By taking a central flux path, estimate the inductance of the sensor shown in Figure

(a) for zero air gap;

(b) for a 2 mm air gap. Assume the relative permeability of core and armature is 104 and that of air is unity.

2.0 cm 200 turns 1.0 cm -3.0 cm- 6.0cm 1.5 cm 3.0 cm 0.2 cm