Force of neodymium magnet inside a electromagnetic coil

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alastairgig
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Hey guys,
Im trying to design a electric gear shiftier for a motor bike. Basically I require about 200N of force to change gear with a 10mm throw (in both directions). I would like to use a tube neodymium magnet. (23mm diameter 25mm high with a 5mm hole throw the centre with a N48 grade)
What I need help with is calculating the number of turns of wire, the current and gauge of wire of the coil. I will be using 12V supply and I am limited to 60amps current draw.
So the magnet will be placed in the middle of the 45mm long coil and the direction of current flow will be changed to make the magnet travel in one direction or the other to change up and down. The magnet will return to the centre of the coil via a recoil spring.

Any help will be greatly appropriated.
Thanks so much guys
Alastair
 
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