Tesla
SI derived unit · quantity: magnetic flux density
01 · Definition
The tesla is the magnetic flux density at which a flux of one weber passes through an area of one square metre. An equivalent definition through force: in a field of one tesla a conductor one metre long carrying one ampere feels a force of one newton.
The unit came out large by domestic standards and small by astrophysical ones. The Earth’s field is fifty microtesla, a school magnet is tenths, a neodymium disc right at its surface passes one; beyond that begins engineering, where the count runs in units and tens. The range over which the quantity is used at all spans twenty-three orders of magnitude: from the femtotesla of the magnetic field of a working brain to hundreds of gigatesla at the surface of a magnetar, where the field distorts the electron shells of atoms and the vacuum stops being empty.
Three windings set a hundred and twenty degrees apart and fed by currents with the same phase shift create a field that rotates in space without a single moving part. The rotor of an induction motor needs neither commutator nor brushes: the field induces currents in it and drags it along. The patent of 1888 became the foundation of the whole of industrial alternating-current engineering, and to this day about half of all the electricity in the world is consumed by motors of exactly this kind.
02 · Conversion
Enter a flux density and the passport will break it down by unit
The gauss holds on more stubbornly than any other CGS unit: geophysics, magnetic materials and plasma physics use it to this day. One tesla is exactly ten thousand gauss, the coefficient is exact, so the conversion is always simple. The gamma is the geophysicists’ unit, equal to the nanotesla: magnetic anomalies are measured in it when prospecting for ore.
The tesla measures the flux density B, the ampere per metre the field strength H. In vacuum they are proportional through the magnetic constant; in iron they differ by thousands of times: steel strengthens the field, while the calculation is carried out in H. That dependence is non-linear, with a hysteresis loop, so the rows “A/m” and “oersted” in the table hold only for vacuum and air.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| T | tesla, the SI unit | 1 | the unit of this sheet |
| mT | millitesla | 1000 | a domestic quantity: hundredths of a tesla |
| µT | microtesla | 1000000 | here lives terrestrial magnetism |
| nT | nanotesla | 10⁹ | the same gamma, only in SI |
| fT | femtotesla | 10¹⁵ | the lower edge of the measurable |
| Wb/m² | weber per m² | 1 | the same thing in other words: the tesla is the weber per square metre |
| A/m | field strength H | 795775 | the row holds only for vacuum and air |
| G | gauss, CGS | 10000 | exactly ten thousand in a tesla — the coefficient is exact |
| kG | kilogauss | 10 | a handy multiple for laboratory fields |
| γ | gamma | 10⁹ | one hundred-thousandth of a gauss, the same as the nanotesla |
| Oe | oersted | 10000 | numerically equal to the gauss in vacuum — hence the confusion |
| T | tesla | 1 | the unit of this sheet |
The tesla is flux density: multiply by area and you get the weber, divide by the magnetic constant and you get the field strength in amperes per metre
03 · Orders of magnitude
twenty-three orders: from the brain to a magnetarOne tesla: the gap of a powerful electric motor
04 · Measuring instruments
What magnetic flux density is measured with
A current in a thin semiconductor plate is deflected by the field, and a voltage proportional to the flux density appears on its side faces. Cheap, small, working from zero to tens of tesla — which is why it sits in every brushless motor and every wheel-speed sensor.
The core is driven into saturation by an alternating current and the asymmetry of the response is watched: an external field shifts the loop, and a second harmonic appears in the secondary winding. The chief instrument of geophysics and of spacecraft, sensitive down to the picotesla.
Protons in a sample of water precess at a frequency strictly proportional to the field: 42.58 megahertz per tesla. The measurement reduces to measuring a frequency, and frequency is the thing we can measure best of all — hence an accuracy of parts per million and the role of a reference method.
A superconducting interferometer counts quanta of magnetic flux and distinguishes femtotesla — a billion times less than the Earth’s field. It works only in a cryostat and inside a shielded room, but it lets the magnetic field of the brain be recorded.
05 · The tesla at work
Which field is where, and what makes it dangerous
Fifty microtesla is the Earth’s field; ten times that, half a millitesla, is the line beyond which people with a pacemaker are not admitted to an MRI room. It is painted on the floor.
The ordinary strength of the machine. In this field a steel object can no longer be held by hand: the attraction grows faster than a person can unclench their fingers.
The diamagnetism of water is weak, but in such a field water is pushed outward — enough for a drop, a grasshopper and a frog to hang in the air.
Above this, magnetic pressure tears the winding apart from within. Beyond it lie only pulsed installations, which live for microseconds.
The field of a scanner draws in a ferromagnetic object with a force that grows as it comes closer, so holding it is impossible: the last metre the cylinder covers at the speed of a car. In 2001 in New York such a cylinder killed a six-year-old boy lying in the machine. The magnet cannot be switched off instantly — the superconducting winding has to be quenched by boiling off the liquid helium, and recovery takes days.
Water is weakly diamagnetic and in a strong non-uniform field is pushed outward. In a Dutch laboratory in 1997, drops of water, a grasshopper and a frog were made to levitate in a field of sixteen tesla — the frog, by all accounts, came to no harm. The experiment brought Andre Geim the Ig Nobel Prize of 2000, and ten years later the same researcher took the Nobel for graphene.
06 · Writing rules
T upper case — lower-case t is the tonne
T upper case — lower-case t is the tonne, and the name in running text is lower case: tesla. The plural is teslas, and the name never takes a capital even though it comes from a surname. A lower-case t next to it is the tonne, an entirely different quantity.
The symbol of the quantity is an italic B, of the unit an upright T. The gauss is not part of the SI: the standards expressly forbid using two units side by side in one document. The prefix micro requires a Greek mu: µT, not uT. In medicine the strength of a scanner’s field is commonly given with no unit at all — a “one-and-a-half”, a “three” — but in documentation it is written out in full.
07 · Neighbouring units
The tesla is flux density; multiplied by area it gives the weber, and divided by the magnetic constant the field strength in amperes per metre. The gauss is the same quantity in the CGS system.
Of the Simetrium passports the tesla is adjoined by weber as a flux of the same nature, gauss and oersted from the CGS system, henry s the ampere from the design of windings, and hertz, in which the frequency of resonance is expressed.
08 · Historical section
What the field was measured in before the tesla
Nikola Tesla showed that three currents shifted in phase create a field that rotates without moving parts. The induction motor did without a commutator and brushes and drove direct current out of industry.
Edison defended direct current and did not shrink from publicly electrocuting animals with alternating current to prove how dangerous it was. The argument was closed by the Niagara power station of 1895: only alternating current could carry energy over distance.
In a laboratory two kilometres above sea level, Tesla drew artificial lightning tens of metres long and lit lamps without wires. The resonant transformer that bears his name passed into engineering and into folklore alike.
The eleventh General Conference, the same one that approved the name “International System of Units”, gave the flux density the name of Tesla. By then the inventor had been dead for seventeen years, and he died in a New York hotel, in debt.
Forty-five and a half tesla is the limit reached at the National High Magnetic Field Laboratory: a superconducting insert inside a resistive magnet. Pulsed installations give up to a thousand tesla, but destroy their own winding in the process within microseconds.
In neutron stars with the strongest magnetic fields the flux density reaches hundreds of gigatesla. At a distance of a thousand kilometres such a field would wipe any bank card, and close up it draws the electron shells of atoms out into cigars.
The field that tears its own winding apart
The upper limit of a magnetic field is set not by electrical engineering but by the strength of materials. Magnetic pressure grows as the square of the flux density: at one tesla it comes to four atmospheres, at ten to four hundred, at fifty already to ten thousand, which exceeds the strength of copper. That is why steady magnets stronger than forty-five tesla cannot exist: the winding would be torn apart from within. Pulsed installations get round the ban by using time — a field of a thousand tesla lives for microseconds, too brief for the destruction to develop, and the coil has to be replaced after every shot all the same. The tesla itself is measured most precisely through frequency: a proton in a field precesses at 42.577 megahertz per tesla, and national standards of flux density are, in essence, frequency counters with an ampoule of water. The gyromagnetic ratio of the proton is itself known to eleven digits, so the uncertainty of a field measurement is set not by physics but by the uniformity of the magnet.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI units that neither engineering nor daily life can do without. Each gets its own sheet: definition, conversion, instruments, writing rules. In 5 languages.
SI derived units with names of their own
the tesla passport is openSI base units
in terracotta — the three units the tesla is built fromMagnetic flux density in other systems
Passport language
5 languages. The symbol T is international, but the habit of measuring in gauss differs: in Russian, Japanese and Chinese literature on magnetic materials the CGS units are still in use today.