Could I make a magnetic foam or film by mixing magnetic dust? I'm a developer and tinkerer more than an academic, and I'm not sure if this question, being more practical and less theoretical, will be welcome or not here. But here goes, with apologies in advance if it's bad form...
I need to (affordably) construct a very large ferromagnetic sphere, about 18" in diameter. I need it to be much more magnetic than household rubber/refrigerator magnets, but an electromagnet would be overkill. Magnetism comparable to the neodymium magnets you can buy in hardware stores and hobby shops would be perfect, but if it was as magnetic as solid carbon steel or iron or nickel, that would be great too.
It's cost prohibitive to have an 18" steel sphere machined, but I have a hollow 18" polycarbonate sphere I'd like to line with a magnetic material somehow. So on to my question(s):
If I mixed neodymium dust or iron dust with some sort of hardenable putty, could I create a magnetic filler? Or would the granules just orient in such a way to have no real outside magnetism? That is what I suspect.
Might there be a process to make a magnetic putty in which the magnetic particles orient in such a way to make the hardened form highly magnetic? Perhaps spreading it out over plastic-covered carbon steel, letting it set halfway, and then shaping it around a curved form?
Are there any semi-flexible materials with strong magnetism that could be shaped into a sphere?
Any advice or insight appreciated. And again, apologies if this is an awkward place to pose this sort of question!
Clarification: It doesn't necessarily need to attract, as long as magnets stick strongly to it.
 A: If you want a field that is radially symmetric, it is not possible.  It would amount to constructing a magnetic monopole.  Making it appear to be a dipole, though, is entirely possible.  
You might consider using a UV-curable resin of the sort that dentists use.  That way you could orient and cure small portions of your sphere at a time.
A: I think ferromagnetic dust (or filings) with some adhesive should work. If the resulting mix has zero average magnetization, you should be able to magnetize it using an external magnet. Beware of the so-called soft iron (zero average magnetization after the external field is removed).
You may wish to try it first with a small amount of mix. 
A: There are plenty of ways to achieve what you are asking of, however the better and more efficient the way - the more costly it is (as with everything :) ).
You could try to make a mixture of a ferromagnetic substance with an adhesive one, like akhmeteli has suggested, but like i commented on his answer - is you use common or widely available materials, the mixture would not be able to attract magnets strongly enough for any normal magnet to actually stick strongly to it. And if you opt to use more special materials, I think it would be better to just try the following:
You can coat your sphere in a ferromagnetic coating. I think there exist ferromagnetic paints or something similar, i am just recalling an idea from the back of my mind, i am not sure about it, but you can just make metal sheets, copper or aluminum ones should be light enough, which you can then attach/bolt/etc. to your sphere to give it a strong outer ferromagnetic outside.A more radical approach would be to go to a steel mill and have your sphere coated in LIQUID METAL, which when cools off should stick to it pretty well, but you probably cannot do that. XD
On a related note: I am not certain of you sphere's melting or burning point, but there could be some metals that have a melting point below its melting/burning point and thus you can grab a bucket of such a metal in liquid form and coat the sphere in it, assuming one exists and is ferromagnetic enough.
