Q:

If a satellite had a huge permanant magnet, how long (if at all) would it take for the other satellites to move towards it?

So if you put two magnets on a table and they are far enough away from each other they won't go together because the friction can at some distance overcome the magnetic attraction. But out in space all the bits of metal would be attracted to the magnet and have little friction. But of course things in orbit are in general very far apart. But given enough time would something happen? Like imagine if the entire international space station was one big magnet...

A:

There is an important conceptual reason that magnets of any strength are very bad at exerting forces over long distances.  Magnets are dipoles. Pushing some fussy vector mathematics under the rug, this means that the force on a remote chunk of iron falls off roughly as the seventh power of distance.  That is fast.  Basically even a strongly magnetic satellite would have to pass within a few ISS radii of your monster ISS magnet to be captured.
If you did want to build a space junk magnet, I suspect it might help to make the monster magnet very long to separate its poles by a long distance.
Your question inspires me to ask another question about your monster ISS magnet, to which I don't know the answer off the top of my head.  Would the ISS magnet be influenced in any interesting way by earth's magnetic field (other than swiveling around trying to align its poles with the field direction)?  I don't have an intuitive grasp of the scale of the force that would try to pull the ISS into the stronger fields near the poles.  Would it be enough to pull the ISS out of a reasonable orbit?

