Work done by battery on a capacitor is QV/2, where V is the final potential across the capacitor plates an Q is the charge. I know that the Q charge which gets stored on the capacitor comes from the connecting wires. However, since
Positive charge on one plate is reducing (Assuming conventional flow) and increasing on the other it is convenient to assume that the charge is going directly from one plate to the other as it makes calculating work done on the charges more easier.
If we say some Q charge left one plate (let us call these charge carriers set A) and some charge Q ended up on the other plate (let this be B).Now, since it is not necessary that A went through the battery let us call the charge Q that went through the battery C. If battery didn't do work on A or B why do we say that the energy stored in the capacitor comes from the WORK done by the battery in transferring charges from one plate to the other.
According to my professor this work done by the battery can be assumed to be on the same charges since electric field is conservative and only depends on the initial and final states of the system.
I have assumed charges A,B and C to have the same magnitude. I know that distinguishing between charges is pointless but I have done so in order to make my question more clear.