How Does a Dielectric Affect Energy Stored in a Capacitor?

[Roodles01]

Homework Statement

A parallel plate capacitor with plates of area, A & separation of d is filled with LIH dielectric of relative permittivity ε. By considering energy associated with the electric field derive an expression for electric energy stored in the capacitance when a voltage of V is applied.

Homework Equations

u = 1/2 D.E
&
D = εε₀E for LIH material
so

The Attempt at a Solution

u = εε₀E²
E = v/d
Energy stored is u x volume between plates
u = εε₀(v/d)² x Ad

u = εε₀* (Av²/d)

I should also be able to derive the same result if I consider capacitance instead of energy associated with the electric field. . . .
. . . . but how?

I know u = 1/2 CV²
and C = Q/v
so . . . . . . . . er!
How, please
Thank you

 

[mfb]

I know u = 1/2 CV²
and C = Q/v
so . . . . . . . . er!
How, please
Thank you

V=Ed
Q=AD
(or D<->E in both equations? not sure, but it should be right that way)

If you fix the missing factor of 1/2 in your first derivation, the result should be the same.