My physics textbook asks (I translate):
A sphere of copper with a radius of 0.72 metres is charged with a Potential of 270,000 Volt. Find its charge and the electric energy it holds.
I found the charge correctly by first calculating the capacitance with the formula C=(1/k)·R, after which I resorted to C=Q/V, which gives me a charge of 0.0000216 Coulomb.
I then miscalculated the electric energy. I should have used the formula U=0.5·C·V^2 given somewhere in the book, but I had forgotten about its existence. Instead I used my own logic, which said that Voltage = Energy/Charge (Volt = Joule/Coulomb), which gave me precisely double the right answer (5.832 Joule instead of the right answer: 2.916 Joule).
I went over the correct formula again, and I understand it and the way it was derived via integration.
However, I am still left wondering why my original logic was wrong, and why the answer I arrived at was precisely double of what it should have been… Where did the other half go to?
Can somebody shed some light on this?
I really feel I need to understand why my logic was wrong in order not to make the same mistake again, because it was very intuitive to go down that path.