A hollow, uncharged spherical conductor has an inner radius \(R\) and an outer radius \(2R\). A point charge \(+q\) is fixed at the center of the sphere's hollow cavity, and the system reaches electrostatic equilibrium. What is the ratio of the surface charge density on the inner surface of the conductor to the surface charge density on its outer surface, \(\dfrac{\sigma_{\text{inner}}}{\sigma_{\text{outer}}}\)?