Magnetic dipole moment of a spherical shell with TRM acquired in a field of internal origin

The acquisition of thermoremanent magnetization (TRM) by a cooling spherical shell is studied for internal magnetizing dipole fields, using Runcorn's new theorems on magnetostatics. If the shell cools progressively inward, inner regions acquire TRM in a net field composed of the dipole source term plus a uniform field due to the outer magnetized layers. In this case the global dipole moment and thus external remanent field are non-zero when the whole shell has cooled below the Curie point and the source dipole has disappeared. The remanent field outside the shell is found to depend on the thickness, radii, and cooling rate of the shell, as well as the coefficient of TRM and the intensity of the magnetizing field. Some implications for the Moon's remanent dipole moment are discussed.