Could a tube with a serie of solenoids be used to move an iron particle? If I had a tube with electric solenoids at intervals along it, could I get small iron particles to move through the tube by turning the on the solenoids further along the tube and turning off the one the particles is closing in on?
If not, how could I control the particles?
Will an iron particle move along the magnetic fields lines of a static solonoid if it is turn on? Or is it the variability of turning the field on and off that is the key? Any formulas of how to calculate it, would also be greatly appreciated.
 A: The magnetic force that moves an iron particle is due to the gradient of the magnetic field strength.  From the perspective of magnetic field lines, that means the particle experiences a force in the direction toward which the magnetic field lines are converging.
The experiment you're proposing should work just fine; the hardest part will be to get the timing right.  One way to control the timing would be to use a larger particle, like a nail.  Get a photocell and light source - like the systems used to keep a garage door from closing if anything is in the way - and set it up to turn off a solenoid when the nail crosses the light beam just in front of the solenoid.  Another way, possibly easier, is to turn the coils on and off synchronously a few times per second.  Use a long tube and adjust the spacing between the coils to optimize the launch speed of your nail.
There are too many unknowns to provide a formula: the mass, size, and permeability of your particle(s), the size and shape of your solenoids, the solenoid current and switching time, and so on.  It's much easier to build the system and experiment with it.
