# Tesla (unit)

(Redirected from Nanotesla)

The tesla (symbol T) is the SI derived unit of magnetic-field strength or magnetic-flux density, commonly denoted as T, (which is also known as "magnetic field"). One tesla is equal to one weber per square metre, and it was defined in 1960[1] in honour of Nikola Tesla. The strongest fields encountered from permanent magnets are from Halbach spheres which can be over 5 T.[2]

The unit was announced during the Conférence Générale des Poids et Mesures in 1960.

## Definition

A particle carrying a charge of 1 coulomb and passing through a magnetic field of 1 tesla at a speed of 1 meter per second perpendicular to said field experiences a force with magnitude 1 newton, according to the Lorentz force law. As an SI derived unit, the tesla can also be expressed as

$\mathrm{T} =\dfrac{Vs}{m^2}\ = N A^{-1}m^{-1} = Wb \ m^{-2} = kg \ C^{-1} s^{-1} = kg A^{-1} s^{-2} = N \ s \ C^{-1}m^{-1}$

(The 5th equivalent is in SI base units).[3]

Units used:

A = ampere
C = coulomb
kg = kilogram
m = meter
N = newton
s = second
T = tesla
V = volt
Wb = weber

## Electric vs. magnetic field

In the production of the Lorentz force, the difference between these types of field is that a force from a magnetic field on a charged particle is generally due to the charged particle's movement[4] 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 meters/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).[5][6]

In ferromagnets, the movement creating the magnetic field is the electron spin[7] (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

1 tesla is equivalent to:[8]

10,000 (or 104) G (gauss), used in the CGS system. Thus, 10 G = 1 mT (millitesla), and 1 G = 10−4 T.
1,000,000,000 (or 109) γ (gammas), used in geophysics. Thus, 1 γ = 1 nT (nanotesla)
42.6 MHz of the 1H nucleus frequency, in NMR. Thus a 1 GHz NMR magnetic field is 23.5 teslas.

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

1000 nT (nanoteslas) = 1 µT (microtesla) = 10 mG (milligauss)
1,000,000 µT = 1 T

Because the tesla is so large in regards to everyday usage, common engineering practice is to report the strength of magnets in gauss. Scientists are split on this issue, with some insisting on proper SI units at all times and some allowing for more practical labeling (though using mT or µT is not less practical than G or mG, and conforms with SI). In publications where fields are reported in teslas, very often they are incorrectly reported with the unit capitalized as "Teslas." However, as with gauss and other units, even those derived from names (watt, joule) the unit is lower-case when written out, but capitalized as a symbol: tesla, T.

For the relation to the units of the magnetizing field (amperes per meter or oersteds) see the article on permeability.

## Examples

• 31 µT (3.1×10−5 T) - strength of Earth's magnetic field at 0° latitude (on the equator)
• 5 mT - the strength of a typical refrigerator magnet
• 0.3 T - the strength of solar sunspots
• 1.25 T - magnetic field intensity 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[9]
• 4 T - strength of the superconducting magnet built around the CMS detector at CERN[10]
• 13 T - strength of ITER fusion reactor[11]
• 16 T - magnetic field strength required to levitate a frog[12], per the 2000 Ig Nobel Prize in Physics.[13]

## References

Notes

1. ^ "Details of SI units". sizes.com. 2011-07-01. Retrieved 2011-10-04.
2. ^ "...our data of 5.16 T dipole magnet...", The Strongest Permanent Dipole Magnet
3. ^ 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
4. ^ Gregory, Frederick (2003). History of Science 1700 to Present. The Teaching Company.
5. ^ Parker, Eugene (2007). Conversations on electric and magnetic fields in the cosmos. Princeton University press. p. 65.
6. ^ Kurt, Oughstun (2006). Electromagnetic and optical pulse propogation. Springer. p. 81.
7. ^ Herman, Stephen (2003). Delmar's standard textbook of electricity. Delmar Publishers. p. 97.
8. ^ McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, ISBN 0-07-051400-3
9. ^ "Ultra-High Field". Bruker BioSpin. Retrieved 2011-10-04.
10. ^ "Superconducting Magnet in CMS". Retrieved 9 February 2013.
11. ^ "ITER - the way to new energy". Retrieved 2012-04-19.
12. ^
13. ^ "The 2000 Ig Nobel Prize Winners". Retrieved 12 May 2013.