The magnetic circuit shown in Figure P18.35 is a very simplified representation of devices used as surface roughness sensors. The stylus is in contact with the surface and causes the plunger to move along with the surface. Assume that the flux ? in the gap is given by the expression ? = ? (x), where ? is a known constant and (x) is the reluctance of the gap. The emf e is measured to determine the surface profile. Derive an expression for the displacement x as a function of the various parameters of the magnetic circuit and of the measured emf. (Assume a frictionless contact between the moving plunger and the magnetic structure and that the plunger is restrained to vertical motion only. The cross-sectional area of the plunger is A.)


Analysis:

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