To store the maximum amount of energy in a parallel-Plate capacitor with a given battery (voltage source), would it be Better to have the plates far apart or close together.

If we multiply the energy density by the volume between the plates, we obtain the amount of energy stored between the plates of a parallel-plate capacitor

Concept:

As equation 24.9 mention, the potential energy stored in a capacitor is given by

Where Q is the magnitude of the charge on each plate, C is the capacitance and V is the potential difference between plates.

As equation 24.2 mention,the capacitance of a parallel plate capacitor in a vacuum is given by

Where A is the area of each plate and d is the distance between the two plates.

Substituting from the previous calculation,then we get

Solution:

As we mentioned before in the concept session,the stored energy in a capacitor is inversely proportional to the distance between the two plates. So, to get the maximum amount of energy in a parallel plate capacitor, the plates should be close together.

Therefore it is better to have plates close together