Experiments conducted by Faraday and others using current carrying coils resulted in 'The Laws of Electromagnetic Induction' which state:

1)  'If the magnetic flux threading through an electrical circuit changes, then an e.m.f. is induced in the circuit'.
 
2) 'The magnitude of the induced e.m.f. is proportional to the rate of change of the magnetic  flux  through the     circuit'. (Faraday's Law)

3) 'The induced e.m.f. has a direction such that  the  current  which  flows  (or  would flow if the circuit is completed) gives rise to magnetic effects that oppose the effects producing it'.(Lenz's Law)

These principle are widely used to convert mechanical power into electrical power - e.g the alternator.These are general principles that are true however the change in flux is produced. It may be due to:

•  moving magnets near the coil
•  changing the current  flowing  in a nearby coil
•  changing the current within the coil itself
•  relative movement between the coil and the magnetic field.

The polarity of the emf produced will act to try to oppose the change causing it. If it is due to an external flux change, the induced emf will drive a current in the coil that itself produces a flux that opposes the change due to the external influence.

If the flux change is due to a change in the current within the coil, the emf generated will act to oppose the change in current. This is called a 'back emf'.
 
Faraday was able to quantify the effect and expressed the observations mathematically as:

v=-Ndq/dt   (Faraday's Law)

 where N is the number of turns on the coil and dq/dt  is the rate of change of flux threading the coil. Effectively, each turn  generates a back emf equal to dq/dt  and since the emfs produced by each turn are in  series, the total back emf is N times that of
each turn considered separately