![]() d ℓ is an infinitesimal vector element of the contour ∂Σ,.The electromotive force is induced along this boundary. ∂Σ is the boundary of the open surface Σ the surface, in general, may be in motion and deforming, and so is generally a function of time.Φ B is the magnetic flux through the open surface Σ,.In other words, Gauss's law for magnetism is the statement: (A "closed surface" is a surface that completely encloses a volume(s) with no holes.) This law is a consequence of the empirical observation that magnetic monopoles have never been found. ![]() 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 equal to zero. If the magnetic field is constant, the magnetic flux passing through a surface of vector area S is 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. 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). ![]() 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). Since a vector field is quite difficult to visualize, introductory physics instruction often uses field lines to visualize this field. 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). Each point on a surface is associated with a direction, called the surface normal the magnetic flux through a point is then the component of the magnetic field along this direction.
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