Re: What are the optimum angles for a coil to magnetic flux induction?

sam,

Your question is a bit ill-posed, but I think I see what you are getting
at.  You may be surprised to learn that this is issue is discussed in most
basic physics texts, at some length, usually with lots of illustrations. 
Certainly in any text for a calculus-based introductory physics class, and
probably also in the texts for non-calculus-based physics intro courses. 
The discussion you are looking for is "Faraday's Law", which generally has
a devoted chapter or two.

For example:
R.A.Serway, "Physics for Scientists and Engineers," 3rd ed., Chapter 31.
S.H.Radin and R.T.Folk, "Physics for Scientists and Engineers," rev. ed.,
Chapter 36.
H.Benson, "University Physics," rev. ed., Chapter 31.
E.Hecht, "Physics (Calculus)," Chapter 22.

There is also a nice lengthy discussion in the "Feynman Lectures on
Physics", Volume II, Chapters 16 and 17.

The short answer to your question is that any particular magnetic field
will have the greatest effect on a particular coil when the field is
perpendicular to the windings themselves.  That is, if you imagine the coil
forming the sides of a drum, the induction effect is greatest when the
field is enters the "drum head" face-on.  But, I encourage you to beg or
borrow an introductory physics text from one of your friends, or from your
college library.  Or just peruse the introductory textbook in the college
bookstore.  With a (very) little effort, you will be able to get the
answers you seek.

Good Luck,
Aaron