We know whenever conductor cuts the magnetic field,e.m.f will induce in conductor.This also applies for conductors in Armature too.When the armature of a d.c. motor rotates under the influence of the driving torque, the armature conductors move through the magnetic field and hence e.m.f. is induced in them as in a generator. The induced e.m.f. acts in opposite direction to the applied voltage  V (Lenz’s law) and in known as back e.m.f or counter e.m.f. denoted with  Eb. 

The back emf  Eb(= PΦZN/60 A) is always less than the applied voltage V, although this difference is small when the motor is running under normal conditions.

It is seen in the generating action, that when a conductor cuts the lines of flux, emf. gets induced in the conductor. The question is obvious that in a dc. motor, after a motoring action, armature starts rotating and armature conductors cut the min flux.So is there a generating action exiting in a motor ? The answer to this question is 'Yes'

After a motoring action, there exists a generating action.There is an induced e.m.f in the rotating armature conductors according to Faraday's law of electromagnetic induction. This induced e.m.f. in the armature always acts in the opposite direction of the Supply Voltage. This is according to the Lenz’s law which states that the direction of the induced e.m.f. is always so as to oppose the cause producing it. In a dc. motor, electrical input i.e. the supply voltage is the cause and hence this induced e.m.f. opposes the supply voltage. This e.m.f tries to set up a current through the armature which is in the opposite direction to that, which supply voltage is forcing through the conductor.

So as this e.m.f. always opposes the supply voltage, it is called back e.m.f. and denoted as Eb Though it is denoted as Eb, Basically it gets generated by the generating action which we have seen earlier in case of generators.So its magnitude can be determined by the emf. equation which is derived earlier. So,