I am trying to build a low power output generator with 12 pole pairs and 9 stator coils. The design will be similar to the one described in this link Basic Principles Of The Homebrew Axial Flux Alternator , but at a different scale/size. I am trying to find some way of estimating the number of turns I will need in the coils to produce an output voltage of 6.5V. The generator should produce this voltage at 100rpm. I am getting very confused about how to use Faraday's law to do my calculations.
$\varepsilon = N\frac{d(BA)}{dt}$
Faraday's Law as explained in this example where the area used is that of the magnet, while Faraday Law of Electromagnetic Induction states at the bottom that A is the area of the coil. Does this difference have to do with when the magnetic field is stationary while the coil is moving versus when the magnetic field is moving relative to a stationary coil? Also, should I be using $$\varepsilon = N\frac{d(BAcos(\theta))}{dt}$$ instead? Thanks very much in advance, and apologies if I am missing something very obvious here.