Cylindrical iron-clad solenoid actuators of the form shown in Fig. 3.29 are used for tripping circuit breakers, for operating valves, and in other applications in which a relatively large force is applied to a member which moves a relatively short distance. When the coil current is zero, the plunger drops against a stop such that the gap g is 2.25 cm. When the coil is energized by a direct current of sufficient magnitude, the plunger is raised until it hits another stop set so that g is 0.2 cm. The plunger is supported so that it can move freely in the vertical direction. The radial air gap between the shell and the plunger can be assumed to be uniform and 0.05 cm in length. For this problem neglect the magnetic leakage and fringing in the air gaps. The exciting coil has 1300 turns and carries a constant current of 2.3 A. Assume that the mmf in the iron can be neglected and use MATLAB to a. plot the flux density in the variable gap between the yoke and the plunger for the range of travel of the plunger, b. plot the corresponding values of the total energy stored in the magnetic field in/x J, and c. plot the corresponding values of the coil inductance in #H.