A relay is essentially an electromechanical switch that opens and closes electrical contacts. A simplified relay is represented in Figure. It is required to keep the fenomagnetic plate at a distance of 0.25 cm from the electromagnet excited by a coil of N = 5000 turns, when the torque is 10 N · m at a radius r = 10 cm. Estimate the current required, assuming infinitely permeable magnetic material and negligible fringing as well as leakage.

(a) Express the storedmagnetic energy W_m as a function of the flux linkage λ and the position x.

(b) Express the coenergy W_m as a function of the current i and the position x.