A variable reluctance sensor consists of a core, a variable air gap and an armature.

A variable reluctance sensor consists of a core, a variable air gap and an armature. The coreis a steel rod of diameter 1 cm and relative permeability 100, bent to form a semi-circle ofdiameter 4 cm. A coil of 500 turns is wound onto the core. The armature is a steel plateof thickness 0.5 cm and relative permeability 100. Assuming the relative permeability ofair = 1.0 and the permeability of free space = 4π × 10−7Hm−1, calculate the inductance of thesensor for air gaps of 1 mm and 3 mm.