A cylindrical solenoid is shown in Figure P18.36. The plunger may move freely along its axis. The air gap between the shell and the plunger is uniform and equal to 1 mm, and the diameter d is 25 mm. If the exciting coil carries a current of 7.5 A, find the force acting on the plunger when x = 2 mm. Assume N = 200 turns, and neglect the reluctance of the steel shell. Assume lg is negligible.
Analysis:
Note that there are multiple air gaps: the one around the plunger, as well as the one between the plunger and the top of the electromagnet.
We assume that the first air gap is negligible because its cross section area (which wraps the plunger) is bigger than the plunger cross section area. The second air gap has the following cross section area (which is on top of the plunger):
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