Electric field inside hollow dielectric field

[-EquinoX-]

Homework Statement

How do I proof that the Efield inside a hollow dielectric sphere is 0?

Homework Equations

The Attempt at a Solution

 

[rl.bhat]

Unless we know how the dielectric sphere is charged, ( whether the charge is on the surface of the sphere or distributed uniformly through out the sphere ) it is not possible to find the field inside the sphere.

 

[nlightner]

To prove that the electric field inside a hollow dielectric sphere is zero, we can use the principle of superposition and Gauss's law.

First, let's consider the electric field inside a solid dielectric sphere. We know that the electric field inside a dielectric material is given by E = E0 / ε, where E0 is the electric field in vacuum and ε is the permittivity of the material.

Now, let's imagine a hollow dielectric sphere with a uniform charge distribution on its surface. By the principle of superposition, we can break down this system into two parts: a uniform charge distribution on the inner surface of the sphere and an equal and opposite charge distribution on the outer surface of the sphere.

Applying Gauss's law to the Gaussian surface inside the hollow dielectric sphere, we can see that the net electric flux through this surface is zero. This is because the electric field inside the dielectric material is perpendicular to the surface and has a magnitude of E = E0 / ε. However, the electric field due to the charge distribution on the inner surface of the sphere is in the opposite direction and has the same magnitude, resulting in a net electric field of zero inside the hollow dielectric sphere.

Therefore, we can conclude that the electric field inside a hollow dielectric sphere is zero.