Tesla
In 1997, in the high-field laboratory in Nijmegen, a live frog rose into the air. Nobody was holding it. It hung inside the vertical bore of a 16 T magnet. The water in the frog's body is weakly repelled by the field, and at such strength the repulsion outweighed its weight. The frog was unharmed, and Andre Geim and Michael Berry received the Ig Nobel Prize for the experiment.
The tesla is the unit of magnetic flux density. It shows how densely magnetic flux passes: one tesla is one weber through a square metre. Earth's field is about 50 µT. A fridge magnet is a few millitesla. A hospital MRI scanner is 1.5 or 3 T.
| Notation | T |
| Definition | weber per square metre · Wb/m² · V·s/m² · kg·s⁻²·A⁻¹ |
| Reference values | a proton in water precesses at 42.576 384 MHz per tesla · 1 T = 10⁴ G |
| Introduced | in the SI since 1960, 11th General Conference · named after Nikola Tesla |
| Standards | ISO 80000-6 · IEC 60050-121 · IEC 60601-2-33 · SI Brochure 9th ed. |
| Typical values | 50 µT — Earth's field · 3 T — MRI scanner · 16 T — a frog levitates |
01 · Definition
A weber on every square metre
Magnetic flux density B shows how strongly a field pushes a moving charge. The Lorentz force equals the charge times the velocity times the flux density. Let a charge of one coulomb fly across a 1 T field at 1 m/s. Then a force of 1 N acts on it. This is how the tesla is expressed through mechanics.
The same tesla is magnetic flux density: a weber through a square metre. So a field is measured in two ways. You can see how much it deflects electrons in a semiconductor — that is how a Hall sensor works. You can measure how fast protons wobble in it — that is how NMR works.
How a sensor notices a field
A semiconductor plate seen from above. A current of 1 mA flows from left to right, so the electrons — magenta dots — run from right to left. The blue circles with a dot are a field pointing towards the reader: the brighter, the stronger. The field deflects the electrons to the top edge. Minus builds up there, plus at the bottom. The voltmeter on the right measures this difference — the Hall voltage.
A magnetic field has two characteristics. Flux density B in teslas is what a charge or a compass needle feels. Field strength H in amperes per metre is what currents create. In a vacuum they are linked by the constant μ₀: a field of 1 T corresponds to 795 775 A/m. Inside iron the same field strength gives a flux density thousands of times greater.
What a field does as it grows stronger and stronger
In the middle is a superconducting magnet in cross-section, with a vertical bore. The circles in the winding are turns carrying current: with a dot — current towards the reader, with a cross — away from the reader. The blue dashed lines are field lines. Inside the bore they go up, outside they return down. The stronger the field, the more of them and the brighter they are. You can put ferrofluid, a cell of water or a drop into the bore, and a paper clip on the table next to it. On the right are three instruments: an electron beam, a proton in water and a compass three metres from the magnet. On the left is the control panel: field, winding current, energy and the liquid helium supply. The “Quench” button switches off the superconductivity of the winding. Time in the scene is sped up: a real magnet is ramped for hours.
Put ferrofluid into the bore and raise the field.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
1 T = 10 000 G. Old magnet data sheets give gauss: “3000 G” is 0.3 T.
Geophysicists count in gammas: 1 γ = 1 nT. A magnetic storm shifts Earth's field by hundreds of gammas.
The oersted is a unit of field strength H, not of flux density. Only in a vacuum does 1 Oe correspond to 1 G.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
A strong field is measured most accurately by frequency. Protons in water wobble around a field line like spinning tops, and the wobble frequency is strictly proportional to the flux density. For a sphere of water at 25 °C the coefficient is known to nine digits: 42.576 384 74 MHz per tesla. The instrument finds the response frequency and divides it by this number. This gives the field with an error of parts per million.
Weak fields, up to a millitesla, are set by Helmholtz coils. These are two identical rings placed one radius apart. Between them the field is almost uniform and is calculated from the current, the number of turns and the radius. The current is measured against quantum standards, the dimensions with a ruler. This gives a reference field against which fluxgates and Hall sensors are calibrated.
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