How Does Material Permeability Affect Force in a Solenoid's Magnetic Field?

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Force Inside a Solenoind ?

Hello

I'm working on a personal project which involves a solenoid. I'm trying derive an equation for the Force(N) that an object would experience due to the flux density inside the coil.

The flux density can be calculated relatively easily by the fallowing equation.

b257e61dee54a7dc009b1a99929d3a92.png


Given the material permeability what force would this object experience due to the B field created by the solenoid?

Any help would be greatly appreciated...
 
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