# Charged metal sphere surrounded by dielectric shell

Hi I have the following electrostatic question involving linear dielectric material.

Given a metal sphere of radius $a$ which carries a charge $Q$ and is surrounded out to a radius $b$ by a linear dielectric material of permittivity $\epsilon$. Why does it follow that $\vec{E}=0$ inside the sphere $(r < a)$? Is the reason because the metal sphere polarizes the dielectric material and thus the polarized material attracts the charge from the metal sphere thus producing a uniformly charged shell which as we know has an electric field of zero inside?

• The metal sphere is solid or hollow? Commented Sep 14, 2016 at 15:08
• @AmritanshSinghal Solid metal sphere.
– Alex
Commented Sep 14, 2016 at 15:10

This statement shall provide you the answer.

"The electric field inside a conductor is 0 and all excess charge resides at the surface of the conductor."

So, no matter whether you have a solid or a hollow metal sphere(that is a conductor) there exists no electric field inside it and all the charge you give resides at the surface of the sphere.

Then what about the role of the dieletric? It turns out that it has no effect. The electric field inside the conductor will still be zero. This is because the electrons are free to move inside a conductor and they ultimately cause the field inside it to be zero.

This is very similar to the phenomenon of electrostatic shielding.

A small explanation of why is it so is given here

• Thanks for your response. I guess my mistake was assuming that a charged metal sphere implies that the sphere is uniformly charged.
– Alex
Commented Sep 14, 2016 at 17:39