Tesla Unit

The tesla (symbol T) is the SI derived unit of magnetic field strength or magnetic flux density, commonly denoted as B. 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 4.5 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{\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{Wb}}{\mathrm{m}^2}

 
= \dfrac{\mathrm{kg}}{\mathrm{C}{\cdot}\mathrm{s}} 
= \dfrac{\mathrm{kg}}{\mathrm{A}{\cdot}\mathrm{s}^2} 
= \dfrac{\mathrm{N}{\cdot}\mathrm{s}}{\mathrm{C}{\cdot}\mathrm{m}}

(The 6th 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
J = joule
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 kG = 1 T (tesla), 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

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