A simple capacitor is a device formed by two insulated conductors adjacent to each other. If equal and opposite charges are placed on the conductors, there will be a certain difference of potential between them. The ratio of the magnitude of the charge on one conductor to the magnitude of the potential difference is called the capacitance (in SI units it is measured in farads). Using Gauss's law, calculate the capacitance of
(a) Two large, flat, conducting sheets of area A, separated by a small distance d;
(b) Two concentric conducting spheres with radii a, b (b > a);
(c) Two concentric conducting cylinders of length L, large compared to their radii a, b(b > a).
(d) What is the inner diameter of the outer conductor in an air-filled coaxial cable whose center conductor is a cylindrical wire of diameter 1 mm and whose capacitance is 3×10–11 F/m? 3 × 10 –12 F/m?