Our formula for the dielectric sphere in Section 10.10 can actually serve to describe a metal sphere in a uniform field. To demonstrate this, investigate the limiting case κ→∞, and show that the external field then takes on a form that satisfies the perfect-conductor boundary conditions. What about the internal field? Make a sketch of some field lines for this limiting case. What is the radius of a conducting sphere with polarizability equal to that of the hydrogen atom, given in Table 10.2?