Part one of term paper
1. With this definition of the flux being , we can now return to Faraday's investigations. He found that the magnitude of the emf produced depends on the rate at which the magnetic flux changes. Faraday found that if the flux through N loops of wire changes by an amount , during a time delta t, the average induced emf during this time is ...

Part two of term paper
... it to the case of relative motion between a magnet and a coil. The changing flux induces an emf, which produces a current in the coil; and this induced current produces its own magnet field. If the distance between the coil and the magnet decreases; so the magnetic field, and therefore the flux, through the coil increases. The magnetic field of the magnet points upward. To oppose this upward increase, the field produced by the induced current must point downward. Thus Lenz's law tells us that the cu ...