well.. uhmm.. i'm not really an expert or nothing closer to that rank.. but i'll give a little explanation the way I see it..
faceplant, you are wondering why there are two formulas differently written apart from the other when they just yield to the same result.. uhmm.. i guess, it's simply because is problem solving, there are different elements/values given in determining the unknown.. it's like one problem gives the values for the current, number of turns, and length without mentioning anything about permeability and area.. so in this situation, naturally, we will use the formula most convenient to solve for inductance.. do you get what i mean?
i'm sorry, if i misunderstood what you are trying to say here and if my explanation is a bit or totally off-track.. i'm not that good and i still have a hang-over and sleepless..
Staigen! anybody! HELP!! ;D was i correct? ???