Faraday's Law defines the fact that an EMF will be produced in a wire which is cutting through a magnetic field. If that wire is part of a circuit, then a current will flow.
The size of the EMF (voltage) produced will depend upon how quickly the wire is moving and upon the strength of the magnetic field it is cutting. If we use a coil of wire then the EMF will again be greater.
This above is a mathematical statement of Faraday’s Law; in words:
The EMF generated is equal to the rate of cutting of the flux.
Since ϕ =BA where B is the flux density and A is the area cut then:
EMF = - B dA/dt assuming B the flux density is constant
That becomes EMF = - NB dA/dt if there are N turns in the coil.
The minus sign indicates that the EMF generated opposes the movement that is generating it (see Lenz’s Law)
Lenz's Law is a special example of the Law of Conservation of Energy. The he law explains that the EMF (voltage) produced by the moving wire cannot in turn cause a current to flow that would make the magnetic field that would help the wire to move, or we would be getting energy for nothing. What actually happens is that the induced EMF caused by movement or a changing magnetic field will cause a current to flow, which will itself produce a magnetic field, which will oppose the movement or change that caused it. There is a more thorough explanation in the video lesson below.