Equipotential transformation of multipole systems to dipole systems

The vector sum of fields produced by a set of magnetic dipoles with different magnetic moments that are both tilted from the planetary spin axis and offset from the planetary center by different amounts can be used to completely represent a planetary magnetic field in the conventional form of spherical harmonic expansion. The scalar equipotential transformation analytically results in 24 equations that may subsequently be solved for the 24 adjustable parameters in dipole systems with the predetermined main dipole. Attention is given to this method's application to the Jovian magnetic field.