## A Charge inside a Metallic Shell

A charge close to a metal induces surface charges. But what happens if one puts some charge inside of a metallic shell? What will happen to the field in- and outside of this cavity? Also find out what how the shell screens the inner structure of an arbitrary charge distribution.

## Problem Statement

Consider a point charge $$q$$ centered inside of an uncharged metallic shell. The shell is not grounded and has inner and outer radii $$R_{1}$$ and $$R_{2}$$.

Calculate the electrostatic potential $$\phi\left(\mathbf{r}\right)$$ and the surface charge densities $$\eta_{1/2}$$ at the inner and outer terminations of the shell.

Finally discuss what happens if an arbitrary charge distribution is put inside the shell. How could you measure anything else but the total charge?