A small conducting ball that carries a charge of \(30.0 \mathrm{nC}\) is located at the center of an electrically neutral hollow conducting sphere of inner radius \(100 \mathrm{~mm}\) and outer radius \(150 \mathrm{~mm}\). What is the surface charge density \((a)\) on the sphere's inner surface and \((b)\) on its outer surface? (c) Determine the electric field as a function of \(r\), the radial distance from the center of the sphere.