[Physics] Is Emf induced in the coil when magnetic Flux passing through it is zero? If so then what is the explanation

Question

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.

Answer 1

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.