Faraday's Law Faraday's law is what makes generators possible. In integral form, the circulation of the electric field around a closed loop is proportional to the rate of change of the magnetic flux through any surface whose boundary is the loop.

In local differential form, the curl of the electric field at a given place and time is proportional to the partial time derivative of the magnetic field vector at that same place and time.

To make an electric generator simply rotate a metal wire loop in a static magnetic field such that the surface with the loop as boundary is ant different angles to the direction of the magnetic field. Therefore, the magnetic flux through that area is changing in time. This causes an electric field in the wire which pushes on mobile electrons in the metal causing a periodic electric current.

One can also make an electric motor by hooking the loop to a battery. Now we need some additional ideas. First the Lorentz-force law which says that a magnetic field exerts a force on a moving charge that points at right angles to both the direction of motion of the charge and to the direction of the magnetic field. In fact this Lorentz force is proportional to the vector product of the magnetic field vector with the charge velocity vector all multiplied again by the size of the charge divided by the speed of light in vacuum. One can then see that a force couple or torque is made on the current-carrying loop in the magnetic field causing the loop to rotate.