A uniformly charged sphere \(5 \mathrm{~cm}\) in radius carries a charge of \(8.0 \mathrm{nC}\). A thick hollow conducting spherical shell of inner radius \(10 \mathrm{~cm}\) and outer radius \(12 \mathrm{~cm}\) having a charge \(4.0 \mathrm{nC}\) is concentric with the sphere.

(a) Calculate the surface charge density on the inner and outer radius of the shell.

(b) Draw three concentric spherical Gaussian surfaces having radius \(8 \mathrm{~cm}, 11 \mathrm{~cm}\), and \(14 \mathrm{~cm}\). What is the electric flux through each of these surfaces?

(c) Compute the electric flux through a spherical Gaussian surface concentric with the sphere, and having a radius of \(2 \mathrm{~cm}\).