In all both my physics textbooks, the number of loops $N$ is left out of the equation for magnetic flux $\phi_B = \int_s \vec B \cdotp\hat n dA$ and only when calculating the Emf induced by an inductor is the number of turns taken into account.
That leads to the question : does the number of loops in a coil effect the magnetic flux?
Consider the following setup. You have a coil of 5 turns/loops placed perpendicularly to a magnetic field. There is no current going through the coil. With the magnetic field, area of the coil, and position of the coil kept constant, the number of loops/turns in the coil is increased to 50. Is an Emf generated across the coil?
In other words, if you were to change the number of loops in a coil, would the magnetic flux change (thus inducing an Emf)?