(a) What is the self-capacitance (in farads) of the Earth? How much energy is required to add one electron to the (neutral) Earth?
(b) What is the self-capacitance (in farads) of a conducting nanosphere of radius 10 nm? How much energy (in electron volts) is required to add one electron to the (neutral) sphere?

(c) Two conducting spheres with radii R_A and R_B are separated by a distance R and carry net charges Q_A and Q_B. Find the potential matrix P and the capacitance matrix C assuming that the two spheres influence one another but that R >> R_A,R_B so that the charge density on each remains spherical.
(d) Compare the diagonal elements of C computed at the end of part (c) with the self-capacitances of the spheres.