And, it's not a world where all sorts of random magic is floating about. There are the only magical things in the tale.
Does not work. Creates a distinct sensation of "author set this up."
You do not, in fact, need a unified field theory of magic. Or even a system. Provided you have the style and rhetoric to convince the readers that it does have a system, that it fits naturally into the world, that there is a reason that your characters get this help from magic, but not that, which they have to work out mundanely. Of course, it helps if the characters don't themselves wield it.
Though you can do a lot of the work by drawing on old tropes. Sword and sorcery often uses the props, or what sounds like the props, of black magic in order to convince that the sorcerer could really do it. And a similiar sort of effect can be seen with spells throughout fantasy, with magical words and waved hands or wands to indicate that magic is being done.
It can be a trick.
