Consider an electromagnet, as shown in Figure, which is used to support a solid piece of steel and is excited by a coil of N = 1000 turns carrying a current i = 1.5 A. The cross-sectional area of the fixed magnetic core is A = 0.01 m². Assume magnetic linearity, infinite permeability of the magnetic structure, and negligible fringing in the air gap.

(a) Develop a general expression for the force f acting to pull the bar toward the fixed magnetic core, in terms of the stored energy, from the basic principle of conservation of energy.

(b) Determine the force that is required to support the weight from falling for x = 1.5 mm.