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Question 4 0 / 9 Pts Consider an electromagnet with a geometry as shown in the Figure E. There is a xed piece and a moveable piece, both made of a ferromagnetic material. The gap length of the moveable piece to the xed piece is set at a distance p when the spring is at rest. The position of the movable piece is dened by variable x, where x = 0 represents a closed gap. Assume the reluctance of the core is negligible, the mass of the movable piece is negligible and that fringing can be ignored. The coil has 100 turns and is supplied by a current of 0.5 A. The air gap has a relative permeability of 1. The dimensions of the core are as follows: h = 100 mm;j = 50 mm; l = 50 mm; m = 50 mm: n = 100 mm; 19 = 0.51'. Solve for the following quanties (keep 2 decimal places): i. Draw the equivalent circuit for the scenario and indicate the direction of ux in the diagram. (2) ii. Determine the force of the electromagnet (in N) when the plunger is in position x = 0.2 mm. 0.01 (5) iii. If equilibrium between the electromagnet and spring is reached at x = 0.2 mm, determine the spring constant (in N/m). 63 (2)