The neutral body could be a Van de Graff generator. If its not equal it brings problems.This link holds more detail
https://www.researchgate.net/publication/308595788_CREATE_ENERGY_ELECTROSTATICS.
Patent CREATE ENERGY ELECTROSTATICS
In additional, in case of a real body, there will be a little dissipation of energy with the charging and the equivalence will be not ideal.
For an ideal system this task can be reduced to the self-evident example: just change the distance between two point charges. The work/energy balance is obvious in this case.
What the strange question?
Denis your right, the uniqueness about a van de Graff generator is their is no electric field inside the dome. Therefore there is no electric field from the dome to oppose the addition of charges. Assuming a 100% efficient van de Graff we shall input energy of 0.5CV^2
Unless that's not the energy equation but if yes it brings up problems shown in my paper.
Max, your reasoning just contains a self-evident mistake. The hint: electric field of the charged sphere and the work done by the electrostatic field in bringing a charge.
Just study electrodynamics (electrostatics in this case) and be more humble :)
Good luck!
Okay I ask humbly whats the equation for electric potential energy stored in the dome of a van de Graff generator?
Max, what do you mean as "the equation for electric potential energy stored in the dome"?
The energy of the charged sphere: W = 1/8πε0 * Q2/R
In a Van de Graaf generator this energy is delivered from the mechanical work (belt movement).
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