A parallel plate capacitor has a uniform electric field 'E' in the space between the plates.If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is : (ε₀ = permittivity of free space)

To find the energy associated with a uniform electric field E inside a parallel‑plate capacitor, we start from the general expression for the electrostatic energy stored in a capacitor:

$\frac{1}{2}$ C V²

Here C is the capacitance and V is the voltage between the plates.

For a parallel‑plate capacitor the capacitance is

C = ε₀ A ⁄ d

and the voltage is related to the electric field by V = E d.

Substituting these into the energy formula gives

$\frac{1}{2}$ (ε₀ A ⁄ d) (E d)² = $\frac{1}{2}$ ε₀ A d E²

This result is the total energy stored in the capacitor. The factor A d is precisely the volume V_vol occupied by the uniform field. Therefore, the energy per unit volume (energy density) u is obtained by dividing the total energy by the volume:

u = (Energy) ⁄ V_vol = $\frac{1}{2}$ ε₀ E²

Thus, the expression that describes the energy stored per unit volume of the field – and the answer selected from the options – is

$\frac{1}{2}$ ε₀ E²

This matches the given correct option.