Monopole, dipole, quadrupole — V ~ 1/r, 1/r², 1/r³ — field patterns and falloff
Multipole Configuration
Multipole expansion: Any charge distribution at large distances is approximated by V = V_mono + V_dip + V_quad + … Each term falls off one power faster: q/r, p·r̂/r², Q_ij r̂ᵢr̂ⱼ/r³. Neutral distributions start at dipole. Neutral with no dipole moment start at quadrupole. The expansion converges for r larger than the source extent.