a) A capacitive sensor consists of two plates in air. The plates are 50 mm square and are separated by a distance of 1.2 mm. A sheet of a dielectric material of 50 mm square and 1 mm thick can slide between the plates. If the dielectric is displaced so that 50% of it is between the capacitor plates, determine the capacitance of the sensor. (The relative permmitivities of the dielectric material and air are 5 and 1 respectively)