$$ u = \frac{1}{2}\varepsilon_0 E^2 $$

The energy density of an electric field in free space is given by the expression above. For a parallel plate capacitor with plate area $$A$$ and separation $$d$$, the volume between the plates is

$$ V = Ad. $$

Multiplying the energy density by the volume gives the total energy stored:

$$ U = u \times V = \frac{1}{2}\varepsilon_0 E^2 \times Ad = \frac{1}{2}\varepsilon_0 E^2 Ad. $$

Thus, the potential energy stored in the capacitor is

$$ \frac{1}{2}\varepsilon_0 E^2 Ad. $$

This corresponds to the option:

$$ \text{Option D: } \frac{1}{2}\varepsilon_0 E^2 Ad. $$