Surface Field Variation from Dipole Offset and Tilt on Uranus and Neptune

This paper examines the geometry of the ice-giant magnetic fields, whose dipoles are strongly tilted and offset. Using only published input values and transparent formulae, the calculation addresses how much the surface field strength varies from place to place purely because the dipole centre is displaced from the planetary centre, and how that geometric effect combines with the large dipole tilts measured by Voyager. The headline results are: dipole_tilt_deg_uranus = 58.6; dipole_tilt_deg_neptune = 46.9; dipole_offset_planet_radii_uranus = 0.3. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. The central finding is that on Neptune the offset alone produces a surface field ratio of several tens between hemispheres, so a single quoted surface field strength for an ice giant is nearly meaningless without a location attached. Agreement and disagreement with independent published estimates are reported at their actual size, and the conclusions are limited to what the budget arithmetic supports.