1. The problem statement, all variables and given/known data a conducting spherical shell has radius R and potential V. If you want, you can consider it to be part of a capacitor with the other shell at infinity. you compress the shell down to zero size while always keeping it spherical,while a battery holds the potential constant at V. 1.What are the initial and final energy stored in the system? 2.What is the final charge on the shell? 3.What is the work done on/by the battery? 4.What is the work done on/by you? 2. The attempt at a solution I took the suggestion of considering as a capacitor, where the outer shell is connected to one of the terminals and the inner shell connected to the other terminal. 1&2. I assume the question only meant electrostatic energy,which is just the energy stored in the capacitor. Hence,Einitial=(CV^2)/2 =0.5*V^2*4*pi*epsilon*R=2*pi*R*epsilonV^2 As the sphere shrinks, C decreases as R decreases, the charges on both shells would start to recede from the surface of the shells. It leads me to think that the inner shell, which has become a point, has zero charge and zero capacitance, therefore Efinal would be zero. 3. During the compression process, charges are forced back from the capacitors against the potential, therefore the battery receives work. However, I'm not really sure what the expression for that would be. If the charges recede then some other charge around the battery should also move as a result of electrostatic repulsion. Thus I suspect the work done on the battery is a multiple of QV, where Q is the magnitude of the charge originally on one shell. 4. I would need to do work against the electrostatic repulsion of the charges on the sphere. By the conservation of energy, the total work I have to supply is Efinal - Einitial -work done on the battery There are several major things I'm confused about: How can the capacitor still maintain potential V while the inner shell shrinks to a point? How about the pattern of the electric field? The fact that there's still a potential difference means there would be an electric field between the two shells, which would probably be radial due to the geometry. However this might also imply that the charge on the 'inner shell' is non-zero.