Magnetic flux

Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. The SI unit of magnetic flux is the weber (in derived units: volt-seconds), and the unit of magnetic field intensity is the weber per square meter, or tesla.

The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element. More generally, magnetic flux is defined by a scalar product of the magnetic field and the area element vector. Gauss's law for magnetism, which is one of the four Maxwell's equations, states that the total magnetic flux through a closed surface is zero. This law is a consequence of the empirical observation that magnetic monopoles do not exist or are not measurable.

The volume integral of this equation, in combination with the divergence theorem, provides the following result:

By way of contrast, Gauss's law for electric fields, another of Maxwell's equations, is

The direction of the magnetic field vector \mathbf{B} is by definition from the south to the north pole of a magnet (within the magnet). Outside of the magnet, the field lines will go from north to south.

A change of magnetic flux through a loop of conductive wire will cause an emf, and therefore an electric current, in the loop. The relationship is given by Faraday's law: