Weber
In 1833 in Göttingen, Carl Gauss and Wilhelm Weber strung a wire about a kilometre long over the rooftops. It connected the observatory with the physics cabinet. This telegraph had no battery. Weber slid a coil along a permanent magnet, and a short pulse of current appeared in the wire. At the other end the pulse turned a magnetic needle.
A current appears in a coil when the magnetic flux through it changes. The faster the flux changes, the higher the voltage. One weber is the flux that, falling evenly to zero in one second, induces a voltage of 1 V in a single turn. That is why the weber equals a volt times a second.
| Notation | Wb |
| Definition | volt-second · V·s · T·m² · kg·m²·s⁻²·A⁻¹ |
| Reference values | flux quantum h/2e — 2.067 834 fWb · 1 Wb = 10⁸ Mx |
| Introduced | name — IEC, 1935 · in the SI since 1960, 11th General Conference |
| Standards | ISO 80000-6 · IEC 60050-121 · SI Brochure 9th ed. |
| Typical values | 35 nWb — Earth's field in a 3 cm ring · 136 µWb — a neodymium magnet in a coil · 15 mWb — a transformer core |
01 · Definition
A volt that lasts a second
Magnetic flux Φ shows how much field passes through a surface. It equals the magnetic flux density times the area times the cosine of the angle between the field and the normal to the surface. A field of one tesla through a square metre gives one weber. If the surface is turned edge-on to the field, the flux becomes zero.
Flux by itself creates no voltage. Voltage appears only when the flux changes: this is Faraday's law. If you add up the voltage over the whole time of the change, you get exactly the change in flux. So a weber can be measured with a voltmeter and a clock: the area under the voltage curve is volt-seconds, that is, webers.
How much field passes through the loop
The vertical lines are a uniform field, seen from the side. The copper ellipse is a loop tilted by the angle θ. Blue marks the lines that pass through the loop; grey ones go past. The blue dashed line under the loop is its shadow on the horizontal, A cos θ: the flux equals the flux density times this shadow.
The same flux passes through a coil of a hundred turns as through a single turn. But a voltage is induced in every turn, and the voltages add up. That is why for a coil the flux linkage is used: the flux times the number of turns. It is also written in webers. Inductance in henries is the flux linkage per ampere of current.
Fast or slow — the same number of webers
In the middle is a coil on a transparent tube, with a magnet hanging on a thread above it. The red half of the magnet is the north pole, the blue half the south pole. The blue dashed lines are the magnet's field lines; copper dots on the turns are the current induced in them. On the right is an oscilloscope screen: the orange line is the voltage across the coil over the last three seconds, the fill is the area under it. On the left is a fluxmeter: it adds up the voltage over the experiment and shows the change in flux linkage. The magnet can be pushed in, pulled out, dropped through the coil or flipped. In “Earth's field” mode a flat loop flipped in the planet's field replaces the magnet.
Push the magnet into the coil slowly, then pull it out fast.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
1 Wb = 10⁸ Mx. In old books the maxwell was simply called a “line”: one of Faraday's lines of force.
The volt-second and the weber are the same thing. Chokes in power supplies are rated in V·s: how much voltage for how long the core can take before saturating.
The gauss is not flux but flux density: a maxwell per square centimetre. The tesla is a weber per square metre, 1 T = 10⁴ Gs.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
There is no physical artefact for the weber. Flux is measured through voltage and time, and their standards are quantum ones. In a Josephson junction every voltage pulse carries an area of exactly one flux quantum, h/2e. Since 2019 the Planck constant and the electron charge have been fixed exactly, so the flux quantum is an exact number too: 2.067 833 848… fWb.
A simple consequence follows. One weber takes about 4.8·10¹⁴ quanta. That is how the voltage standard works: thousands of junctions on a single chip are irradiated with microwaves, and each passes flux quanta at a known frequency. The volt comes from the frequency, and the weber from the volt and the second.
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