My google searches and book reading have come to naught on this issue - I'm obviously niether using the right search terms online nor checking the good chapters.

I wish to calculate physical force between two concentric coils given the ampere-turns of each and the distance.

Specifically:

if I wind N1 turns on a pipe (avg coil dia D1) and supply A1 amps dc through it,

and I have N2 turns on a rod inside the pipe (avg coil dia D2) with A2 amps dc through,

then how hard will the rod be pushed/pulled?

(Let's assume that there are L millimeters between the midpoint of each coil, and that each coil is much longer than D. I suspect that permeabilities of the pipe and rod will make a difference as well.)