N}}{\mathrm{A}{\cdot}\mathrm{m}} = \dfrac{\mathrm{J}}{\mathrm{A}{\cdot}\mathrm{m}^2} = \dfrac{\mathrm{H}{\cdot}\mathrm{A}}{\mathrm{m}^2} = \dfrac{\mathrm{Wb}}{\mathrm{m}^2} = \dfrac{\mathrm{kg}}{\mathrm{C}{\cdot}\mathrm{s}} = \dfrac{\mathrm{N}{\cdot}\mathrm{s}}{\mathrm{C}{\cdot}\mathrm{m}} = \dfrac{\mathrm{kg}}{\mathrm{A}{\cdot}\mathrm{s}^2}$

(The last equivalent is in SI base units).^[4]

Units used:

A = ampere

C = coulomb

kg = kilogram

m = metre

N = newton

s = second

H = henry

T = tesla

V = volt

J = joule

Wb = weber

Electric vs. magnetic field

In the production of the Lorentz force, the difference between these fields is that a force from a magnetic field on a charged particle is generally due to the charged particle's movement,^[5] 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/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).^[6][7]

In ferromagnets, the movement creating the magnetic field is the electron spin^[8] (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).

Conversions

One tesla is equivalent to:^[9]

10,000 (or 10⁴) G (gauss), used in the CGS system. Thus, 10 kG = 1 T (tesla), and 1 G = 10⁻⁴ T.

1,000,000,000 (or 10⁹) γ (gamma), used in geophysics.^[10] Thus, 1 γ = 1 nT (nanotesla).

42.6 MHz of the ¹H nucleus frequency, in NMR. Thus, the magnetic field associated with NMR at 1 GHz is 23.5 T.

One tesla is equal to 1 Vs/m². This can be shown by starting with the speed of light in vacuum,^[11] c=(ε_oμ_o)^-1/2, and inserting the SI values and units for c (2.998x10⁸ m/s), the vacuum permittivity (ε_o=8.85x10⁻¹² As/Vm), and the vacuum permeability (μ_o=12.566x10⁻⁷ Tm/A). Cancellation of numbers and units then produces this relation.

For those concerned with low-frequency electromagnetic radiation in the home, the following conversions are needed most:

1000 nT (nanotesla) = 1 µT (microtesla) = 10 mG (milligauss)

1,000,000 µT = 1 T

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

Examples

• 31.869 µT (3.2 × 10⁻⁵ T) – strength of Earth's magnetic field at 0° latitude, 0° longitude
• 5 mT – the strength of a typical refrigerator magnet
• 0.3 T – the strength of solar sunspots
• 1.25 T – magnetic flux density at the surface of a neodymium magnet
• 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^[12]
• 4 T – strength of the superconducting magnet built around the CMS detector at CERN^[13]
• 8 T – the strength of LHC magnets.
• 11.75 T – the strength of INUMAC magnets, largest MRI scanner.^[14]
• 13 T – strength of the superconducting ITER magnet system^[15]
• 16 T – magnetic field strength required to levitate a frog^[16] (via 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 superconductor in lab as of July 2014^[18]
• 27 T – maximum 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]
• 10⁸ - 10¹¹ T (100 MT-100 GT) – magnetic strength of the average magnetar

Notes and references

1. "Details of SI units". sizes.com. 2011-07-01. Retrieved 2011-10-04.
2. http://www.magnet.fsu.edu/mediacenter/factsheets/records.html
3. "Strongest non-destructive magnetic field: world record set at 100-tesla level". Los Alamos National Laboratory. Retrieved 6 November 2014.
4. 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
5. Gregory, Frederick (2003). History of Science 1700 to Present. The Teaching Company.
6. Parker, Eugene (2007). Conversations on electric and magnetic fields in the cosmos. Princeton University press. p. 65.
7. Kurt, Oughstun (2006). Electromagnetic and optical pulse propagation. Springer. p. 81.
8. Herman, Stephen (2003). Delmar's standard textbook of electricity. Delmar Publishers. p. 97.
9. McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, ISBN 0-07-051400-3
10. "Geomagnetism Frequently Asked Questions". National Geophysical Data Center. Retrieved 21 October 2013.
11. Panofsky, WKH; Phillips, M (1962). Classical Electricity and Magnetism. Addison-Wesley. p. 182. ISBN 978-0-201-05702-7.
12. "Ultra-High Field". Bruker BioSpin. Retrieved 2011-10-04.
13. "Superconducting Magnet in CMS". Retrieved 9 February 2013.
14. "ISEULT - INUMAC". Retrieved 17 February 2014.
15. "ITER – the way to new energy". Retrieved 2012-04-19.
16. "Of Flying Frogs and Levitrons" by M.V. Berry and A.K. Geim, European Journal of Physics, v. 18, 1997, p. 307–13.". Retrieved 12 May 2013.
17. "The 2000 Ig Nobel Prize Winners". Retrieved 12 May 2013.
18. "Superconductor Traps The Strongest Magnetic Field Yet". Retrieved 2 July 2014.
19. "Mag Lab World Records". Media Center. National High Magnetic Field Laboratory, USA. 2008. Retrieved 2015-10-24.

External links

• Gauss<->Tesla Conversion Tool