# A rubber ball of radius a is covered by a thin shell of metal which has negligible thickness and a charge Q Spread uniformly over it [closed]

this is a screen shot of a past paper exam, sorry that I could not get better quality.

I am struggling to answer this question (b) and (c), I believe that once I solved for (c) it should be easy to get (d)

If this was the other way round(metal ball surrounded by a rubber dielectric) the I could solve it but this way seems tricky.

I would really appreciate it if you could help me out

I believe that for a metal(conductor) to have a Q charge total spread over there must -Q on the underside of metal shell(due to negligible thickness and no other charge, but possibly what the metal shell could be covering), thus there must be an overall Q source charge inside the rubber because the sum of surface bound charge and volume charge should = 0. But this doesn't help my case it seems

Using the Gauss's Law given in (a) and the spherical symmetry of the problem, you can calculate $$\vec{D}$$ everywhere. Note that this calculation is possible with the knowledge of only $$\textit{free}$$ charges. The only free charge present in this problem is the charge $$Q$$ spread uniformly over the metal's surface. The remaining steps are straightforward.
• The metal is assumed to have zero thickness, so we can't technically give the value of $D$ $\textit{inside}$ the metal shell. Right below the metal's surface, $D$ will be zero. Sep 15 at 20:02
• $D=0$ is equivalent to $E=-\frac{P}{\epsilon_0}$. In case of the linear dielectric, $E=P=0$ holds. Sep 15 at 20:20