The fallacy in the argument given in the problem lies in the fact that we do not take into consideration the work done in immersing the charges in water and raising them from the water. As the charges approach the dividing line between water and air, polarization charges are caused on the surface of the water so that the motion of both charges in a vertical direction (when the distance between them does not alter) is linked with the performance of work, which cannot be neglected. The work expended on displacing the charges vertically when they are apart will be greater than when they are together (since the field at the edge of the dielectric is greater), and the full amount of work done in the cycle will equal zero.