A solid conducting sphere of radius \(R=10 \mathrm{~cm}\) is embedded in an electrically neutral nonconducting spherical shell that has inner radius \(R\), outer radius \(2 R\), and is made of a material having dielectric constant \(\kappa\). The potential at the center of the sphere is \(540 \mathrm{~V}\). The electric field at the outer surface of the shell is directed away from the surface of the shell, and has a magnitude of \(900 \mathrm{~V} / \mathrm{m}\). What are 

(a) the dielectric constant of the shell

(b) the electric charge on the sphere?