A capacitor consists of three concentric cylindrical shells with radii R, 2R, and 3R. The inner and outer shells are connected by a wire, so they are at the same potential. The shells start neutral, and then a battery transfers charge from the middle shell to the inner/outer shells. (a) If the final charge per unit length on the middle shell is -, what are the charges per unit length on the inner and outer shells? (b) What is the capacitance per unit length of the system? (c) If the battery is disconnected, what happens to the three charges-per-length on the shells if new is added to the outer shell?