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I thought Emf would not be induced if the coil doesn't cut the magnetic Flux . But since the graph in my paper shows Emf is induced when magnetic Flux is zero , I got confused. I thought since the relationship between Emf and magnetic Flux is directly proportional , one would be zero if the other is zero too.

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Electromotive force (EMF), if generated, whenever the magnetic flux changes in time. In other words, it is proportional to its derivative viz. $$\mathscr E= -\frac{\mathrm d\Phi_\textrm{total}}{\mathrm dt}$$ where $\Phi_\textrm{total}= \textrm{total magnetic flux}= \Phi_\textrm{external} + \mathrm Li\;.$

So, it can be generated also in the moment when the flux goes through zero; and moreover, in an ordinary transformer fed by a sine wave AC current, the EMF reaches its maximum at this very moment.

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    $\begingroup$ I've made a substantial inclusion in your answer. If you don't like it, please, feel free, to rollback my edit. $\endgroup$ – user36790 Apr 9 '16 at 8:35
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It's not the value of flux that creates the induced emf, rather it's time rate of change. The magnetic flux cannot go to zero instantaneously. Any small change in magnetic flux (here the decay of flux) creates an emf that opposes that change (decay). But, however the emf cannot win completely in this scenario. i.e., the emf cannot completely oppose the change. So there will be some decay of flux, but that happens only in an appreciable time interval.That's why I said the magnetic flux cannot go to zero instantaneously. So you would see an emf even though the flux reached zero (but the rate of change of flux is not zero at that time).
It's the rate of change of flux w.r.t. time that is proportional to the induced emf, not the value of flux at an instant. But if you cut off the magnetic flux and the flux remains zero for some time, then if you measure the emf it will be zero as there is no change in flux. The flux remains in a steady value (0) for all instants.
This property of inducing an emf in the body when flux change occurs on it is a characteristic property of the material which we call the material's self-inductance.

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