# Homework Help: Percentage of energy in a dielectric placed between a parallel plate conductor

1. Apr 21, 2009

1. The problem statement, all variables and given/known data

A dielectric of dielectric constant 3 fills three fourth of the space between the plates of a parallel plate capacitor. What percentage of the energy is stored in the dielectric?

E(r) = 3, distance between plates = d, thickness (t) = (3/4) * d, C=capacitance of the capacitor, q= charge of the capacitor, V= potential difference, A =area of plates, E(0) = permittivity of free space

2. Relevant equations

E = C(V^2)/2,
C = E(0)A/( (d-t) + t/E(r) ),
C= q/V

3. The attempt at a solution

I solved this (sort of) as follows:
The capacitance C' if there was no dielectric = E(0)A/ d
The capacitance C with the dielectric = 2 E(0)/ d [ after giving t = 3/4 d and simplifying ]
The energy E' in the absence of dielectric = C'(V^2)/2
The energy E in the presence of the dielectric = C(V^2)/2 = 2E'
percentage of energy in dielectric = (2E' - E')/2E' * 100 = 50 %