Problem 1 (Adapted from Textbook 1.11) For the elementary electromagnet shown in Fig. 2.1, assume that the cross-sectional area of the stationary member, movable member, and the gap is the same

and A₁ = Ag = 6 cm². Assume the total length of the core (including the stationary and movable parts) is l₁ = 25 cm. Also, N = 400, and the relative permeability of the core material is pri = 1500. (a) Derive an expression for Lm (x) assuming x > 0. (b) Determine the minimum value of x where the approximation that Lm is inversely proportional to x yields an error less than 15%. Figure 2.1 H Elementary electromagnet.