Magnetic flux
[1] Magnetic flux is usually measured with a fluxmeter, which contains measuring coils, and it calculates the magnetic flux from the change of voltage on the coils.
The magnetic interaction is described in terms of a vector field, where each point in space is associated with a vector that determines what force a moving charge would experience at that point (see Lorentz force).
The magnetic flux through some surface, in this simplified picture, is proportional to the number of field lines passing through that surface (in some contexts, the flux may be defined to be precisely the number of field lines passing through that surface; although technically misleading, this distinction is not important).
The magnetic flux is the net number of field lines passing through that surface; that is, the number passing through in one direction minus the number passing through in the other direction (see below for deciding in which direction the field lines carry a positive sign and in which they carry a negative sign).
[2] More sophisticated physical models drop the field line analogy and define magnetic flux as the surface integral of the normal component of the magnetic field passing through a surface.
where the line integral is taken over the boundary of the surface S, which is denoted ∂S.
This law is a consequence of the empirical observation that magnetic monopoles have never been found.
In other words, Gauss's law for magnetism is the statement: for any closed surface S. While the magnetic flux through a closed surface is always zero, the magnetic flux through an open surface need not be zero and is an important quantity in electromagnetism.
This is a direct consequence of the closed surface flux being zero.
For example, a change in the magnetic flux passing through a loop of conductive wire will cause an electromotive force (emf), and therefore an electric current, in the loop.
where: The two equations for the EMF are, firstly, the work per unit charge done against the Lorentz force in moving a test charge around the (possibly moving) surface boundary ∂Σ and, secondly, as the change of magnetic flux through the open surface Σ.
By way of contrast, Gauss's law for electric fields, another of Maxwell's equations, is where The flux of E through a closed surface is not always zero; this indicates the presence of "electric monopoles", that is, free positive or negative charges.
