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)

The correct answer is 1/2 ∈₀E²Ad.

To find the energy stored in a parallel plate capacitor, we need to use the formulas for the capacitance of a parallel plate capacitor and the energy stored in a capacitor.

The capacitance ($C$) of a parallel plate capacitor is given by the formula:

$C=\frac{{\epsilon }_{0}A}{d}$

where ${\epsilon }_0$ is the permittivity of free space, $A$ is the area of each plate, and $d$ is the distance between the plates.

The potential difference ($V$) across the capacitor plates is related to the uniform electric field ($E$) by the equation:

$V=Ed$

The energy ($U$) stored in a capacitor can be expressed as:

$U=\frac{1}{2}C{V}^2$

Now, we substitute the expressions for $C$ and $V$ into the energy equation:

$U=\frac{1}{2}\left(\frac{{\epsilon }_{0}A}{d}\right){\left(Ed\right)}^2$

Expanding the squared term gives:

$U=\frac{1}{2}\left(\frac{{\epsilon }_{0}A}{d}\right)\left(E^2{d}^2\right)$

Canceling one $d$ from the numerator and denominator, we get the final expression for the stored energy:

$U=\frac{1}{2}{\epsilon }_0{E}^{2}Ad$

This result shows that the energy stored in the capacitor is exactly 1/2 ∈₀E²Ad. Note that the volume of the space between the plates is $Ad$, and $\frac{1}{2}{\epsilon }_0{E}^2$ represents the energy density of the electric field.