The Russian scientist H.F. Lenz in 1835 discovered a simple law giving the direction of the induced current produced in a circuit.
Lenz’s law states that the induced current produced in a circuit always flows in such a direction that it opposes the change or cause that produces it.
If the coil has N number of turns and φ is the magnetic flux linked with each turn of the coil then, the total magnetic flux linked with the coil at any time is Nφ
so, e = – d/dt (Nφ)
e = – Ndφ / dt = N(φ2 – φ1) / t