An actuator with a rotating vane is shown in fig you may assume that the permeability of both the core and the vane are infinite (? ? ?). The total air-gap length is 2g and shape of the vane is such that the effective area of the air gap can be assumed to be of the form (valid only in the range |?|?

a. Assuming the coil to be carrying current i, write an expression for the magnetic stored energy in the actuator as a function of angle ? for |?|?

b. Find the corresponding inductance L(?). Use MATLAB to plot this inductance as a function of ?.

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40 Ag = Ao 1 Pivot Pivot Vane 14 Air gap Vane Core Core N-turn coil Coil +did (b) (a)