Force on Magnet from Electromagnet

[aarothepharo]

Hello Everyone:
Take a look at the following diagram

Assuming the coil build above. How would you determine the force pushing-pulling the Neodymium Magnet in the center of the plastic pipe. I know the number of turns, length, amperage are in effect.

 

[mfb]

Forces between magnets are problems that are easy to write down but hard to solve. Depending on the setup, there might be some approximation that makes it easier. The general case: work out the energy in the fields for different positions (probably needs a numeric simulation), the gradient gives the force.