If you look in side a discarded computer power supply you may find an inductor that contains a core. Many of the inductors that I see in supplies like that are toroidal inductors - google on that and you should see a picture. It looks like a ring or donut with windings.
You could strip the windings off - and just add your own. If a single winding you might just add your own over top.
You might also find an AM loopstick antenna with a rod or bar core.
Lots of ways to handle this one. I think the solid iron/steel might work to demonstrate the principles but probably not well. In transformer cores are laminated or sintered so that the iron is not a continuous conductor.
Amidon Associates, among others, sell toroidal cores.