Weber

The weber (symbol Wb) is the SI unit of magnetic flux. It is defined by Φ = ∫B·dA — the integral of the magnetic field's normal component over a surface — so 1 Wb = 1 T·m². Equivalently, 1 Wb is the flux that, decreasing uniformly to zero over one second, induces an EMF of one volt in a one-turn coil enclosing it: 1 Wb = 1 V·s.

The weber is a mid-sized electromagnetic unit. A typical bar magnet might carry on the order of a millimicroweber of total flux through its central cross-section. The flux through a 100-turn coil in a small motor, generating useful EMF at line frequency, is a fraction of a millimicroweber per turn. Power transformer cores carry tens of milliwebers of peak AC flux per turn. The total magnetic flux of the Earth's dipole field crossing a hemisphere is about 5 × 10⁹ Wb.

The weber is the natural unit for Faraday's law of induction (EMF = −dΦ/dt, voltage equals rate of change of flux), and for any calculation involving flux quantization in superconductors — where the fundamental quantum of flux is the magnetic flux quantum Φ₀ = h/(2e) ≈ 2.068 × 10⁻¹⁵ Wb, the smallest amount of magnetic flux that can thread through a superconducting ring. SQUID magnetometers (superconducting quantum interference devices) measure changes of fractions of a flux quantum, making them by far the most sensitive magnetic-field detectors ever built — sensitive enough to measure the few-femtotesla magnetic fields produced by neural currents in a working human brain.

The weber was named in 1935 by the International Electrotechnical Commission, in honour of Wilhelm Eduard Weber (1804–1891), the German physicist who built the first practical electromagnetic telegraph between Gauss's observatory and his own laboratory in Göttingen in 1833 (a 1.2 km link), and who established the absolute system of electromagnetic units that defined unit electric current via measurable mechanical force. Weber's collaboration with Gauss is the reason the SI tesla, weber, and gauss all carry German names from the same generation.