The problem:
Consider a uniformly charged sphere of radius $R$ and charge $Q$ and then they separate into two spherical halves of equal volume and charge, and both get to stabilize. Determine the variation of the electrostatic potential energy of the system after the division of the first sphere of fluid into the other two, assuming they are separated by a great distance.
(I'm just ignoring the "fluid" in "sphere of fluid" and assuming it's a typo)
What I think
At the beginning there is only one charge, so the electric potential energy (is it the same as electrostatic potential energy?) is zero. That's because we need at least two charges to talk about potential energy.
After the division into two spheres, we can use the formula: $$ U_f=\frac{1}{4\pi \varepsilon_o} \frac{\frac{Q}{2}\frac{Q}{2}}{L} \approx 0 $$ where $L$ is the distance between the two spherical halves. The electric potential should be zero because the separation is a "great distance". Finally, the change in electrostatic potential is zero, because it's zero at the beginning and it's zero at the end.
Questions
I haven't used the radius $R$ and the problem seems too trivial. I feel like I don't really understand what's going on and am missing something. Also, does the solution differ in any way if we divide the sphere into two halves of a sphere (two semispheres), and not into two spherical halves as the problem says?