1. An electromechanical clutch assembly is depicted below. It consists of a flat circular steel plate and a steel cup assembly containing a coil. The reluctance of the steel components may be neglected along with the field fringing effects. a. Derive an expression for the total reluctance of the system in terms of the gap between the face of the cup and the plate, x, as shown below. b. Derive an expression for the force applied to the clutch plate in terms of the MMF of the coil. c. Assuming that a force of 15 Newtons is required to close the clutch assembly, compute the minimum current required in the coil. Assume N=400, x=0.5 cm, a=1.5 cm, b=3 cm and c=4 cm. b a C