Magnetic Pull Strength in Reluctance Transducer

Hello. Am looking for the derivation and results for how one goes about calculating the magnetic pull strength/force for an electromagnet or reluctance transducer given the magnetic energy (which goes like the square of the B field). The derivative is taken in terms of a linear dimension which reduces the relation from a squared term in the magnetic energy to a linear term in the force formula. I think the result is proportional to the permeability, and inversely related to the separation distance. It may go like the perpendicul cross-sectional area and the square of the number of turns of the coil. I found this result in a vintage electrical engineering book that was the property of the roommate of my mother but loaned it out and neglected to get it back. Chapter 14 was on the reluctance transducer.
Geoffrey E. Harris
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We are given the charge, its velocity, and the magnetic field strength and direction. We can thus use the equation F = qvB sin θ to find the force.
I don't think that is it. I think you are looking at the Lorentz Force of a charged particle moving in a B field.
I think it is rather this relation F= (Number of turns x I)^2 x (magnetic permeability)x Cross Sectional Area /2 (separation distance)^2
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