Suppose a coil has N turns flux through it changes from an initial value of Ø₁ webers to the final value of Ø₂ webers in time t seconds. Then, remembering that by flux linkages is meant the product of number of turns by the flux linked with the coil,

            Initial flux linkages        =   N Ø₁

              Final flux linkages          =   N Ø₂

                                                      N Ø₂ - N Ø₁ 

            Induced e.m.f               e   =   -----------------       Wb/s   or   volt

                                                                           t   

                                                             Ø₂ -- Ø₁

                                                =   N  ------------  volt

                                                                   t

Putting the above equation in differential form, we get

                                                         d 

                                            e =   ------- ( N Ø )  volt

                                                        dt 

                                                 d Ø 

                                           e =  - N -------  volt      

                                                             dt

   Usually a minus sign is given to the right-hand side expression to signify the fact that the induced e.m.f. sets up current in such a direction that magnetic effect produced by it opposes the very cause producing it)