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Magnetic flux is the rate at which a magnetic field (whose flux density is measured in teslas) crosses a surface perpendicular to the flow of the field. If a varying magnetic field passes perpendicularly through a loop of (conducting) material, the field induces a voltage across the loop. If the induced potential is one volt, then the flux is changing at one weber per second. This effect was demonstrated by Michael Faraday, and it's thus called Faraday's Law
Conversely, if the current flowing through a loop changes, it will induce a magnetic field. A change of one ampere per second in the coil induces a flux of one weber.
Magnetic flux in a ferromagnetic core can also be created by passing direct current through a coil wrapped around the core, according to Ampere's Law.
The dimensions for the weber are, in derived units, volt-seconds (V新). In SI base units, they are kg搶2新-2嫂-1.