weber
SI coherent derived unit with special name and symbol
Name | Symbol | Derived quantity | Expressed in terms of SI base units | |
weber | Wb | magnetic flux | kg m^{2} s^{−2} A^{-1} | |
DefinitionThe weber, symbol Wb, is the SI coherent derived unit of magnetic flux. One weber is the magnetic flux that, linking a circuit of one turn, would produce in it an electromotive force of one volt if it were reduced to zero at a uniform rate in one second. |
The weber is named after the German physicist Wilhelm Eduard Weber (1804 – 1891).
The weber may be defined in terms of Faraday’s law, which relates a changing magnetic flux through a loop to the electric field around the loop. A change in flux of one weber per second will induce an electromotive force of one volt (produce an electric potential difference of one volt across two open-circuited terminals).
A flux density of one Wb/m^{2} (one weber per square metre) is equal to one tesla.
Magnetic flux
The magnetic flux, symbol Φ or Φ_{B}, through a surface is the surface integral of the normal component of the magnetic field B passing through that surface.
For a constant magnetic field, the magnetic flux passing through a surface of vector area S is
where:
- B is the magnitude of the magnetic field, the magnetic flux density, measured in webers per square metre, symbol Wb/m^{2}, or teslas, symbol T,
- S is the area of the surface, measured in metres, symbol m^{2},
- θ is the angle between the magnetic field lines and the normal (perpendicular) to the surface S.
For a varying magnetic field, we first consider the magnetic flux through an infinitesimal area element dS, where we may consider the field to be constant:
A generic surface, S, can then be broken into infinitesimal elements and the total magnetic flux through the surface is then the surface integral
From the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also be defined as:
where the line integral is taken over the boundary of the surface S, which is denoted ∂S.
Magnetic flux through a closed surface
Gauss’s law for magnetism states that the total magnetic flux through a closed surface is equal to zero.
Measurement
Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the magnetic flux.