Chapter 17, Problem 29P

* Two small objects with charges + Q and -Q are fixed a distance a apart. (a) Show that if a third small object with an arbitrary charge q is placed halfway between the first two objects, the total electric potential energy does not change even though we have added a new object to the system. (b) While solving this problem, your friend came to the following conclusion: “If adding the third charged object does not change the total electric potential energy of the system (the system comprises all three objects), then there must be a way to remove the third object from the system without doing any work." Do you agree or disagree with your friend? If you disagree, explain why. If you agree, describe a path along which you can remove the third object from the system so that the total work done on the third object is zero.