Question

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.

Short answer

To get Maximum amount of energy in parallel-Plate the Plates should be closed together

Step-by-step solution

About Energy in a parallel-Plate capacitor

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

:Determine the plate position for maximum amount of energy 

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

Determine the Position

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