Calculating Magnetic Force on an Object in a Solenoid?

[Integrated]

Let's say I have a magnetic ball within a solenoid that has current passing through it. How would I calculate the magnetic force on the ball?

 

[UltrafastPED]

For a solenoid the internal field is constant: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html

The force on the ball depends upon the material (it's magnetic permeability) - do you mean that it is a ferromagnetic material (soft iron, iron nickel, etc), or that the ball is an actual magnet?

Note that the magnetic field inside the solenoid can be vastly increased by including a highly permeable core:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

What would happen if an iron core were fully inserted into the solenoid? What is the equilibrium position?

Hold the solenoid vertically - what would happen?

Here is an easy one: if the current is turned off, what happens?

Start with the iron core at rest just below the solenoid, then throw the switch to start the current. What happens?

See this lecture for "the force produced by a magnetic field".

 

[Integrated]

It'll have to be an air core (since something will be inside it) and inside will be a Neodymium N48 nickel-plated quarter-inch diameter ball, so it's an actual magnet.

 

[UltrafastPED]

Then if you've worked through the material posted, and the questions ... you should be good!

 

[Integrated]

I apologize if I missed something, but I can't find what I need in those articles. I'm looking for how to calculate the force, in Newtons, on an object with known permeability within the solenoid caused by the known magnetic field. I greatly appreciate any help you can offer.