A parallel-plate capacitor has area A and plate separation d, and it is charged to voltage V. Use the formulas from the problem introduction to obtain the formula for the energy U of the capacitor

U = (ε0AV^2) / 2d

Explanation:

Where C = capacitance of the capacitor

ε0 = permittivity of free space

A = cross sectional area of plates

d = distance between the plates

V = potential difference

First, the capacitance of a capacitor is obtained by:

C = ε0A/d.

Starting at the formula, U = (CV^2) / 2. Formula for energy stored in a capacitor

Substitute in for C:

U = (ε0A/d) * V^2 / 2

Hence:

U = (ε0AV^2) / 2d