Faraday's law states that an EMF is induced in a conductor when the magnetic flux cutting through the conductor is changing with time. (the total magnetic field lines through the conductor is changing with time). This can happen in 2 ways, the area of your conductor is changing with time, or the magnetic flux density ie the B field strength is changing with time. Now the magnitute of the EMF is ONLY dependent on the rate of change of magnetic flux, it has nothing to do with its magnetitude at any given time. Now I=|EMF|/R where I is current magnititude, R is resistance of conductor. Directions of current is so that it creates a B field that oppose the change in flux that created it ie Lenz's law.