Energy density of electric field of condenser

* Energy density of electric field of condenser:

Electric potential energy storage in per unit volume of condenser is called energy density. It is represented by u and its unit is Joule/cm³.

we know that the capacitance of parallel plate condenser,C = (A.£o.K)/d

Where,
A = Area of cross section of plates
d=  Distance between two plates
K = Dielectric constant of a medium

Energy stored in the condenser
U = 1/2 CV²

Putting the value of C

U = 1/2 (A.£o.K.V²)/d

But, Electric field intensity, E = ∆V/∆X = V/d
V = E.d
Hence, U = 1/2 (A.£o.K)/d × E²d²
U = 1/2 (A.d) £o.K.E²

Here, A.d = volume of condenser
Putting A.d = 1 then
U = u (energy density)

Hence, u = 1/2 (1) £o.K.E²

[ u = 1/2 £o.K.E² ]