A parallel plate air capacitor having area of each plate ' A ' and the distance between the plates ' d ' has uniform electric field E in the space between the plates. The energy stored in the capacitor is ( ₀ = permittivity of free space.)

Step-by-step solution

The capacitance of a parallel plate air capacitor is given by C = ₀ A d . The potential difference between the plates is related to the uniform electric field by V = E d . The energy stored in the capacitor is given by U = 1 2 C V^2 . Substituting the values of C and V , we get: U = 1 2 ( ₀ A d ) (E d)^2 U = 1 2 ₀ A E^2 d Alternatively, the energy density (energy per unit volume) in an electric field is u = 1 2 ₀ E^2 . The volume of the space between the plates is V = A d . Total energy stored is U = u V = 1 2 ₀ E^