A capacitor consists of three concentric spherical shells with radii R,2R and 3R. The inner and outer shells are connected by a wire (passing through a hole in the middle shell, without touching it), so they are at the same potential. The shells start neutral, and then a battery transfers charge from the middle shell to the inner and outer shells.

(a) If the final charge on the middle shell is -Q, what are the charges on the inner and outer shells?

(b) What is the capacitance of the system?

(c) If the battery is disconnected, what happens to the three charges on the shells if charge q is added to the outer shell?