Two pieces of gadolinium, each measuring 100 um x 750 m and 604 nm thick, are used to construct a capacitor. The two plates are arranged such that they face each other and are separated by a 100 nm gap. Calculate the resulting capacitance if (a) the intervening dielectric has a permittivity of 13.880: (b) the intervening dielectric has a permittivity of 500eo; (c) the plate separation is increased by 100 nm and the gap is filled with air; (d) the plate area is quadru- pled and the 100 nm gap is filled with air.