A solid conducting sphere of radius \(R\) is embedded in an electrically neutral nonconducting spherical shell that has inner radius \(R\), has outer radius \(2 R\), and is made of a material having dielectric constant \(\kappa\). Inside the shell the electric field magnitude is \(E=3 Q /\left(4 \pi \epsilon_{0} r^{2}\right)\) and, relative to a potential of zero at infinity, the potential at the surface of the sphere is \(+15 Q /\left(16 \pi \epsilon_{0} R\right)\), where \(Q\) is a constant with dimensions of electrical charge. What are \((a)\) the charge on the sphere and \((b)\) the dielectric constant of the shell?