I can tell you how you know what direction the magnetic field moves, if that helps.
(Though the explanation of why one appears requires a little deeper knowledge of the quantum model of electrons, and the quantum explanations of natural-magnetism.(ferromagnetism))
The trick is to point your thumb in the direction of the current, (negative to positive) and then the field induced will be in the direction your fingers are pointing.
Here; Imagine this is you, holding a wire through which a current is passing:
The current is passing in the direction of the arrows, to keep it simple.
Then the magnetic field will be rotating around the wire in this -> direction.
(note the small thumb in positive direction.)
Incidentally, the relativistic answer is that it DOESN'T, and that magnetism doesn't exist. Instead "magnetism" is what happens to the effect of an electric field which is being caused by a moving quantity of charge. That is, the underlying field still comes from the electrostatic force (as in stationary charges), but the effect of the field is changed by the fact that the particles are in motion. If I remember correctly the change is described exactly by a Lorentz transformation.
Magic.Why/How does a current that passes through a wire create a magnetic field?
Sorry, without getting into the details of special relativity, the short version is that "magnetism" as a distinct force doesn't actually exist. Instead, when you move a particle that is creating an electric field (by virtue of being charged) sufficiently fast, its electric field gets changed significantly by relativistic effects. The changes result in the sort of phenomena that we commonly observe as magnetism.I'm not smart enough to understand that... sorry but I appreciate your great knowledge.
But what cogwolf and proxyamenra said is an answer I'm quite comfortable with...
Although conductive metals like copper tend to be diamagnetic and orient themselves opposite to applied fields.Hint; It has to do with orientation of valence electrons in the shells. (which in a conductive metal are dislocated, and thus when they are externally effected will orient themselves (sorta) to mimic the ferromagnetic fields we find in natural magnets.)