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?

 

[nlightner]

I would approach this problem by first defining the terms and variables involved. A hollow dielectric sphere is a sphere made of insulating material, with a hollow interior. The electric field refers to the force exerted on an electric charge at a given point in space. The homework equations provided are the equations for electric field due to a point charge and for the electric field due to a charged surface.

Next, I would consider the setup shown in the picture provided. The two dotted circles represent Gaussian spheres, which are imaginary surfaces used to calculate the electric field at a given point. The solid circle represents the hollow dielectric sphere, and P is a point inside the sphere.

To prove that the electric field at P is zero, we need to show that the net electric field at P due to the charges on the two Gaussian spheres is zero. This can be done by using the superposition principle, which states that the total electric field at a point is the sum of the electric fields due to each individual charge.

Using the equations for electric field due to a point charge and the electric field due to a charged surface, we can calculate the electric field at P due to each charge on the Gaussian spheres. Since the charges on the Gaussian spheres are distributed uniformly, we can use the surface charge density (σ) and the area (dA) of each sphere to calculate the electric field.

Once we have calculated the electric field due to each charge, we can add them together to get the net electric field at P. If the net electric field is zero, then we have proven that the electric field at P due to the charges on the hollow dielectric sphere is zero.

In summary, to prove that the electric field at P is zero for a hollow dielectric sphere, we need to use the superposition principle and the equations for electric field due to a point charge and a charged surface to calculate the electric field at P due to the charges on the two Gaussian spheres. If the net electric field is zero, then we have proven that the electric field at P is zero for a hollow dielectric sphere.