A variable reluctance sensor consists of core, variable air gap and armature.The core steel rod of diameter 1cm and permeability of 100 bent to form semicircle of diameter 4cm.a coil 500 turn is wound on to the core.The armature is steel plate of thickness 0.5cm and relative permeability 100.assuming relative permeability of air is 1,permeability of free space 4pi*10pow-7.calculate inductance of sensor for air gap of 1mm and 3mm?