Is there any way (If you pumped a lot of current through a copper penny by shorting a circuit out through it with leads on either end) to create a magnetic field in the penny and lift it with a (very strong) magnet positioned right above the penny- say neodymium?
The "copper-lifting magnet" is a cool old physics demonstration. It's a method to lift aluminum or copper plates. It should work on pennies, in theory. But probably it will require water-cooling, and the penny will heat up fast, since the principle is much like an induction furnace.
Here's the secret: make a laminated-core AC electromagnet. Then bolt a thick ring of aluminum or copper onto the end. When you turn on the coil, the metal ring will have a huge AC short-ciruit current, like a shorted transformer winding. It will try to fly off the end of the electromagnet core (by inductive repulsion.) But if it remains attached, and if you put the solid ring against a metal plate, the ring attracts the metal plate.
How? The AC electromagnet induces closed circles of current in both the metal ring and the metal plate. The currents are in the same direction. So, although the electromagnet will try to repel both of them, the two metal objects will attract each other. So, permanently affix the metal ring to the end of the AC electromagnet. Like magic you have a "non-ferrous magnetic attractor."
Unfortunately the whole process involves quite large currents, kiloamperes, and for a small electromagnet (lifting a small metal object,) I think the problem gets worse.
Sure, it's theoretically possible, assuming the leads stay attached to the penny as it's lifted.
Not sure "shorting a circuit out" is the right description but driving enough current through the penny will create a magnetic field around it and could create an attraction to a fixed permanent magnet.
Depending on the permanent magnet strength and distance from the penny you may get into thermal trouble due to I2R heating. Many pennies are no longer solid copper making the thermal issue worse.