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
Magnetic field work needed also depends on how the magnetic field is created. For linear non-dispersive materials, though, the general equation leads directly to the simpler energy density equation given above. A changing magnetic field, such as a magnet moving through a conducting coil, generates an electric field (and therefore tends to drive a current in such a coil). This is known as "Faraday's law" and forms the basis of many electrical generators and electric motors. Mathematically, Faraday's law is: where formula_27 is the electromotive force (or "EMF", the voltage generated around a closed loop) and is the "magnetic flux"—the product of