3.3 An actuator system is shown in Fig. P3.3. All dimensions are in centimeters. The mag- netic material is cast steel, whose magnetization characteristic is shown in Fig. 1.7. The magnetic core and air gap have a square cross-sectional area. The coil has 500 turns and 4.0 ohms resistance. (a) The gap is d = 1 mm. (i) Determine the coil current and supply voltage (dc) required to establish an air gap flux density of 0.5 tesla. (ii) Determine the stored energy in the actuator system. (iii) Determine the force of attraction on the actuator arm. (iv) Determine the inductance of the coil. (b) The actuator arm is allowed to move and finally the air gap closes. (i) For zero air gap determine the flux density in the core, force on the arm, and stored energy in the actuator system. (ii) Determine the energy transfer (excluding energy loss in the coil resistance) between the dc source and the actuator. Assume that the arm moved slowly. What is the direction of energy flow? How much mechanical energy is produced? 5 10 5 10. 5 5 4 Ω 500 turns + O V All dimensions are in centimeters FIGURE P3.3 Flux density, B (tesla) 1.4 1.3 Silicon sheet steel 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 Cast steel Cast iron 0.4 B* 0.3 0.2 0.1 0 200 400 600 Field intensity, H (At/m) - 800 1000 FIGURE 1.7 Magnetization curves.