A solenoid having a cross section of 5 cm2 is shown in Figure P13.42.a. Calculate the forc...

A solenoid having a cross section of 5 cm2 is shown in Figure P13.42.

a. Calculate the force exerted on the plunger when the distance x is 2 cm and the current in the coil (where N = 100 turns) is 5 A. Assume that the fringing and leakage effects are negligible. The relative permeabilities of the magnetic material and the nonmagnetic sleeve are 2,000 and 1.

b. Develop a set of differential equations governing the behavior of the solenoid.

Figure P13.42