Suppose dΦ_m Is the change in the magnetic flux through a coil or circuit in time dt. Then, by Faraday’s second law of electromagnetic induction, the magnitude of the einf Induced is 

e ∝ \(\cfrac{dΦ_m}{dt}\) or e = k \(\cfrac{dΦ_m}{dt}\)

where dΦ_m/dt is the rate of change of magnetic flux

linked with the coil and k is a constant of proportionality. The Sl units of e (the volt) and dΦ df (the weber per second) are so selected that the constant of proportionality, k, becomes unity. Combining Faraday’s law and Lents law of electromagnetic induction, the induced emf

e = - \(\cfrac{dΦ_m}{dt}\)

where the minus sign is Included to indicate the polarity of the induced emf as given by Lents law. This polarity simply determines the direction of the induced current in a dosed loop. If a coil has N tightly wound loops, the induced emf will be N times greater than for a single loop, so that

e = – N \(\cfrac{dΦ_m}{dt}\)

where \(\cfrac{dΦ_m}{dt}\) is the rate of change of magnetic flux through one loop.