Repelling a weak permanent magnet with an electromagnet I have a question about magnetic repulsion. Suppose I have a permanent magnet (axially magnetized) placed on top of the iron core of an electromagnet. I want to switch on the elctromagnet to repel the permanent magnet. (Please assume the permanent magnet is contained in some kind of tube that allows up and down movement but prevents it from spinning around. Please also assume that the electromagnet always produces a field strong enough to repel the permanent magnet - whatever that may be) 
If the permanent magnet's magnetic field is very weak, will the electromagnet have trouble repelling it?
I know that if the electromagnet were attracting the permanent magnet, the only thing that would matter would be the strength of the electromagnet. What about repelling the permanent magnet? Assuming the electromagnet is always strong enough, does the magnetic field of the permanent magnet play any role? Is there a chance that an extremely weak magnet would simply act as a piece of ferrous metal and not be repelled by the electromagnet at all?
 A: Take it to the limits to examine the problem. Imagine that your weak permanent magnet is really incredibly weak, weaker than the Earth's field, while it's mass is in the kg. When the electromagnet is turned on is the repulsion of that tiny field enough to overcome the attraction of a few kg of "spare" ferromagnetic material to the electromagnet?
Well, from experiments I did when I was a kid, a really powerful magnet will "overpower" a much weaker one no matter what it's orientation.
A: The critical concept here is magnetic saturation of your ferromagnet material.
In the ideal case, if your weak PM magnet is saturated (completely magnetized,) then the electromagnet can only repel, not attract.  Of course this would only occur if you'd  designed a ferromagnet material which gives the desired value of weak field when fully magnetized.
On the other hand, if you weakly magnetized a hunk of steel, the material will be far from saturation.  In that case your electromagnet may attract the steel itself more strongly than it repels the alike-pole of the permanent magnet.
Thought experiment:  Make a PM magnet ring by placing two steel horse shoe magnets together.  Fully magnetize this object by using a high-current pulser coil (with windings passing through the hole in the donut.)   In the ideal case, the permeability will fall to zero, and the fully saturated ring will act like empty space.  It's made of steel, yet it won't be attracted by external magnets.  For real-world materials the BH curve isn't a perfect square, so an outside magnet would attract such a ring only weakly.  Perhaps eliminate this small attraction by winding a toroid coil around your ring magnet and applying a large direct current to guarantee that the material is completely saturated.  (A similar trick is used in the sensor-ring of a Flux-Gate Compass.)
