Could someone please explain to me why we want to take the "magnitude" of the emf?
Just reinforcing @jak and adding my own two pence here really.
I think it is because you are not trying to determine the motion of the current, therefore you don't need it. I also think you don't have enough information to determine the sign.
There is no N number of coils in this, but I think the texas note has a nice example of an induced emf problem, which may help you visualize what is going on. Though is is a bit different to your question. Essentially the direction of the emf tells you whether the current is clockwise or anti-clockwise round a coil.
The texas notes have helped me with a few emag problems so it's worth having a look at them generally, in my view.
Also, although it is not explicitly asking for magnitude in the text. It does seem to be using the magnitude symbol in the mathematical notation, so that would be them asking for the magnitude of induced emf, right there.
Hope that helps.
To solve induction problems, you first need to define an orientation of the coil, this orientation induces a positive a negative side for any surfaces whose boundary is the coil, then you can compute the magnetic flux and at last the emf. A positive result means the emf runs a current in the positive orientation of the coil. Since you don't know much about the geometry of B, you can't decide if the emf is positive or negative, that is why you are not asked for the sign.