The Moon has no magnetic field outside of itself, despite the observed permanent magnetization of rocks collected by lunar missions. One explanation supposes that the Moon once had a geodynamo (like the Earth) confined to a core region (r < b) that produced a dipole field everywhere outside the core. As a result, the lunar crust (b ≤ r ≤ a) became permanently magnetized proportional to (and parallel to) the local dipole field. Later, the geodynamo ceased, along with its dipole field. Show that the still-present magnetization of the crust produces zero magnetic field outside the surface of the Moon (r > a). Sketch the lines of B(r) inside the Moon.