enter near its south pole, but inside the magnet -field lines continue through the magnet from the south pole back to the north. If a -field line enters a magnet somewhere it has to leave somewhere else; it is not allowed to have an end point. More formally, since all the magnetic field lines that enter any given region must also leave that region, subtracting the "number" of field lines that enter the region from the number that exit gives identically zero. Mathematically this is equivalent to Gauss's law for magnetism: where the integral is a surface integral over the closed surface (a closed surface is one that completely surrounds a region with no holes to let any field lines escape). Since points outward, the dot product in the integral is positive for -field pointing out and negative for -field pointing in. Faraday's Law 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 is the electromotive force (or EMF, the voltage generated around a closed loop) and is the magnetic flux—the product of the area times the magnetic field normal to that area. (This definition of magnetic flux is why is often referred to as magnetic flux density.) The negative sign represents the fact that any current generated by a changing magnetic field in a coil produces a magnetic field that opposes the change in the magnetic field that induced it. This phenomenon is known as Lenz's law. This integral formulation of Faraday's law can be converted into a differential form, which applies under slightly different conditions. Ampère's Law and Maxwell's correction Similar to the way that a changing magnetic field generates an electric field, a changing electric field generates a magnetic field. This fact is known as Maxwell's correction to Ampère's law and is applied as an additive term to Ampere's law as given above. This additional term is proportional to the time rate of change of the electric flux and is similar to Faraday's law above but with a different and positive constant out front. (The electric flux through an area is proportional to the area times the perpendicular part of the electric field.) The full law