Inductors as electromagnets

I'm trying to figure out what kind of inductor to use for a sort
of unusual use. An inductor is an electromagnet. My theory is
to put a fixed magnet on an axle such that it it can rotate
freely. If I then put an inductor under it, I can switch which
side of the fixed magnet is up by switching the direction of
current in the inductor. The scale of all of this is tiny -- the
fixed magnet would probably be the exclamation point from a
magnetic poetry set or smaller. I could put the inductor
directly under the fixed magnet - perhaps 1 mm away.

The problem is that I can't figure out what size of inductor to
buy. I want dozens of these, so I don't really want to mess with
building them myself. They're all measured in Henries (or,
realistically, microhenries), and I don't know what a microhenry
translates to in terms of force at a given current. Can anyone help?

The force generated by a magnetic field can be calculated but you need to know things about the inductor. Read this for a start:-

It sounds like what you are trying to create is a small motor. Inductors designed for uses other than electro magnets will probably not be suitable for your application because these are almost always wound on a core of ferrite and while it increases the inductance per turn of a coil the pay off is that they easily saturate when you try and generate much of a magnetic field.

I decided to just go ahead and buy some inductors anyway on the theory that it was worth a try. And in fact, I was right: this 330 microhenry inductor worked fine.