Is the Electric Field Inside a Hollow Dielectric Sphere Zero?

[-EquinoX-]

Homework Statement

I am asked to find if there exists an electric field of a hollow dielectric field at a sphere is 0 and proof it.

Homework Equations

The Attempt at a Solution

I've drawn this picture:

http://img19.imageshack.us/img19/2295/hollowp.th.jpg

\omega \rightarrow 0
\delta q \rightarrow dq \rightarrow 0

E1 = k \frac{dq1}{r1^2}
E2 = k \frac{dq2}{r2^2}

if \vec{E_1} + \vec{E_2} = \vec{0} for p
\vec{E_net} = \vec{0}for all p
k \frac{dq_1}{r_1^2} = \frac{k\sigma\dA_1}{r_1^2}
k \frac{dq_2}{r_1^2} = \frac{k\sigma\dA_2}{r_2^2}

Explanation of the picture:
1. The two dotted circles are gaussian sphere each with radius r1 and r2.
2. The solid circle is the hollow dielectric sphere viewed from one side
3. P is just a point inside the dielectric sphere

So far this is all I got, can someone please guide me what to do next in this proof..

 

[-EquinoX-]

anyone?