[brickanna (OP)]

I have a very naive understanding of magnetism, hence this question.

If I bring the tip of an iron screw close to the North pole of a permanent rod magnet (so that the screw and the magnet are in line) the screw will be attracted to the magnet.  Why?  Here's my naive explanation: because the many tiny "magnets" within the screw rotate such that their South poles face the permanent magnet's North pole, and so the two objects attract each other.  (Never mind the underlying physics of why in fact opposite poles attract and similar poles repel; I'm assuming that's immaterial to the question.)  Why don't the tiny "magnets" align with their North poles facing the permanent magnet instead?  Because that would be an unstable configuration.  Any slight deviation from perfect alignment would flip them around.  (Perhaps this isn't even a question of stability; I am imagining these "magnets" to be rigid bodies that could in theory be perfectly aligned so as to be repelled from the permanent magnet without rotating, but the reality is very likely different.)

Now suppose I wrap a coil around the screw and drive some current through it, so that the screw becomes a weak electromagnet.  Suppose the direction of the current is such that the screw's North pole is now facing the permanent magnet's North pole.  The question is, will the electromagnet be repelled from the permanent magnet, or attracted to it?  Based on my naive understanding, in order for the objects to repel each other the current would have to be sufficiently strong to stabilize the tiny "magnets" in the repelling orientation and prevent them from flipping over.  If it's too weak, they will realign and the objects will attract each each other.  Is this correct?  If so, how weak can the current be before attraction sets in?  (Of course I'm not asking for numbers; just an answer such as "the electromagnet should be of roughly the same strength as the permanent magnet" or "the electromagnet could be much weaker than the permanent magnet and they would still repel.")

[Pmb]

Why don't the tiny "magnets" align with their North poles facing the permanent magnet instead?

Since north poles attract south poles the magnetic field generated by the magnet exerts a torque on the dipoles causing them to be aligned as such. That configuration results in the lowest potential energy and thus is the most stable configuration.

Now suppose I wrap a coil around the screw and drive some current through it, so that the screw becomes a weak electromagnet.  Suppose the direction of the current is such that the screw's North pole is now facing the permanent magnet's North pole.  The question is, will the electromagnet be repelled from the permanent magnet, or attracted to it?

Opposite poles always attract while like poles always repel.