Magnetic flux area S is where "B" is the magnitude of the magnetic field (the magnetic flux density) having the unit of Wb/m (tesla), "S" is the area of the surface, and "θ" is the angle between the magnetic field lines and the normal (perpendicular) to 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
Current density law (one of Maxwell's equations), which relates current density to magnetic field. In special relativity theory, charge and current are combined into a 4-vector. Charge carriers which are free to move constitute a free current density, which are given by expressions such as those in this section. Electric current is a coarse, average quantity that tells what is happening in an entire wire. At position r at time "t", the "distribution" of charge flowing is described by the current density: where J(r, "t") is the current density vector, v(r, "t") is the particles' average drift velocity (SI unit: m∙s), and