The APU(Auxiliary Power Unit) needs a set of complex pipeline for the fuel supply system where some of the main valves controlling the flow rate consist of the servo valve worked with a torque motor. The input electric current produces an induced magnetic field almost perpendicular to the background magnetic filed generated by fixed permanent magnets. The induced torque deforms the tubular bushing, and directly rotates an armature, which can open and close the valve. In this study, we start from a basic analytic model using a simple electro-magneto-statics, and expand our model to the three-dimensional one computationally applying a commercial code named COMSOL. The result is compared with each other, and reasonable numerical data are obtained for the dynamic behavior and multi-physics system.