Is the number of turns in a loop part of the magnetic flux?

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)?

• You are not explaining the scenario very well. Yes, for a coil with a current, the number of turns influences the flux by changing the magnetic field. Commented Nov 22, 2015 at 0:40
• I've added an example for the particular senario am now wondering about. Is that more clear? Thank you for your comment. Atleast half my question is now answered. Commented Nov 22, 2015 at 0:55